SOVIET ATOMIC ENERGY VOLUME 14, NO. 1

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• Document Creation Date: January 4, 2017
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• Publication Date: December 1, 1963
• Content Type: REPORT

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Volume 14, No; 1
December, 1963
SOVIET
ATOMIC
ENERGY
ATOMHAA 3HEP11411
(ATOMNAYA iNERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU
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SOVIETThe rapid pace of deve
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POWDER' . ?-? POWDER METALLURGY,
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ATOMNAYA ENERGIYA
EDITORIAL BOARD
A. I. Alikhanov A. I. Leipunskii
A. A. Bochvar M. G. Meshcheryakov
N. A. Dollezhal' M. D. Millionshchikov
K. E. Erglis (Editor-in-Chief)
V. S. Fursov
I. N. Golovin
V. F. Kalinin
N. A. Kolokol'tsov
(Assistant Editor)
A. K. Krasin
I. F. Kvartskhava
A. V. Lebedinskii
I. I. Novikov
V. B. Shevchenko
A. P. Vinogradov
N. A. Vlasov
(Assistant Editor)
M. V. Yakutovich
A. P. Zefirov
SOVIET ATOMIC
ENERGY
A translation of ATOMNAYA ENERGIYA
A publication of the Academy of Sciences of the USSR
5 1963 CONSULTANTS BUREAU ENTERPRISES, INC.
227 West 17th Street, New York 11, N. Y.
Vol. 14, No. I
December, 1963
CONTENTS
PA
ENG.
G E
RUSS.
Editor's Note
1
3
Vasil'evich Kurchatov - I. K. Kikoin
3
5
V. Kurchatov and Nuclear Reactors - V. V. Goncharov
7
10
Spontaneous Fission and Synthesis of Far Transuranium Elements - G. N. Flerov, E. D. Donets,
and V. A. Druin
14
18
Investigation of Properties of p-Mesic Atoms and p -Mesic Molecules of Hydrogen and
Deuterium at the Dubna 680-MeV Synchrocyclotron - V. P. Dzhelepov
22
27
Longitudinally Polarized Proton Beam in the Six-Meter Synchrocyclotron - M. G.Meshcheryakov,
Yu. P. Kumekin, S. B. Nurushev, and G. D. Stoletov
33
,38
On the Theory of Rotational Spectra - A. Bohr and B. R. Mottelson
36
41
On Delayed Protons?N. A. Vlasov
40
45
The Isotope Effect in Elastic Scattering of Protons on Nuclei - A. K. Val'ter and
A. P. Klyucharev
43
48
Collective Interactions and the Production of a High-Temperature Plasma - E. K. Zavoiskii
51
5,7
British Research in Controlled Thermonuclear Fusion - Sir John Cockcroft
59
66
Cyclotron Instability in Ogra - V. I. Pistunovich
63
72
Screw and Flute Instabilities in a Low-Pressure Plasma - B. Lehnert
72
82
The Initial Stages of the Evolution of the Universe - Ya. B. Zel'dovich
83
92
The Age of Nuclei and the Nuclear Synthesis Time - V. A. Davidenko
92
100
Causality in Present-Day Field Theory - D. I. Blokhintsev
97
105
Lobachevskian Kinematics and Geometry - Ya. A. Smorodinskii
102
110
Electrokinetic Effects in Liquid Mercury - A. R. Regel' and S. I. Patyanin
114
122
BIBLIOGRAPHY
Bibliography of the Published Works of Academician I. V. Kurchatov
120
128
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EDITOR'S NOTE
Translated from Atomnaya Energiya, Vol. 14, No. 1,
January, 1963
The present issue of Atomnaya Energiya is devoted to Igor' Vasil'evich Kurchatov ? a great Soviet physicist,
head of atomic science and technology in the Soviet Union ? in honor of the 60th anniversary of his birthday.
Some of the articles presented here are outside the usual range of topics reported in this journal. The authors
of these articles, mostly colleagues or students of Igor' Vasil'evich, are engaged on the most widely differing scien-
tific problems and in these papers they have tried to present material which is as interesting as possible, to form a
worthy tribute to I. V. Kurchatov. The articles dealing directly with the activity of L V. Kurchatov do not pretend
to give a complete presentation of his very varied activity, but only present some of its aspects.
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IGOR' VASIL'EVICH KURCHATOV
I. K. Kikoin
Translated from Atomnaya Energiya, Vol. 14, No. 1,
pp. 5-9, January, 1963
Original article submitted November 19, 1962
In the biography of an outstanding scientist our interests are broader than a mere recital of his concrete scientif-
ic achievements and discoveries. No less instructive are the views of important scientists on social problems, organi-
zational problems in science, problems of the relationship between science and technology. The relationships be-
tween important scientists and those about them are also of considerable interest.
The name of Igor' Vasil'evich Kurchatov is so popular in our country (and abroad) that his main scientific
achievements are quite widely known, and it is hardly necessary to repeat them. The reader might like to have a
certain understanding of the character, ideas, and views of this outstanding Soviet physicist, state and social worker,
scientific head of atomic science and engineering in the Soviet Union.
The author first met Igor' Vasil'evich, then a young physicist, in 1927 during a lively scientific argument at a
seminar in the Leningrad Physicotechnical Institute with Abram Fedorovich Ioffe. I. V. Kurchatov was the speaker
and they were discussing one of the papers on the theory of current rectification by crystals. Some of those present
disagreed with the views of the speaker, which is usual in seminars, However, the manner in which the disagreements
were answered was unusual. Igor' Vasil'evich reached complete clarity in the argument and was not satisfied until
each of his opponents expressed his wholehearted agreement. If the agreement was not sufficiently clear, the speaker
again and again returned to his arguments, presenting new proof, until at last he achieved his aim. This aspect of the
character of Igor' Vasil'evich, his impatience with any lack of agreement, with any outside tendency to smooth over
roughnesses, has appeared in his varied activity throughout his life. He demanded clarity in the statement of a
scientific problem, in the method of its solution, in the interpretation and formulation of the results. He was equally
impatient with vagueness in the solution of organizational problems.
When he had clearly grasped some new scientific problem and decided that it had to be solved, he devoted
more time and energy to its solution than would be possible for an ordinary person. This was the case, for example,
when he was engaged in his investigations of ferroelectricity. When it became clear to him that ferroelectrics were
the electrical analog of ferromagnets, he immediately embarked upon a series of very difficult and unusually con-
vincing experiments to prove this. He soon brought in specialists on the growing of Rochelle salt single crystals; he
organized the production of large single crystal specimens of very high quality, developed unusual new methods for
the investigation of dielectrics, piezoelectrics, thermal, and other properties of Rochelle salt. To develop a rigid
theory of ferroelectricity, Kurchatov often traveled from Leningrad to Kharkov to consult with L. D. Landau and other
theoreticians to avoid being limited by the discussion and advice of the theoreticians of the Leningrad school. When
he was sure that the phenomenon of ferroelectricity could have technical importance, he organized the combined
work of physicists and leading engineers. In particular, V. P. Vologdin and a large group of engineers were brought
into this work. Only when the basic scientific problems had been solved and the technical problems had been given
a sufficient and reliable industrial base did Igor' Vasil'evich permit himself to go on to other problems.
Purposefulness in the solution of problems was a feature of the whole of his scientific and organizational activity.
It enabled him to become a leader in scientific problems connected with the development of atomic science and tech-
nology in the Soviet Union.
I. V. Kurchatov demonstrated a tremendous capacity for work. When he worked in the Leningrad Physicotech-
nical Institute he could be seen in the laboratory from early morning to late at night. A typical episode comes to
mind. A new imported high-voltage apparatus arrived in the Institute, For several evenings the Institute scientists
could see Igor' Vasil'evich, with his sleeves rolled up, together with his co-workers, assembling the transformer and
its safety devices, kenotrons, insulators, and other components. In those days physicists did not help laboratory tech-
nicians. Naturally, the assembly of specimens and the measurements themselves were performed directly by scientists.
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Relaxation in the laboratory consisted of tidying it up, and the favorite occupation of Igor' Vasil'evich when he was
tired was painting the tables and parts of the equipment.
A few years later, when I. V. Kurchatov was working on nuclear topics, the Institute workers were often wit-
nesses to the following amusing scene. A man with some tiny object in his hand would dash along the corridor of the
Institute at the speed of a 100-meter sprinter. This was I. V. Kurchatov hurrying to deliver a target which had just
been irradiated by a neutron source to the laboratory for an investigation into the short-lived nucleus.
In spite of the fact that his experimental work kept him busy, he found time to write monographs and textbooks,
although this was usually done at night or during his vacations. At this time he published such serious works as Ferro-
electricity, The Neutron, etc.
His breadth of perception enabled him to switch to a new, hitherto unfamiliar topic with surprising speed and
almost immediately to become a leader in this new field. For example, during the Great Fatherland War he was
working on the problem of ship protection. Together with A. P. Aleksandrov he brilliantly solved this technical pro-
blem, although he had not hitherto dealt with problems of this kind.
Perhaps the clearest example is his changeover to nuclear physics at the start of the 1930's. At that time in
the Leningrad Physicotechnical Institute there was practically no "nuclear" tradition, apart from the small laboratory
of D. V. Skobel'tsyn, dealing with the physics of cosmic rays. The only place where radioactivity was studied to any
extent, and where there was a small cyclotron, was the L. V. Mysovskii Laboratory in the Radium Institute. L V.
Kurchatov established a close connection with this Institute and he soon published a number of papers together with
L. V. Mysovskii. The appearance of Igor' Vasil'evich within the physics section of the Institute abruptly changed the
character of the work, A new group of scientists was brought in and interest was aroused in the new and rapidly de-
veloping branch of physics. The work of this laboratory, under the leadership of I. V. Kurchatov, was soon brought
up to the level of foreign laboratories with considerable experience in this field.
As a real scientist, L V. Kurchatov quite rightly assumed that a scientist should be constantly thinking about
his work (except, perhaps, when he is asleep). In fact, his close friends felt that he did not stop thinking about scien-
tific work for a minute. In the last years of his life, when his doctors ordered him to stay in bed, he had bedside tele-
phones installed in order to keep in touch with the Institute laboratories and keep abreast of all fundamental work.
When friends visited his house and tried to draw the conversation away from day-to-day scientific and organizational
work, he invariably steered the discussion back to topics connected with work.
L V. Kurchatov had outstanding organizational talent. He was convinced that any important scientific problem
could be successfully solved by the correct organization of work. Very few great scientists have been able to com-
bine scientific and organizational work with such brilliance. It is these qualities which have enabled him to organize
a huge army of scientists and engineers of the most widely differing specialties, and to direct their energies to the so-
lution of problems in atomic energy in the USSR.
To organize this work, he brought in a few men who formed the nucleus of the Institute which he founded (now
the L V. Kurchatov Institute of Atomic Energy, Order of Lenin). The number of people occupied on the problem (and
then scientific institutions, planning and industrial organizations) increased according to an exponential law.
Throughout the development of atomic science and up to his death, Igor' Vasil'evich was a real scientific
leader and took a lively interest in all aspects of the work. The most outstanding scientists of widely varying special-
ties came to his study; he discussed urgent scientific problems in detail with them; he was visited by the heads of the
planning organizations with whom he worked out technical tasks; important builders came to see him, future heads of
atomic installations, etc. It was usually three o'clock in the morning before the light in Igor' Vasil'evich's study was
switched off.
During the building of atomic installations where he was directly responsible, for many months he transferred
his working center to the construction site; he looked into all details of the building and assembly.
Although occupied with the solution of current problems requiring urgent investigational work, supervizing the
planning, design of equipment, and the commissioning of atomic installations, not for one minute did Igor' Vasil'-
evich forget the future problems of science. He himself understood deeply and never failed to impress on others, not
only scientists but also leaders of the national economy and industry, that the successful and rapid development of
technology requires the widest development of science and the encouragement of even those investigations which do
not promise an immediate practical result. This is because, in the most difficult days, when Igor' Vasil'evich was
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overcoming daily cares connected with the operational solution of urgent scientific and technical problems, he found
time to help in the organization of investigations into cosmic rays, the building of accelerators, the development of
biology; briefly, in the organization of fields of science which were outside the sphere of his own scientific interests.
Igor' Vasil'evich organized a course of lectures on general problems in nuclear theory and he himself was invariably
present at these lectures.
During the period when nuclear engineering was being established, Kurchatov and his closest co-workers had to
set up the closest connections with a number of industrial plants. The serious problem arose of the correct relation-
ships between the scientists and workers in industry. Difficulties appeared here because, at first, the engineering and
technical workers of production and technical organizations were unfamiliar with the scientific principles of the prob-
lems which they had to solve; they were not familiar with scientific ideas, which they were required to translate into
engineering terms. However, the technical solution of the problems could not be delayed. It was therefore necessary
to combine the education of the main personnel with the simultaneous fulfillment of all production tasks. It was
clear that at first the main, even purely technical solutions would be suggested by the scientific leaders of the various
sections and, of course, primarily by Kurchatov himself. Under these conditions it was essential to exhibit considerable
tact in dealings between scientists and engineers. Matters were still further complicated by the fact that it was neces-
sary to change the already accepted and partially established technical solutions, and to insist on a new. method being
used. Igor' Vasil'evich was able to do this so tactfully and cleverly, and to instruct his co-workers to do the same,
that in most cases serious friction was avoided. Problems of authorship or so-called priority were especially delicate.
There were cases when scientists came to Igor' Vasil'evich complaining that the industrial workers were claiming the
authorship of ideas which had been introduced by the scientists. Igor' Vasil'evich very firmly (at least at first) refuted
this kind of pretention. He explained that the tremendous responsibility which rested on the scientists and the leading
part which was entrusted to them were incompatible with trivial priority disputes and, furthermore, that such disputes
interfered with real productive collaboration between the scientists and production workers. He was firmly convinced
that the initial development of the new technology should be controlled by scientists; he understood control in the
widest sense of the word, not only providing ideas but also giving the scientists sufficient rights. It was essential, he
added, that notice should be taken of-the opinion of scientists (and not merely listened to). When necessary, Kurchatov
turned to the party leaders and government for help. At the same time, he felt that it would be very dangerous for
science to have too much control over technology, and that at certain stages of its development the initiative
management should gradually transfer to the technologists. In particular; when a number of fundamental scientific
problems in nuclear engineering were successfully solved and nuclear engineering became an industry, the scientists
were to act mainly as consultants and Kurchatov himself became actively engaged in the new and exciting problem
of the controlled thermonuclear reaction.
The whole activity of Igor' Vasil'evich and his co-workers in the scientific managment of nuclear engineering
brilliantly proved the correctness of these views.
We have already mentioned that the solution of nuclear engineering problems needed a large staff of workers.
In particular, the Institute of Atomic Energy headed by Kurchatov rapidly became filled with new people. During the
organization period he was very concerned as to how to form these people into a single working group enjoying good
relationships; they differed in qualifications, professions, and ages. Before him was the experience in the development
of the Leningrad Physicotechnical Institute by his teacher A. F. Ioffe, who had considerable personal charm and un-
questionable authority. Igor' Vasil'evich himself modestly felt that he did not have sufficient scientific authority to
build up this large group of people into a unit. Looking back we can state that the personal qualities of Igor' Vasil'-
evich as an administrator played an important part in the formation of the Institute; it has become a first-class scien-
tific institute.
Despite the fact that he was head of a large group of scientists and that he insisted on the purposeful solution of
the problems with which the Institute was concerned, he did not restrict the personal initiative of the scientists to the
slightest degree, neither the more experienced scientists nor the young scientists. Unlike some managers, he was not
guilty of the fault of "omniscience." On the contrary, he was not afraid to show his ignorance of some particular
problem, and he was happy to learn where and when possible. This still further increased his authority with those
around him. Even though he was the director, he did not mind sitting in the auditorium to listen to a course of lec-
tures on radioelectronic methods in nuclear physics, which was given by one of the young scientists of his Institute.
He respected the interests of the people with whom he came into contact. He devoted much time and energy
in helping people, either to help them out of some misfortune, or to help them in their work, and even to arrange
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their living accommodations and family life; he concerned himself with encouragement and awards for success in
work. He was particularly concerned about all cases which might affect the health of his staff. Igor' Vasil'evich
was careful with his promises. But all those who dealt with him knew that he was a man of his word. He did much
that he did not have to do. Everyone was familiar with his famous notebook which he always carried with him and
in which he wrote his "obligations,"
Igor Vasil'evich loved life in all its aspects. He not only reacted in a lively manner to all important events,
but at times he also interested himself in the small but characteristic details of these events. He was able to listen
to his colleagues; he himself was a man of few words. When he was able to tear himself away for a rest, he tried, in
his own words, to "gather as many impressions as possible." He took great pleasure in telling of his trip in Central
Asia, which made a tremendous impression on him. He loved humorous folk tales and expressions and originated
some himself. Many were familiar with his phrase "go and work on yourself" (which meant "go to sleep"). When he
wanted to finish a conversation politely, he would say: "right, have a rest." He loved giving his friends funny, good-
natured nicknames, and he did not mind if the Joke sometimes went against himself.
He loved and understood serious music and tried to attend at least a few good concerts. In the last concert he
heard (a few days before his death), the Mozart Requiem was played.
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I. V. KURCHATOV AND NUCLEAR REACTORS
V. V. Goncharov
Translated from Atomnaya Energiya, Vol. 14, No. 1,
pp. 10-17, January, 1963
Original article submitted October 18, 1962
Working with Igor' Vasil'evich Kurchatov from the very start of the organization of the atomic energy institute
which bears his name today, I have had some connection with the course of problems in the use of atomic energy,
and I want to tell of Igor' Vasil'evich's part in the solution of many of the most important problems.
First of all, it must be noted that I. V. Kurchatov's leadership was characterized by direct participation in ex-
periments and by daily discussions of results and of plans for future work.
One of the achievements of fundamental importance for the future development of reactor construction was the
establishment, under the guidance of I. V. Kurchatov, of the first nuclear reactor in our country in which a chain re-
action was realized. This was preceded by intensive experimental and theoretical work on the fission process, and on
the measurement of neutron-nucleus constants, and by other studies which were carried out on a broad front with the
active participation of I. V. Kurchatov.
In the first reactor, natural uranium was used as fuel (at that time, enriched uranium was not available), and
the moderator was graphite.
Extremely rigid requirements were set for the purity of the uranium and graphite. Suffice it to say, for example,
that the admixture of boron in graphite was limited to a few parts per million. The problem was complicated because
uranium and graphite of such purity had never been produced, and because they were required in large quantities? up
tb fifty tons of metallic uranium and hundreds of tons of graphite.
Because of the energetic measures taken by I. V. Kurchatov, a capability for the production of high-purity graph-
ite was developed within a comparatively short time, and its commercial production in the required amounts was ar-
ranged. Production of uranium of the required purity was also successfully achieved.
I. V. Kurchatov himself went out into the factories and laboratories, posed questions, was of on-the-spot help
in overcoming difficulties, and kept in constant touch with the progress of the work.
Under the direct supervision of I. V. Kurchatov, the successful startup of the first nuclear reactor with natural
uranium and graphite moderator was accomplished.
In a foreword to the brochure Nuclear Radiations in Science and Technology, he write: "I remember the emo-
tion with which I and a group of my associates, for the first time on the European continent, achieved a chain fission
reaction in the Soviet Union with a uranium-graphite reactor."*
The exceptionally valuable experience obtained from the first reactor and from the nuclear physics studies per-
formed with it, made it possible to pass on to the planning and building of other reactors.
I. V. Kurchatov initiated the creation of an all-around experimental basis within the Institute of Atomic Energy
for carrying out tests of experimental fuel elements, construction materials, and coolants without which further develop-
ment of new power, transport, and research reactors would have been impossible. Such a basis was created, consisting
of the RFT research reactor, experimental loops with various forms of coolants and varying test modes, and a "fuel"
materials technology laboratory. The reactor was put in use in April, 1952; its thermal power was 10,000 kW, and the
maximum thermal neutron flux was 5 ? 1013 neut/ cm2-sec. Graphite and in part water, served as reactor moderator;
10% enriched uranium was used for fuel.
* L V. Kurchatov, Nuclear Radiations in Science and Technology [in Russian] (Moscow, 1958), p. 5.
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One of the difficult problems which arose during the building of the RFT reactor was the creation of fuel ele-
ments of complicated construction which had to operate under high specific energy deposition and thermal loading.
As investigation showed, the problem was complicated by the fact that uranium pieces underwent violent changes in
shape and size under irradiation. This eliminated the possibility of manufacturing fuel elements from enriched me-
tallic uranium operating with high U235 burnup.
The complex problem of creating nonswelling and nondeformable fuel elements with maximum lifetime?under
conditions of stress for RFT and other reactors was successfully solved by the basically new idea of dispersing fission-
able material in a diluent.
It is of interest to note that experts in the USA followed the same path in creating dispersed fuel elements for
reactors operating with enriched uranium at high specific loading, in particular, for the MTR reactor which went in-
to operation in 1952, as reported by American scientists at the 1955 Geneva conference.
Dispersed fuel elements were successfully used in RFT and other types of reactors in the Soviet Union.
L V. Kurchatov devoted a great deal of attention to the investigation of the behavior of fuel elements in re-
actors and to the development of new types of elements.
A rebuilding of the RFT reactor, which was done for the purpose of significantly broadening its experimental
possibilities, was successfully accomplished in 1957-1958 with the support of L V. Kurchatov. After rebuilding, re-
actor power was increased to 15,000-20,000 kW, maximum neutron flux was raised to 1.8 ? 1014 neut/cm2 ? sec in
the uranium and to (3-4) ? 1014 neuti cm2 ? sec in the central, water-filled channel. The number of experimental
channels for testing fuel elements was considerably increased.
The basis of the reconstruction was a loading of new fuel elements, original in construction and in manufactur-
ing technique, of 90%-enriched uranium, and with highly developed cooling surfaces. Within a fuel element assembly
of six concentrically located thin-walled pipes, irradiation of various samples could be done. The walls of the pipes
were made of an aluminum-uranium alloy with an aluminum cladding. Fuel elements with the same kind of steel -"?
were used in a number of other reactors in the Soviet Union.
Tests of a large number of experimental fuel elements in the RFT reactor were of great value in working out
and selecting the most reliable and efficient construction of elements for a number of new reactors (those of the First
Atomic Power Station, the water-cooled, water-moderated reactors of the Novo-Voronezh atomic power station, the
gas-cooled reactor of the Czechoslovakian atomic power station, the reactors of the icebreaker "Lenin," and others).
Extremely interesting phenomena which were of great importance for reactor operation, and which concerned
the action of radiation on matter, were discovered under the leadership of L V. Kurchatov.
Through studies of the physical properties of graphite under conditions of intense neutron irradiation, tremen-
dous changes in the properties were discovered; reduction of thermal and electrical conductivity, changes in volume
and mechanical strength. It was further established that latent energy, stored in the crystal lattice, was released by
the annealing of irradiated graphite. These studies made it possible to explain the physical nature of the changes in
graphite associated with deformations of the crystal lattice and with a shift of its constants, and to solve a number of
practical problems which arose in the planning and use of graphite-moderated nuclear reactors.
Most valuable results for the study of graphite properties, particularly the buildup of latent energy and the
41I nature of its release, were obtained after a very bold experiment, pushed by I. V. Kurchatov, involving the dismant-
r---
cling of the pile of the 50,000-kW uranium-graphite IR reactor after four years of use.
I. V. Kurchatov made a tremendous contribution to the development of nuclear power in the USSR.
,
He deserves great credit for creating the Soviet atomic power station, the first in the world, whose startup was
the first step in the development of nuclear power in our country.
I. V. Kurchatov considered that nuclear power might prove to be more economical than thermal in isolated re-
gions of the country despite the fact that the Soviet Union possesses a wealth of natural power resources.
In his appearance before the Twentieth Congress of the Communist Party of the Soviet Union in 1956, he stated,
"...although the capital investment per installed power unit in an atomic power station is approximately one and one
half times more than that of the corresponding coal-fired station, the cost per kilowatt-hour of power from an atomic
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or coal power station may be approximately the same. To a great extent, this arises from the fact that fuel consump-
tion in an atomic power station is negligibly small."*
On the initiative of I. V. Kurchatov, and with his active participation, construction was started on large atomic
power stations, so that this grand experiment might allow us to accumulate experience in the construction and use of
atomic power stations with mass production of fuel elements and their processing, to discover more technically re-
liable and more economical means for building atomic power stations, and to determine what portion atomic power
should occupy in the over-all power picture of our socialist government. At the present time, assembly has been com-
pleted on two large industrial power stations: Beloyarsk and Novo-Voronezh.
The wealth of experience accumulated during the building and operation of the First Atomic Power Station was
employed in the construction of the Beloyarsk atomic power station which bears the name of I. V. Kurchatov. Its re-
actors with nuclear superheated steam are a further development of the reactor of the First Atomic Power Station.
The planning of the Novo7Voronezh atomic power station with water-cooled, water-moderated reactors was
carried out under the leadership of L V. Kurchatov. The great compactness, the reliability, the possibility of achiev-
ing more thorough fuel burnup (which has been verified by operating experience with such reactors, for example, in
the icebreaker "Lenin"), all point out the prospect for the application of water-cooled, water-moderated reactors in
atomic power stations.
Lecturing at the English atomic center, Harwell, in 1956, I. V. Kurchatov said, "From the point of view of the
possibility of U238 burnup, the nuclear fuel recirculation process is of great interest, i.e., a succession of operating
periods in a uranium-water lattice. There are reasons to expect that greater utilization of U238 may be achieved by
the use of nuclear fuel circulation in a uranium-water lattice... In connection with the possibility of achieving more
thorough burnup (including that during a single run), the problem of building fuel elements capable of extended
operation under irradiation takes on great practical significance."**
L V. Kurchatov carefully saw to the experimental work on the building and testing of such fuel elements for
water-cooled, water-moderated power reactors.
Fuel elements with calcined-uranium dioxide cores in a zirconium alloy cladding underwent extensive and pro-
longed tests in reactors. The tests indicated that the elements were capable of operating reliably while achieving
thorough burnup ? up to 25,000 MW ? days per ton of uranium.
I. V. Kurchatov directed the tests on many critical assemblies. :The results of these tests were the basis for the
development of reactors for various purposes.
Research reactors of various types were built in the Soviet Union under the guidance of I. V. Kurchatov. Among
the first, as mentioned, were reactors with graphite moderators.
In many institutes of the Soviet Union and of the people's democracies, the building of water-cooled, water-
moderated research reactors assured a firm basis for carrying out research in the fields of reactor construction, neutron
physics, radiochemistry, and biology, for producing radioactive isotopes, and also for training scientific and engineer-
ing cadres.
New methods of calculation were required for the particular physics of water-moderated reactors. Problems
arose in connection with the securing of chain reaction stability and with core construction. At that time, many
physicists had doubts about the possibility of safe operation of a reactor in which the entire moderating material was
in motion with accompanying density fluctuation of various kinds. They pointed out the danger that the moderator
density fluctuations might lead to uncontrolled runaway with serious consequences? rupture of the core or even a
small atomic explosion.
As a result of theoretical and experimental studies of a water-moderated reactor, methods were devised which
allowed fairly accurate estimation of core dimensions, critical loading, and other parameters.
The VVR-2 reactor, the first water-cooled, water-moderated research reactor in the USSR with enriched urani-
um and channel-free core, was built at the Institute of Atomic Energy. This reactor served as the prototype for the
VVR-S reactor.
**Pravda," February 22, 1956.
**L V. Kurchatov, Atomnaya Energiya No.3, 5 (1956).
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The first water-cooled, water-moderated research reactor of the swimming-pool type, the lIZT reactor, was al-
so built at the Institute of Atomic Energy. Both types of reactor (VVR-S and IRT) received wide distribution. L V.
Kurchatov took energetic measures toward the further improvement of research reactors and toward the creation of
new types of reactors intended for the attainment of higher neutron fluxes (above 1018 neut/cm2 ? sec) in order to
carry out certain physical experiments.
The development of research reactors followed the line of creating reactors which operated at constantly main-
tained power levels with provision for continuous removal by circulating coolants, of the heat released in the reactor.
Relatively recently, there appeared the idea of building reactors of a new type ? impulse or pulsed reactors in which
extra-high neutron fluxes can be obtained momentarily. Intense bursts for a short period of time can be obtained in
such relatively simple and small reactors which have no special cooling system.
L V. Kurchatov deserves great credit for the creation and construction of pulsed reactors in the Soviet Union
with neutron fluxes up to 1018 neut/cm2 ? sec, which exceed the maximum neutron fluxes in the most powerful oper-
ating reactors by three to four orders of magnitude.
An important role was played by L V. Kurchatov in the creation of many atomic research centers in our country.
The planning of a network of research reactors in the Soviet Union and the direction of the research at them
was done with consideration of such factors as the existence of established scientific schools at the locations, the neces-
sity for the solution of problems vital to the national economy of the Union republics and the autonomous regions, the
training of cadres possessing modern research methods.
In 1956, L V. Kurchatov visited Uzbekistan and afterwards, at one of the meetings at the Institute of Atomic
Energy, he stated that if there were an experimental reactor in Tashkent, this would permit the successful solution of
problems associated with the further development of cotton growing and the production of mineral fertilizers in Uz-
bekistan. At a meeting called by the Academy of Science of the UzbekSSR, it was discovered that Uzbekistan had
cadres which had already done much in the fields of agriculture and medicine. However, the progress of a number of
operations, including the development of the best fertilizers from Kara-Tau phosphate rock and the development of
measures to fight saline soils, which are of enormous importance to the republic, has been hindered because of the ab-
sence of short-lived radioactive isotopes with lifetimes of tens of minutes. Such short-lived isotopes can only be ob-
tained in a reactor on the spot, and can only be used in experimental work carried out in the immediate vicinity of
the reactor. The research reactor VVR-S, which went into operation in 1959, was built in Tashkent with the coopera-
tion of L V. Kurchatov. He was elected honorary member of the Academy of Science of the UzbekSSR, and, in Tash-
kent, the national costume was presented to him. I remember how he, with delight, gave his impressions of the trip
to Tashkent and Bukhara and of his meeting with the Uzbek scientists, all the while wearing those clothes (robe, sash,
and skull-cap).
Attaching great importance to the study of the properties of matter at very low temperatures in a reactor, and
taking into account the existence of Georgian schools of cryogenics, I. V. Kurchatov proved to be of great help in the
construction of the IRT research reactor in Tbilis, which also went into operation in 1959.
In his last article, "The development of atomic physics in the Ukraine," which was published in Pravda on the
day of his death, February 7, 1960, I. V. Kurchatov wrote, "Work on the investigation and peaceful application of the
energy from nuclear transformations is being carried on at the Institute of Physics of the Academy of Science of the
Ukrainian SSR." He further noted, "In the Institute of Physics, they have completed a group of interesting studies on
the scattering and capture of fast neutrons by atomic nuclei which essentially broaden our ideas about the structure of
the nucleus and about nuclear transformations. A proton accelerator is being used in this Institute and, in the near
future, one of the best nuclear reactors in the Soviet Union will be placed in operation.
With this technical base, they will carry out nuclear physics research, and they will develop various applica-
tions of radioactive isotopes in physics and other branches of science, in industry, in agriculture, and in medicine."
The VVR-M reactor, to which I. V. Kurchatov referred, was put in operation in Kiev in March, 1960.
After the construction of a number of research reactors in the Soviet Union, it became necessary to coordinate
the scientific research being carried out with them. Through the initiative of L V. Kurchatov, successful preparations
were made in the Academy of Science of the USSR for conducting a broadly coordinated meeting of the directors of
all the research reactor centers in the Soviet Union. The meeting was to have been under the direction of I. V.
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Kurchatov. His unexpected death made this impossible. The meeting was held in March, 1960 under the direction
of A cademician A. P. Aleksandrov, and all the basic purposes of I. V. Kurchatov ? the determination of the principal
direction of scientific activity at each center, the elimination of unnecessary parallelism, the division of the leading
institutes according to individual problems, the interchange of experiments between institutes ? were reflected in the
decisions taken.
It was decided that work on problems in neutron spectroscopy and capture y -ray spectroscopy, work on problems
in neutron thermalization, and other work would be developed mainly at the L V. Kurchatov Order of Lenin Institute
of Atomic Energy; work on problems in the effects of radiation on semiconductors and work on nuclear isometry would
be developed in Leningrad at the Physicotechnical Institute of the Academy of Science of the USSR; work on the
chemistry of hot atoms would be developed at the Institute of Physics of the Academy of Science of the Georgian SSR;
and work on activation analysis would be developed at the Institute of Geochemistry and Anal tic Chemistry of the
Academy of Science of the USSR.
Activation analysis was taken as a basic area of research for the VVR-S reactor of the Uzbek SSR Academy of
Science in Tashkent. This decision was determined by the fact that the Uzbek SSR, like the other Central Asian re-
publics, possessed rich and far from completely explored mineral resources and, therefore, they were very interested
in the development of express methods for the analysis of samples into their various components, and also in the de-
velopment of methods for the detection of micro-iEnpurities. Important results have already been obtained in the
field of activation analysis (development of a method for controlling boron impurity in silicon, the production of mass
determinations of copper in cores obtained by exploratory drilling, etc.).
Materials analysis through capture y -ray spectra and through neutron resonance absorption has been developed
here along with the usual activation analysis.
These procedures were developed in connection with the study of capture y -radiation and in connection with
neutron spectroscopy studies in the Soviet Union. The experience acquired in other USSR institutes, particularly in
the Institute of Atomic Energy, and data on equipment (y -spectrometers, mechanical neutron choppers, multichannel
time analyzers) were passed on to the Institute of Nuclear Physics of the Uzbek SSR Academy of Science.
The study of the action of nuclear radiations on the biologic properties of various agricultural products ? cotton,
temp, jute, grapes ? has great economic significance for the Uzbek SSR. These studies are also carried out with the
help of a reactor.
Extremely interesting and promising results were obtained in the radiation destruction of silkworm pupa within
the cocoon.
With its IRT reactor, the Institute of Physics of the Georgian SSR Academy of Science is carrying out work on
low-temperature neutron spectroscopy of solids and quantum liquids; it is studying the effect of nuclear radiations on
diffusion in single crystals of metals and alloys; it is making observations of the formation of dislocations in ionic
crystals; it is investigating the breakdown of solid solutions under the influence of neutron fluxes and the effect of ir-
radiation on the semiconductor properties of materials. A great deal of the work is involved with studies of reactions
which involve the participation of hot atoms or recoil atoms.
By instruction from L V. Kurchatov, scientific workers from the Institute of Physics of the Georgian SSR A cademy
of Science did preliminary work in the selected fields at the Institute of Atomic Energy even while the reactor was be-
ing built. The Georgian scientists received technical documents on mechanical monochromators, cold neutron filters,
neutron detectors, time analyzers, all needed for scientific work. Such a system of cadre training and instrumental
information was also used in the organization of reactor centers in Tashkent, Minsk, Riga, and other places.
The VVR-M reactor of the Leningrad Physicotechnical Institute of the USSR Academy of Science has been
called upon to meet the requirements of the research institutes of one of the most important scientific centers in the
Soviet Union ? Leningrad.
With the VVR-M reactor of the Ukrainian SSR Academy of Science, great advances are being made in work on
neutron spectroscopy, in studies of thermalization processes, and in work on capture y -rays. Work on solid state physics,
in particular with reference to radiation effects on materials, and work in radiobiology are also typical of the workbe-
ing done with the reactor in Kiev.
The basic directions of the work being done with the IRT reactor at the Institute of Physics of the Latvian SSR
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Academy of Science are studies of capture y -ray spectra and the spectra from short-lived isotopes, studies in solid
state physics, including the study of the properties of magnetic materials, and studies in radiobiology.
With the IRT reactor at the Power Institute of the Belorussian SSR Academy of Science, investigations will be
carried out in solid state physics (the structure of ferrites and other magnetic materials, and of semiconductors, the
dynamics of the condensed state), in nuclear spectroscopy, in the radiation resistance of various organic coolants,etc.
Because of the great benefit derived from the first coordinating meeting, such meetings came to be held yearly.
I. V. Kurchatov was the principal initiator in the creation of the largest scientific center in the world ? the
Joint Institute for Nuclear Studies in Dubna ? and he has promoted, in every way possible, cooperative organizations
among the socialist countries and the creation of reactor research centers in them. At the Twentieth Congress of the
Communist Party of the Soviet Union, I. V. Kurchatov said, "Through atomic reactors, we shall carry out work in con-
junction with the scientists and engineers of the countries in the socialist camp who, with the help of the Soviet Union,
will build for themselves atomic reactors for scientific purposes, and who will plan the construction of atomic power
stations. Our common effort with the scientists of the countries of the socialist camp will be broadened and deepened,
and certainly will lead to outstanding results."*
In 1956, in one of his speeches, he emphasized the great importance of the help which was being given to the
socialist countries in the planning and construction of research reactors and in the training of cadres, and he expressed
confidence that these cadres would safetly operate the reactors and would carry out research with them. The Soviet
Union began to give such help in 1955. Research reactors of various types were put into operation from 1957 on in
Rumania, Czechoslovakia, East Germany, Poland, China, Hungary, Bulgaria, and other countries. These countries
then had at their disposal modern equipment which enabled them to train national cadres of scientists and engineers
and to develop research in various branches of science and engineering.
It then became necessary to discuss and plan the scientific work to be done with the reactors, to make an effi-
cient selection of research goals, and to coordinate them. I. V. Kurchatov expedited these activities in every possible
way.
The first such meeting took place in Dubna in the spring of 1959. At it, there was discussed information about
the status and course of research work at reactors built in the Joint Institute for Nuclear Studies member-countries.
The meeting was faced with the problem of coordinating the efforts of the socialist countries toward the greater de-
velopment of peaceful uses of atomic energy.
With the support of I. V. Kurchatov, an international conference of scientists and engineers of the socialist
countries on the problems of operation and use of research reactors was arranged. This conference, which took place
in June, 1960 in Dresden, was an important landmark in a new stage of brotherly cooperation between our countries
in the matter of the peaceful use of atomic energy. About 150 scientists and engineers from nine countries partici-
pated. At the conference, the experience acquired in a number of socialist countries in the operation of research re-
actors was reviewed, along with the extension of their experimental possibilities and their use for scientific work. A
number of scientific and engineering problems were presented which were to be solved in a short time, since some
countries which had the experience and specialization offered to take upon themselves the solution of individual prob-
lems. This important meeting offered prospects for strengthening the collaboration between brother scientists in the
countries. In turn, yearly meetings began to be held in the various countries, meetings which dealt with reactor re-
search, reactor physics, and the exchange of experiences with the operation and improvement of reactors.
The reactor research centers established with the help of the Soviet Union became full-fledged scientific or-
ganizations in the majority of the socialist countries, actively working in timely fields of science and engineering,
making their contribution to world science, and meeting the demands of the economy of their countries.
We see how true were the words spoken by I. V. Kurchatov in 1956 in connection with the creation of research
reactor centers in the socialist countries, and to what successful results this has led.
I. V. Kurchatov strove for close collaboration with the scientists of all countries. It is well known what a great
role in the development of international collaboration of scientists was played by the lecture of I. V. Kurchatov which
was given in England, and which dealt with the work being carried on in the USSR in the field of thermonuclear fusion.
In a second lecture, he dealt with some problems in the development of nuclear power.
*"Pravda," February 22, 1956.
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I. V. Kurchatov more than once played the host to foreign scientists newly arrived in the Soviet Union, showed
them the experimental equipment at the Institute of Atomic Energy, as well as the results of investigations, and led
Joint seminars. For example, F. Joliot-Curie visited him in 1958, he received a delegation of English scientists under
the leadership of J. Cockcroft that same year and, in 1959, a group of American scientists, among whom were such
outstanding scientists in the field of reactor construction as A. Weinberg and W. Zinn.
Through the initiative of I. V. Kurchatov, and under his guidance, a session of the USSR Academy of Science,
was arranged which met in July, 1955, and which was devoted to the peaceful uses of atomic energy. At this session,
80 reports were read in which the results of important investigations being carried on in the Soviet Union were pre-
sented for the first time. These reports aroused great interest and proved useful to the scientists of other countries.
I. V. Kurchatov was in charge of the preparation of reports for the International Conference on the Peaceful
Uses of Atomic Energy held in Geneva in 1955.
The reports at the July session of the USSR Academy of Science and at the Geneva conference were a great con-
tribution of Soviet science to the problems of the peaceful uses of atomic energy. Among the reports presented at the
Geneva conference, an important position was occupied by reports on the First Atomic Power Station, on the course
of the development of nuclear power, on a reactor for physical and technical research, by reports about the VVR-2,
VVR-S, and TVR research reactors, by reports on reactor theory, and a number of others.
At the conference, at which the representatives of 79 countries were present, the Soviet Union submitted 102
reports. From the tribune of the Twentieth Congress of the Communist Party of the Soviet Union, I. V. Kurchatov de-
clared, "We derived great satisfaction from the fact that, at this conference, the reports of our scientists and engineers
received a high rating from the world scientific community."*
Again with the active participation of I. V. Kurchatov, preparations also went forward for the Second Inter-
national Conference on the Peaceful Uses of Atomic Energy (Geneva, 1958). For the first time, a considerable number
of papers were devoted to the problem of thermonuclear fusion. The speech by L V. Kurchatov in England led to the
open discussion of this most important scientific problem.
A great deal of interest was aroused by the Soviet scientists' reports on a number of subjects: the construction
of the atomic icebreaker "Lenin," the operating experience with the First Atomic Power Station, the plans for new
atomic power stations with uranium-graphite reactors producing high-pressure superheated steam as well as stations
with water-cooled, water-moderated reactors, the experimental fast reactor,s, the building of the intermediate research
reactor SM-2 with high thermal neutron flux, the rebuilding of the existing RFT, IR, VVR-2, and TVR reactors, the de-
velopment of rod-shaped fuel elements for VVER-type reactors, and the reactors of the atomic icebreaker "Lenin,"
the tubular elements for research reactors, and many n1ore. An especially powerful impression was made by the unex-
pected news of the start-up, in the Soviet Union, of the first new atomic power station of its kind (100,000 kW).
The high scientific level of the reports presented assured the prestige of the Soviet Union.
The brilliant life and career of that outstanding Soviet scientist and man, L V. Kurchatov, which are forever
engraved in our hearts, will serve for all as an example of unselfish service to the Motherland.
*"Pravda," February 22, 1956.
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SPONTANEOUS FISSION AND SYNTHESIS OF
FAR TRANSURANIUM ELEMENTS
G. N. Flerov, E. D. Donets, and V. A. Druin
Translated from Atomnaya Energiya, Vol. 14, No. 1,
pp. 18-26, January, 1963
Original article submitted August 30, 1962
The,possibility of spontaneous fission of nuclei was predicted theoretically in 1939 on the basis of a model rep-
resenting the nucleus as a drop of charged liquid [1]. Immediately after the publication of that article, intensive re-
search was started in the laboratories of many countries to investigate the spontaneous fission of uranium and thorium,
the heaviest elements known at that time. At the Lenin-
grad Institute of Physics and Technology of the Academy
.020 of Sciences of the USSR Professor I. V. Kurchatov's labora-
1018 tory developed a highly sensitive procedure by means of
which K. A. Petrzhak and G. N. Flerov were able, for the
101 first time in 1940, to observe spontaneous fission fragments
10" of U238 [2].
/ 232
1
Th .1
6236.
u235 x Np237
.23',
2.6
Th
pu239
,Rm
238?
.
241
232 ?
244'.
242 ?
40 -
238
PU
e?
, 8,4,24,3 ? cy
249
24 4+
248 ? .
? 242
YOL
x
250
251?
Z93
C
48
Cm
?46
. 252?
s
Es f /If .
25 ?
Cf
254?
?
258
?
Fm
1012
101
10
102
100
10-
10"
10-
35 36 37 38 39 40 Z
Fig. 1. Period of spontaneous fission Tsf as a function
of the fissility parameter Z2/A.
The experimental discovery of the fission of U238
from the ground (unexcited) state greatly heightened the
interest in the study of this new form of radioactive decay
of nuclei. Investigations were conducted along two main
lines: to explain the mechanism of spontaneous fission, and
to find new nuclei in which it took place. It was found that
many transuranium elements obtained artificially in re-
actors or accelerators undergo spontaneous fission.
Some Laws Governing the Spontaneous
Fission of Nuclei
By 1952 a large amount of experimental material on
spontaneous-fission periods had been collected, and this
enabled Seaborg to publish the first systematic study of
these data [3]. He constructed a graph of the spontaneous
fission period Tsf as a function of the fissility parameter
Z2/A, which in the liquid drop model represents the ratio
of the Coulomb energy tending to force the protons apart to
the stabilizing surface energy of the nucleus. This system-
atization was later refined and extended [4,5]; its present
form is shown in Fig. 1. We can observe three basic features in the behavior of the spontaneous-fission periods of the
various elements: 1) a general tendency for Tsf to decrease as Z2/A increases; 2) the "parabolic" shape of the curves
on which the values of Tsf lie for the various isotopes of one element; 3) a value of Tsf in nuclei with an odd number
of neutrons or protons which is 103 to 106 times the Tsf value of an even-even nucleus for a given Z2/A value. The
first of these features agrees qualitatively with the predictions based on the hydrodynamic model, while the latter two
cannot be explained from he viewpoint of this nuclear model. The development of the theory of spontaneous fission
is closely related to that of the general theory of nuclear structure and nuclear reactions. The various models to rep-
resent nuclear structure were also used to explain features of the Tsf versus Z2/A graph. Evidently, for a correct under-
standing of what happens in the fission process we must consider not only the collective properties of the nucleus, but
also the behavior of the individual nucleons when the nucleus as a whole is deformed. As was shown by Nilsson [6],
the energy of the individual nucleons changes considerably as the nuclear deformation increases, and this may produce
an appreciable change in the hydrodynamic fission barrier. Johansson [7] used the Nilsson diagram for an analysis of
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? 14
12
10
8
6
4
2
-2
----1--
? Pu
V
? 1.
?
*
Ik
II
NM
vi
Cf
.
,
II
III
? 35 36 37 38 39 40
72/g
Fig. 2. Graph of experimental values of
Tsf as a function of Z2/A after single-
particle corrections are applied [7].
effective barriers; the analysis indicated that the graph of Tsf as a func-
tion of Z2/A can be made considerably more regular by taking single-
particle corrections to the hydrodynamic barrier into account. The dis-
persion of the points is considerably reduced, and they are grouped about
a straight line (Fig. 2).
Despite the substantial theoretical advances in the understanding
of spontaneous fission, the theory is still only qualitative. In particular,
it is very difficult to give a theoretical estimate for the lifetimes of the
far transuranium elements. For such estimates, therefore, we resort to
various semi-empirical formulas and to the extrapolation of experiment-
ally observed relationships to the range of the unknown nuclei. The
Swiatecki [8] and Dorn [9] formulas are widely used. These formulas
were based on the fact that the experimental values of the nuclear masses
in the ground state do not agree with the points on the smooth mass sur-
face which were calculated on the basis of the hydrodynamic model, us-
ing the quantity m, and that the spontaneous-fission periods determined
experimentally disagree with those expected from this model when the
quantity ST is used.
Swiatecki observed a well-defined correlation between 6T and
Sm. This seems natural today, since we already know that the hydro-
dynamic formula for the masses ignores the shell structure of the nuclei,
the fluctuations in the pairing energies, the nonuniformity of the angular
and radial charge distributions, etc., but all these energy effects influ-
ence the nucleus lifetime for spontaneous fission. By applying empirical
corrections KS m to the observed spontaneous-fission periods, Swiatecki
obtained a smooth curve of Tsf + KS m versus Z2/A for even-even nuclei with K = 5 ?(Z2/A ? 37.5).
Dorn made a slight change in the Swiatecki formula by adding a 4Z/A term, thereby smoothing the curves
even more. An analytic expression of the Swiatecki-Dorn formula for periods of spontaneous fission is the following:
Ig Teven- even
Ig Todd A
Ig Todd-odd
--30,06
--23,46
--I8,56,
172 .
0,07302 +.1389 - (4 ? 0) ow,
?7,80 f
where 0 = Z2/A ? 37.5, Tsf is expressed in seconds, and 6m is expressed in MeV. To estimate the spontaneous-fis-
sion periods of unknown nuclei, 6 m may be defined as the difference between Cameron's tabulated mass value [10]
and a point on the smooth mass surface;
= 1000A-8,3557A+19,12A2/3+0,76278 Z2 -I 25,444 (N?AZ)2 +0,420(N?Z).
A.113
Figure 3 shows the spontaneous-fision periods calculated by the Swiatecki-Dorn formula fora number of isotopes
of curium, californium, fermium, and elements 102 and 104. For comparison purposes, experimental points have
been shown by crosses, and broken curves have been drawn through them. It can be seen that satisfactory agreement
with the formula is found in the case of californium isotopes, while in the case of fermium the position and behavior
of the broken curve differ considerably from those of the solid curve. For heavy isotopes of curium, the formula pre-
dicts a sharp increase in the probability of spontaneous fission, and in the case of elements 102 and 104, the periods
of spontaneous fission decrease somewhat more slowly in the N > 152 range than those of,californium and fermium.
In [11], analyzing the curve of emission of various transuranium elements from the "Mike" thermonuclear explosion,
Dorn showed that the formula yields lower values of Tsf for very heavy isotopes (for example, Fm2s4 and Fm255). Ac-
cording to his conclusions, the emission curve can be explained only if we assume that in the region far from the beta
stability curve spontaneous fission cannot take place more rapidly than beta disintegration, i.e., that the Swiatecki-
Dorn formula is not valid for neutron-enriched nuclei. We cannot at present determine the range of'N values for
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10'2
10"
10"
io9
10,
io7
14-
1(75
103
10:
10
10 -
VI 150 152 154 156' 158 160 N
248
x
I
I
xef
C Is
,cfr+s
\
Cm
Fm2sz,
1\C
I.
2
? 1
\I
x m
\
fm ? \
2,
?
104
?102F
Nmk
LX .
NIII
[
k.
1
Om.
?4q1
.i. 104
Fig. 3. Values of Tsf calculated by the Swiatecki-
Dorn formula as a function of the number of neutrons
N in the nucleus; 0 calculated values; - -x- -
experimental data.
value of Tsf for FM258 is a few minutes, but Johansson
for Cf256 is between one year and one month.
Only experimentation can provide the answers to all these questions. However, the experimental determination
of the spontaneous-fission periods of some relatively heavy isotopes of fermium and californium is hampered by seri-
ous difficulties in the problem of synthesizing them.
In order to estimate the various possible ways of obtaining such isotopes, we shall first consider the present state
of the problem of obtaining new transuranium elements and studying their properties, and we shall try to note some
methods which will enable us to advance further into this range.
Synthesis of Transuranium Elements Using Multicharge Ions
The start of work in this direction in the USSR is closely linked with the name of Igor' Vasil'evich Kurchatov.
The first reactor, the first cyclotron accelerating multicharged ions, and later the large heavy-ion accelerator at
Dubna, were established with his direct participation, guidance, or enthusiastic support. The installation of the 300-
cm cyclotron at the Joint Institute of Nuclear Studies, which makes it possible to obtain intense beams of ions in a
wide range of Z and A values, opened a wealth of new possibilities for conducting experiments in the synthesis of new
elements. Various multicharged ion accelerators have been set up and put into operation in a number of countries
during the past few years.
Up to the present time, heavy ions have been successfully used to synthesize all previously known transuranium
elements, as well as the new elements 102 and 103 (lawrencium) [12-15].
Judging by the successes achieved with this method, we may consider it the most promising for the synthesis of
new elements. Nevertheless, the difficulties encountered in its use are so great that we are forced to analyze and
test all processes which are even the least bit likely to extend the possibilities of this method.
which this formula is valid. If we consider the new, still
undiscovered elements immediately adjacent to those we
have studied, the most reliable method of estimating their
spontaneous-fission lifetimes still appears, up to the pres-
ent time, to be the extrapolation of empirical curves of
Tsf versus Z and A. For this purpose we may use, for
example, curves of Tsf as a function of the number of neu-
trons N in the nucleus when Z is constant (Fig. 4), or of Tsf
as a function of the number Z of protons in the nucleus
when N is fixed (Fig. 5). Simple graphical extrapolation
yields values of Tsf for elements 102 and 104 which differ
considerably from the calculated values. In particular, a
lifetime of 0.01-1 sec may be expected for the isotope
104260 on the basis of Figs. 4 and 5, while the Swiatecki-
Dorn formula yields a value of one hour for the period.
A very important question in predicting the proper-
ties of elemen,ts is just how much the subshell with N =152
affects the fission barrier for high values of A.
For very high A values, the parameter Z2/A becomes
considerably smaller than (Z2/ A)N=152 . According to the
position of the hydrodynamic model, such nuclei should be
more stable with regard to fission. The competition from
the shell effect reduces the value of Tsf, but the import-
ance of this effect may be considerably less beyond N
= 152, and we may then expect a rise in the right-hand
branches of the curves in Fig. 4. It is diffidult to predict
where this rise will begin. Johansson [7], analyzing the be-
havior of neutron levels up to the value of N = 160, con-
cludes that the heavier isotopes of californium and fermi-
um will have longer lifetimes than might be expected from
graphical extrapolation. For example, the extrapolated
estimates it at one hour. The value of Tsf similarly obtained
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1020
to"
to"
w"
to"
? 10"
1? 08
? 108
104'
102
100
10-8
10-4'
10-s
10-8
232
IS
1111111
Th
x
N237
xr,?z3
nix/1117241
ED,V233
?Ea
152
neutron
ir
v
240 242
I.111
I
238
imh214.
nal
Cf 2+9 x x5A-249
SW
242
244
I
6
,,

,
P0
r 253
xcS 251T
x Es
2+0III
2 4
C
ik 252
ird
SkIIIC FM2
011isPriak"
C
iiiii
I
102M
II
1164,06.
140 142 14'41't6' 14e 150 152 154 156 158
Fig. 4. Tsf as a function of the number N of neutrons
in the nucleus.
10
106
102
104
10
10
r
i
250
1
250
252
2'2
's,
?..
-?
'+54
?
\
? .....
256.
A
?
254
'0.,254
?
?
?
\.256
\
?
?..
11.152
256
\
'_258
'IN.134
\
\
\
?
258
?
?
?
?
?
160
1 V:.156
.96 98
100
102
104
106
Fig. 5. T91 as a function of the number Z of protons
in the nucleus.
The synthesis of a heavy element BAz from a target
.A.P',1 and an accelerated ion IAz2 depends on a nuclear re-
z1 2
action of the type
AA1 0:12 xn)BA
zi Z2 Z ?
The heavy ion, accelerated to an energy somewhat greater
than that of the Coulomb barrier, penetrates into the target
nucleus with a cross section close to the geometric cross
section and contributes all its kinetic energy to the com-
pound nucleus. Since the nucleons in the compound nucle-
us are less firmly bound than in the target nucleus and in
the nucleus of the heavy ion, part of this energy is expended
in unpacking, and the remainder (usually 30-60 MeV), is
used to excite the compound nucleus. The nucleus may re-
lease this energy by the evaporation of a number of nucle-
ons (usually three to five). However, since we are dealing
with heavy nuclei, i.e., nuclei with a low fission barrier,
the main form of disintegration of the compound nucleus
is fission, which usually predominates over all stages of
nucleon evaporation. As a result, the yield cross sections
of far transuranium elements are found to be smaller by
several orders of magnitude than the geometrical cross sec-
tions and usually have values of 10-29 to 10-33 cm2.
Sometimes a reaction of the type
A); (1):32, Bz?
is used to synthesize a heavy element. This reaction differs
from the previous one in the fact that an alpha particle is
emitted when the heavy ion is captured; in other respects,
the process is similar. Since this case also includes an
evaporation stage, the cross section of B/A1 isotope forma-
tion is also smaller by several orders of magnitude than the
geometrical cross sections.
Experimenters of today have at their disposal some
fairly high-intensity ion beams containing B10'11, C12,13,
N14,15,
016,18, and Ne26'22, and a good supply of target ma-
terials from U238 TO Cf232. The choice of Z1 for the target
and Z2 for the particle used to synthesize an element with
a given Z = Z1 + Z2 remained uncertain for a long time.
The hypothesis was expressed that increasing Z2 by one, and
decreasing Z1 accordingly should reduce the yield cross sec-
tion of the element with atomic number Z by a factor of
ten. However, an analysis of studies made earlier [16, 17],
and of the data obtained in [18] indicates that these esti-
mates were too pessimistic. The transition from the synth-
esis of Fm269 by the Pu241(C13,4n)Fm268 reaction to the synth-
esis of Fm269 by the Th232 (Ne22,4n)Fm256 reaction reduces
the cross section only by a factor of 20, rather than by four
orders of magnitude as was supposed earlier.
Thus, it is possible even today, in theory, to synthesize all the elements up to an including 108. However, when
we try to apply this possibility, we encounter difficulties involving not the synthesis itself, but the study of the proper-
ties of the newly obtained elements and new isotopes.
Neutron evaporation reactions generally result in the formation of light isotopes of new elements which have a
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short alpha disintegration lifetime. For this reason, chemical methods of identification cannot be used. This con-
siderably complicates the entire investigative process and often reduces the reliability of its results.
The method of physical identification of a new alpha-active element with a short lifetime is based on the re-
cording of alpha-activity with a systematically assumed energy. At the same time, all possible background influ-
ences must be eliminated. It has been found experimentally that in reactions with heavy ions in mixtures of lead,
bismuth, and other elements in the target, alpha-active nuclei in the Ac?Po region may appear, with disintegration
properties close to the expected properties of the new elements [13, 19].
Moreover, recent studies [20, 21] analyzing the products of Th + Ne nuclear reactions indicated that such back-
ground activity comes about as the result of deep-detachment reactions. The additional background sources may be
unknown light isotopes of californium, fermium, etc.
Any further advance toward the synthesis of heavier elements by the alpha-activity recording method will be-
come increasingly difficult, and its results will become less and less reliable. The reason for this is that as we pass
to heavier particles, the number of background activities will increase and the cross sections of formation of new ele-
ments will decrease. At the present time, experimenters have approached the synthesis of element 104. This is the
region in which spontaneous fission may come to predominate over other forms of disintegration.
It has been found considerably iimpler to show that a new element has been formed by using its spontaneous
fission than by using alpha disintegration or electron capture, since the absence of background makes the method very
sensitive. The nuclei produced in the reactions taking place in the mixtures of the target cannot undergo spontane-
ous fission. To identify a new element it would be sufficient to use the complex study of the excitation functions of
the formation of a spontaneously-splitting product (this would give the value of the atomic weight A) and the yields
of .a given nucleus under crossed irradiation of different targets by particles with varying A1 and Z1 values (to deter-
mine the atomic number Z of the product under consideration). However, in practice this has been found more com-
plex than might have been expected.
It was shown in [22] that when heavy ions (Ne22, 016, Bli, etc.) interact with nuclei of uranium, we obtain a
spontaneously splitting isotope with an anomalously small half-life (about 0.015 sec). A study of the excitation func-
tion for the formation of this isotope in various reactions led the authors to conclude that this synthesis takes place be-
cause some of the nucleons of the incident nucleus are transmitted to the target nucleus, and that it has an atomic
number not exceeding 97. The maximum cross section of the U238 + Ne22 reaction is approximately 2 ? 10-32 cm2. On
the other hand, the cross section. of the U238 + B11 reaction is several times the above value in experiments with neon.
The authors suggest the hypothesis that the observed effect is caused by spontaneous fission from the isomeric state.
Indeed, if U238 is irradiated with B11 ions, we obtain known isotopes with elements with Z :s 97. All of these have in
the ground state a lifetime considerably greater than 0.015 sec, while the spontaneous-fission periods Tsf of these iso-
topes are found to be not less than 107 years. It follows from this that the spontaneous fission of the resulting nuclei
has been made easier by a factor of more than 1016.
Thus far no direct evidence exists as to whether this isomeric is a unique case or whether the phenomenon is
widespread in nature and isomers with various lifetimes may be found in the reactions concerned. An extensive study
of these nuclei will make it possible to obtain further information on the mechanism of "ordinary" spontaneous fission.
Thus, the problem of synthesizing and identifying transfermium elements by their spontaneous fission from the
ground (unexcited) state is found to be related to the obtaining of the heaviest isotopes; this would make it possible to
make not only physical studies of the new elements, but chemical studies as well, and would considerably increase
the reliability of the identification.
After these preliminary remarks, we shall now consider a number of possible reactions which would enable us,
in theory, to synthesize a nucleus with a number of neutrons considerably exceeding the "magic" number N = 152;
this could not be achieved by neutron evaporation reactions even if the heaviest targets were used. For example, if
Cm248 is irradiated with C13 ions, we cannot obtain isotopes of element 102 with a weight of more than 257; irradia-
tion with N16 cannot produce isotopes of element 103 heavier than 259, and these isotopes, as is indicated by the sys-
tematic study, should have short lifetimes.
Incomplete-Fusion Reactions Using Heavy Particles. If ArfS or Ca2,1 is used as the bombarding particle, we may
hope that in the reaction involving boundary interaction with the target nucleus there will be capture of a consider-
able portion of the incident particle, and the nucleus will remain near the ground state.
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As an example, let us consider reactions to synthesize a number of heavy isotopes of fermium, using the inter-
action of At? with uranium:
U238-1-- Ar48 FIn288-+ Ne22;
U238 +Ar40 Fm258
Ne20:
u238+Ar4o ?> Fm260 4_ Nets.
Our hopes of success of such reactions are based on the following: First of all, these reactions are threshold reactions,
and their thresholds lie above the Coulomb barrier. The reason for this is that oxygen nuclei are captured from the
bound state in the At.? into the bound state in fermium. Consequently, there is an energy range of the bombarding
particles within which any considerable excitation of the fermium nuclei will be impossible, from energy considera-
tions, so that there will be neither nucleon evaporation nor fission. In the second place, we have at our disposal data
indicating that in reactions with multicharged ions there has been observed a considerable yield of such products,
which may be formed, in particular, by a mechanism noted above (for example, U238 + N14 Cm242-244). In the third
place, we know reliably [21] that a large cross section is found in the reactions which include the capture of a large
number of nucleons of the target nucleus by the incident particle. If the mass and charge of this particle are in-
creased, by accelerating, for example, argon or heavier elements, we may expect the reverse reaction to take place
as well: the reaction in which a large number of nucleons from the incident particle are captured by the target nu-
cleus.
In order to check this method, it is most convenient to use the first of the above reactions, in which we obtain
the spontaneously splitting isotope Fm266 with Tsf = 2.7 hours, which should assure a high degree of sensitivity.
Radiative Capture of a Heavy Ion. A second possibility for approaching the region of beta stability may be
found in reactions involving the radiative capture of a heavy ion. In these reactions, the emission of a high-energy
gamma quantum should reduce the excitation energy of the compound nucleus to a level below the fission threshold.
Such reactions should yield products with mass numbers four units greater than those usually obtained in nucleon
evaporation reactions. Clearly, the process of emission of one high-energy gamma quantum from a heavy compound
nucleus will constitute little competition for the processes of fission and nucleon evaporation. Nevertheless, the fact
that in this process there is only one stage of emission of a gamma quantum [ry (rf + Fn + Fp + ry )]1, as compared
to the usual four stages of neutron evaporation [n /0'n + 1-f)14, gives some hope that the effective cross section of
this process will not be very small.
Unfortunately, at present there are only a very small number of studies [23, 24] devoted to reactions involving
radiative capture of a heavy ion, and all of these investigations were carried out on light targets. In this case the
cross section is about 10-36 cm2. There is no way of obtaining from this result a cross section corresponding to the re-
gion of heavy transuranium elements.
Here, we believe, the simplest procedure is to establish experimentally the cross section for the radiative cap-
ture of 0" by a U2" nucleus to form Fm266:
U238 (018, y)
The sensitivity of this method, when a 100-?A current of 0" ions is used, enables us to observe reactions taking place
with a cross section of 10-36 cm2. The effect in the case of such a cross section is about ten fissions per hour.
Nucleon Evaporation Reactions Using the Products of Nuclear Reactions as Bombarding Particles. Let us con-
sider in some more detail the data obtained in [21].
When Th232 was irradiated with Ne22 ions, the authors of the present study observed large-scale emission of the
isotopes A c224, AC225, A c226, and T1i227. The only mechanism capable of explaining this result is the stripping of a
number of nucleons from the target nucleus. At the same time, the authors obtained data indicating that the stripped
nucleons, in all probability, were transferred to the incident particle. Thus, when Th232 is irradiated with Ne22 ions,
there is a beam of secondary particles which will include very heavy isotopes of neon, sodium, and magnesium.
Let us estimate the possible intensity of the beam of secondary particles. Starting from the data of the study,
it may be expected that the cross section of formation of these particles may be about 10-27 cm2. With a 100-uA cur-
rent of Ne22 ions and a Th232 target with a thickness of 10 mg/ cm2, we shall have about 106 particles per second. Put-
ting aside the question of the energy distribution of the secondary particles, we note that such a beam is completely
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adequate for the study of reactions taking place with a cross section a-10-28 cm2 , if the reaction products make pos-
sible the recording of several events per hour.
A cross-section value of 10-28 cm2 is not too large even for the region of far transuranium elements, since the
fissility of the compound nucleus in this case must be considerably reduced by reason of its increase in mass, and the
neutron evaporation process can successfully compete with the fission process. In each case, the possibility can be
checked without much difficulty; we can do this by irradiating a thick Th232 target with Ne22 ions of sufficiently high
energy. The thorium will not only transform the beam, but will also serve as the target at which the Th232(Ne28,4n)Fm256
and Th232(Na28, 4n) md256 electron capture> Foss reactions will take place.
The means of synthesis of enriched neutrons of the far transuranium elements which we have considered above
could considerably widen, in our opinion, the possibilities in this direction of the method of multicharged ions.
It remains only to note certain particular cases in which individual heavy nuclei are obtained, and to analyze
briefly the reactions involving the evaporation of protons from compound nuclei, since such reactions also lead to the
formation of heavy isotopes of transuranium elements.
From the viewpoint of a systematic study of spontaneously splitting nuclei, the synthesis of Cf288 and Fm298 is of
great interest, since the lifetimes of these isotopes, as estimated by different methods, are too contradictory.
The isotope Cf 296 may be synthesized, in quantities sufficiently large for study, by a reaction of the type
ces4(018, 016)c f256,
provided the experimenter has at his disposal at least 1019 nuclei of Cf254.
In reactions involving multicharged ions [for example, Cm248(B11, 4n)md255 electron capture Fm255, for which
Tia = 21.5 hours], we can accumulate about 109 nuclei of Fm299; if the reaction in which three neutrons are captured
by some particle takes place with a cross section of about 10-28 cm2, we can synthesize enough Fm288 for study
(several disintegrations per hour).
Reactions involving the evaporation of charged particles provide another possibility of obtaining relatively
heavy isotopes. For example, Pu242(Ne22, p3n)1032" may be such a reaction. There is good reason to expect the iso-
tope 1032" to be unstable with respect to electron capture. Electron capture will result in the formation of the iso-
tope 1022, which should be spontaneously fissile.
The (Ne22 , p3n) nuclear reaction was used successfully to synthesize element 101, Md258, by irradiating U238
[25, 26]. A similar reaction involving the evaporation of a proton and two neutrons may yield still heavier isotopes.
In particular, it may be hoped that the Pu2(Nen, 42 p2n)103281 reaction"will yield a relatively long-lived isotope of
element 103.
A reaction in which a proton and only one neutron are emitted is very unlikely. The reason for this is the small
cross section of formation of a compound nucleus in the case of a low-energy incident particle. Experiments indicate
that the cross section of the U238(Ne29, pn)Md258 reaction is not more than 10-38 cm2. This sets a limit to the use of
charged-particle evaporation reactions in synthesizing heavy isotopes.
Conclusion
The further study of the properties of spontaneous fission is closely related to an advance into the region of still
undiscovered elements and to the synthesis of heavy isotopes of californium, fermium, and element 102.
Moreover, a study of the phenomenon in which we are interested ? the fission of isomers of the transuranium
elements and the nuclear reaction in which they are formed? will also provide a great deal of new information on the
mechanism of nuclear fission from the ground state.
On the basis of recent studies establishing a relationship between the probability of spontaneous fission and the
energy-level distribution of nucleons in the nucleus [7, 27, 28], we may hope to obtain additional information on the
structure of nuclei if we study their periods of spontaneous fission.
Furthermore, by studying the rules of variation of the periods of spontaneous fission over a wide range of Z and
A values, we may be able to answer the question of how important spontaneous fission is for those isotopes of trans-
fermium elements which ought to be obtained in the very near future.
The synthesis of a new element is a very complex problem. To solve this problem we must develop a large
number of different specialized methods, and the choice of any particular method will depend to a great extent on
the type of disintegration and the lifetime of the element under study. The more we know about spontaneous fission,
the more exactly we will be able to determine Tsf for the new element, and the greater will be our chances for a
successful solution of the problem of synthesis.
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Thus, the problem of the further study of the rules governing spontaneous fission and that of the synthesis of
new elements, are inseparably connected, so that progress in one yield will necessarily constitute progress in the other.
LITERATURE CITED
1. N. Bohr and J. Wheeler, Phys. Rev., 56, 426 (1939).
2. K. A. Petrzhak and G. N. Flerov, ZhETF., 10, 1013 (1940).
3. G. Seaborg, Phys. Rev., 85, 157 (1952).
4. B. Foreman and G. Seaborg, J. Inorg. and Nucl. Chem., 7, 305 (1958).
5. V. Druin, I. Brandshtetr, and Ya. Maly, Offal Preprint, 17-875 (Dubna, 1962).
6. S. Nilsson, Symposium: Deformation of Atomic Nuclei [Russian translation] (IL, Moscow, 1958).
7. S. Johansson, Nucl. Phys., 12 , 449 (1959).
8. W. Swiatecki, Phys. Rev., 100, 937 (1955).
9. D. Doris, Phys. Rev., 121, 1740 (1961).
10. A. Cameron, Report CRP-690 (1957).
11. D. Dorn, Phys. Rev., 126, 639 (1962).
12. P. Fields et al., Phys. Rev., 107, 1460 (1957).
13. G. N. Flerov et al., DAN SSSR, 120, 73 (1958).
14. A. Ghiorso et al., Phys. Rev. Lett., 1, 18 (1958).
15. A. Ghiorso et al., Phys. Rev. Lett., 6, 473 (1961).
16. T. Sikkeland, S. G. Thompson, and A. Ghiorso, Phys. Rev., 112, 543 (1958).
17. V. V. Volkov et al., ZhETF., 37, 1207 (1959).
18. E. D. Donets et al., ZlifTF., 43, 11 (1962).
19. G. N. Flerov et al., ZhfTF., 38, 82 (1960).
20. L Brandshtetr et al., Offal Preprint, P-978 (Dubna, 1962).
21. G. Kumpf and E. D. Donets, Offal Preprint, P-1071 (Dubna, 1962).
22. S. M. Polikanov et al., ZhfTF., 42, 1464 (1962).
23. D. Fisher, A. Zucker, and A. Gropp, Phys. Rev., 113, 542 (1959).
24. R. Coleman, D. Herbert, and J. Perkin, Proc. Phys. Soc., 77, 526- (1961).
25. G. B6ranova et al., Offal Preprint, P-856 (Dubna, 1962).
26. V. A. Druin, OIYaI Preprint, P-874 (Dubna, 1962).
2.7. J. Wheeler, Symposium: Niels Bohr and the Development of Physics [Russian translation] IL, Moscow, 1958).
28. J. Newton, Progr. in Nucl. Phys., 4, 234 (1955).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all el this peri-
odical literature may well be available in English translation. A complete list of the cover- to-
cover English translations appears at the back of this issue.
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000600100001-7
INVESTIGATION OF PROPERTIES OF ? -MESIC ATOMS AND
-MESIC MOLECULES OF HYDROGEN AND DEUTERIUM
AT THE DUBNA 680-MeV SYNCHROCYCLOTRON
V. P. Dzhelepov
Translated from Atomnaya Energiya, Vol. 14, No. 1,
pp. 27-37, January, 1963
Original article submitted September 14, 1962
The first stages in the development of a new field of physics in our country, the physics of high-energy particles,
are linked to the building of the synchrocyclotron at Dubna in 1949. This machine is capable of producing protons of
680 MeV, and pions and muons of energies up to 400 MeV. An important initiating and managing role is credited to
the late Igor' Vasil'evich Kurchatov both in the stages of the installation and assembly of this unique accelerator,and
in the stages of performing research on the machine. Being in possession of a broad scientific horizon typical of an
outstanding scientist and prominent public activist, in harmony with the solution of the country's most pressing and
grandiose large-scale problems in practical applications of nuclear energy, Igor' Vasil'evich always took the long for-
ward view and expended intense efforts in cementing the necessary base for the future potentialities in scientific re-
search in the field of the atomic nucleus and elementary particles. The Nuclear Problems Laboratory, where the ac-
celerator was installed, was over a long period a branch of the Institute of Atomic Energy of the USSR Academy of
Sciences, over which L V. Kurchatov presided in the post of Director. The 680-MeV synchrocyclotron, now turned
over to the Joint Institute of Nuclear Research, has made it possible to complete a huge volume of research on a vari-
ety of topics, with extremely valuable scientific results.*
I. V. Kurchatov consistently felt a passionate urge in science toward what was new, important, of broad scope,
and appealed to his disciples to follow in that direction. It is a pleasure for us to report, in this issue of the periodical
which is devoted to the memory of our beloved teacher, on one of these new trends in research developed in recent
years in work with the Dubna synchrocyclotron, the study of mesoatomic and mesomolecular processes in hydrogen,
all the more so in that some of these investigations touch on the problem of the thermonuclear fusion of light ele-
ments, to the study of which Igor' Vasil'evich devoted, with the tremendous involvement and energy characteristic of
him, the last years of his scientific activities.
Introduction
As a result of the completion of a number of high-precision experiments with ? -mesons (measurement of the
gyromagnetic ratio of the ? -meson [1], study of muon scattering on carbon [2], etc.), particularly in recent years, it
has been established to a high order of reliability that the ? -meson, possessing a mass 200 times larger than that of
the electron, is entirely similar to the electron in its electromagnetic properties. One of the manifestations of this
similarity is the fact that negative muons may be captured into atomic orbits and there form mesic atoms and mesic
molecules of various elements, in a manner similar to the way electrons form the familiar atomic and molecular sys-
tems. The distinguishing features of mesoatomic systems are, however, the fact that the lifetimes of these systems
are relatively short and are determined, in the case of the light elements, by the lifetime of the [I -meson (2.2 ? 10-6
sec) , while their dimensions are approximately 200 times smaller than the dimensions of conventional atoms. Meso-
atoms and mesomolecules constitute a great new world of particles of matter existing in a very special state. In this
article, we shall be dealing with a study of the properties of mesoatoms of the simplest element, hydrogen.
The radius of the first Bohr orbit of the hydrogen mesoatoms is at most 2.5 ? 10-11 cm, and this fact, along
with the electroneutrality of these atoms, leads to a whole series of specific physical phenomena.
*The most important of these results have been published in the periodical Atomnaya Energiya in articles authored
by V. P. Dzhelepov and B. M. Pontecorvo, 3, 11, 413 (1957), and D. I. Blokhintsev, 10, 4, 317 (1961),
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10
9
Fig. 1. Arrangement of experimental equipment. 1)
Inner proton beam from 680-MeV synchrocyclotron;
2) beryllium target; 3) p- and 1.--mesons, of 260
MeV/ c momentum; 4) shielding wall; 5) collimator;
6) deflecting and defining magnet; 7) lead shield; 8)
copper filter; 9) diffusion-chamber solenoid magnet;
10) stopping of p--mesons; 11) diffusion chamber.
Fig. 2. Scheme of mesoatomic and mesomolecu-
lar processes and nuclear reactions between hydro-
gen isotopes, with p--mesons in a hydrogen-deuteri-
um mixture as causal factors.
The most salient and interesting of these phenomena
may be termed the catalysis of p -mesons of nuclear reac-
tions between hydrogen isotopes. The possibility of such
a process had been predicted theoretically by the Soviet
scientists A. D. Sakharov and Ya. B. Zel'dovich [3], and
independently by F. Frank [4] in the West. The phenome-
non of muon catalysis was first detected experimentally
by L. Alvarez and co-workers [5] in 1957. One character-
istic trait of the process is that, in the presence of p -mesons,
nuclear reactions involving hydrogen isotopes may go
ahead in "cold" hydrogen while, for example in thermo-
nuclear reactors, plasma must be heated to millions of de-
grees to bring about fusion. The brief lifetime of the p -
meson, as well as the fact that the meson has a certain
probability of forming a helium p -mesoatom in the p + d
and d + d reactions, render impossible the achievement of
a sustained nuclear chain reaction by means of p -mesons.
Nevertheless, because of the fact that nuclear reactions
brought about by p -mesons not infrequently take place
under conditions entirely distinct from those under which
they are observed in accelerator arrangements, the study
of p -meson catalysis may well furnish a source of new in-
formation on nuclear reactions at very low energies.
The heightened interest displayed by physicists in
p -mesoatomic processes in hydrogen, as of recent years,
is due in large measure to that peculiar part played by
these processes in the solution of one of the fundamental
problems in the contemporary physics of elementary par-
ticles? that of determining the value of the weak muon-
nucleon interaction constant from experiments on the cap-
ture of muons by protons:
(1)
In actual practice, this reaction iiroceeds in hydro-
gen from the pp-mesoatom state or the ppp-mesomolecule
state. It has been demonstrated theoretically [6-8] that
the probability of reaction (1) depends on the spin state of
the original system. As a result of the fact that the p-
meson has half-integral spin (Sp = );,. the ground level
of the pp-mesoatom is split into two sublevels belonging
to a hyperfine structure of total spins equal to zero and
unity. Similarly, the spin state of the mesomolecule ppp
may be represented as a mixture of singlet and triplet
states. This means that a correct interpretation of the rate
of reaction (1) as measured in an experiment requires that
quantitative data be available on the probability of forma-
tion of ppp-mesomolecules, and that a solution be reached
to the problem of what spin state the pp-mesoatom is in
prior to capture. The urgency of the problems referred to has stimulated the development of experimental research
at the Joint Institute on mesoatomic processes and on the catalysis of nuclear reactions in hydrogen and deuterium,
as well as deeper probing into the theory underlying these phenomena.
*The fact that the spin of the p-meson is one-half was first established by investigations reported by A. E. Ignatenko
et al. [9], performed on the synchrocyclotron of the Nuclear Problems Laboratory at the Dubna Joint Institute.
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The article sheds light on the principal results amassed in the first stage of these investigations, as reported at
the July 1962 International Conference on the Physics of High-Energy Particles at Geneva [10, 11]. These investiga-
tions were completed in the 1960-1962 period by a team of Joint Institute workers including S. S. Gershtein, P. F.
Ermolov, Yu. V. Katyshev, E. A. Kushnirenko, V. I. Moskalev, M. Friml, and the author of this article.
Our attention was concentrated on the study of the following phenomena: elastic scattering of pp-mesoatoms
on protons, the Jumping of a p -meson from a proton to a deuteron, the formation of ppp-mesic molecules, p -catalysis
of (p + d)- and (d + d)-reactions, the probabilities of formation of the corresponding mesic molecules, and the
jumping of p -mesons from protons and deuterons to complex nuclei.
The existing theoretical development of the circle of phenomena discussed is presented in [8, 12-14], and opens
up rather broad vistas for comparison of experimental material and theoretically computed data. As the material is
presented in its full scope, the amount of harmony between experimental results and theory, as well as the attendant
complications, will become evident.
1. Experimental Procedure
The study of mesoatomic and mesomolecular processes in hydrogen is a relatively complicated job. This is
due, in the first instance, to the multiplicity of possible phenomena and the need to separate out each of these vari-
ants in some reliable manner. The second major difficulty is of a more basic nature. The trouble here is that some
of the processes (e.g., formation of mesomolecules) do not present a directly observable effect and the absolute proba-
bility of these processes may be determined either by some indirect approach or as a result of the observation of the
yields from the corresponding nuclear reactions. We must take cognizance here of the fact that the energies of the
reacting particles are very low, and the ranges of the reaction products in condensed-phase material (liquid hydrogen)
are also very short. Several processes, e.g., diffusion of pp-mesic atoms, are in general impossible to observe direct-
ly when the hydrogen density is very high.
Analysis shows that most of these difficulties can be coped with successfully when the processes are studied in
a gaseous medium. Our investigations therefore involved the use of a diffusion chamber filled with either hydrogen
or a mixture of hydrogen and deuterium. The use of ordinary industrial-grade deuterium could not be countenanced
in these experiments, since this grade always contains tritium in relatively large quantities (about 10-12 at. fract.),and
the radioactivity of the tritium results in a complete deterioration of chamber sensitivity. It was mandatory, there-
fore, to fill the chamber with specially purified deuterium in which the tritium concentration was kept below 5? 10-14
at. fract. Special experiments were set up to determine the effect associated with the robbing of p -mesons by the com-
plex nuclei of the ambient medium, i.e., the vapors of the chamber working fluid (oxygen, carbon). One contributor
to improved conditions for identifying events and enhancing chamber efficiency in revealing stopping of p -mesons
was the fact that the chamber was operated in a magnetic field of 7000-Oe intensity.
A diagram showing the layout of the apparatus at the exit of the meson beam from the synchrocyclotron is
shown in Fig. 1. Muons and pions of 260-MeWc momentum, generated by 680-MeV protons from the synchrocyclo-
tron, were employed in the experiments. Since p -mesons form mesic atoms and mesic molecules under conditions
where their speed is close to the speed of the orbital electrons belonging to the atoms, the p -mesons are slowed down
directly prior to their energy into the chamber in a filter installed near the chamber wall, to such a low speed that,
on entering the chamber, they are brought to rest in the gas filling the chamber. The filter thickness is made such
that the it -mesons present in the beam will be fully absorbed and fail to gain entry into the diffusion chamber.
Under usual operating conditions, one stoppage of a p -meson was observed in every three to five stereophoto-
graphic shots of the chamber sensitive volume. Two hundred thousand stereophotographic shots were taken. They
were processed with the aid of a projector and measuring microscope.
2. Scattering Cross Sections: pp- Mesoatoms on Protons
The multiplicity of processes brought about by p-mesons in a hydrogen?deuterium mixture may be illustrated
graphically by the layout presented in Fig. 2. The initial system (low deuterium concentration in the hydrogen) for
the subsequent processes was the pp -mesic atom existing in the 1S-state and moving at thermal speed. At all stages
along the chain of mesoatom transformations listed in the scheme, muon decay acted as a competing process: p
+ v + 0, proceeding at a rate X0 = 0.45 ? 106 sec-1 (denoted by the broken line).
One of the simplest processes occurring in hydrogen with the participation of pp -mesoatoms is scattering of the
latter on protons. This scattering may be either elastic or inelastic. The latter case results in a transition of the pp-
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Fig. 3. Formation of pp--mesoatoms in gaseous hydro-
gen. The slow p --meson formed, at the point where it was
brought to rest, a pp -mesic atom, which traversed by dif-
fusion a path of about 1 mm (the gap from the end of the p- -
meson track and the beginning of the electron track). At
the end of the diffusion path, the If -meson jumped from
the proton to a complex impurity atom, and decayed. A
"point" (Auger electron) is clearly visible at the start of
the decay-electron track.
mesic atom from the energetically higher triplet state to the singlet state.* The spin realignment, according to
S. S. Gershtein's calculations [15], is necessarily a rapid process proceeding to completion in 5 ? 10-10 sec at the
density of liquid hydrogen. One of the consequences of this spin realignment must be the rapid depolarization of
muons which had been longitudinally polarized as a result of decay.
Experiments on the measurement of muon depolarization in liquid hydrogen, carried out with the synchrocy-
clotron in our laboratory [16], apparently serve to confirm this inference. We note that depolarization is determined,
in this experiments, on the basis of measurements of the asymmetry in the angular distribution of electrons from mu-
on decay, by the method of the precession of the spin in a magnetic field.
Another possible effect due to spin realignment should be, again as demonstrated theoretically by S. S. Gersh-
rein, the fact that the elastic scattering cross section for scattering on protons of mesic atoms in the singlet state
(o? p+) turn out roughly two orders of magnitude smaller than the?cross sections in the triplet state. This circum-
stance, in principle, opens the way for the solution of one of the most crucial and pressing problems outstanding in
the area of muon-proton interactions, that of determining from experiment the spin state of the pp-mesoatom from
which the capture of the ?-meson by the proton took place.
In order to study elastic scattering, we availed ourselves of the same principle which underlies the measurement
of the thermal neutron scattering cross section, namely measuring the diffusion length in hydrogen of the pp-meso-
atom over a finite time interval. Since the formation of mesic molecules may be neglected at low hydrogen densi-
ties, the diffusion time is determined principally in terms of the probability of free muon decay and the probability
of the muon jumping to complex nuclei. Since the pp-mesic atom fails to produce any ionizing effect in its motion,
the diffusion process of the pp-mesic atom must be observed, in diffusion chamber photographs, as a displacement of
the origin of the track of the decay electron relative to the end of the track of the stopped II-meson (as a discontinuity
or gap between the end of one track and the beginning of the other). Actually, in the course of the first experiment,
with the hydrogen pressure in the chamber placed at about 20 atm, such displacements were successfully observed
in dimensions of from the half-width of a ?-meson track (0.25 mm) to 1.5 mm. An example of this case is shown in
Fig. 3. Further experiments were carried out both at high hydrogen pressure (23 atm) and at low hydrogen pressure
(5 atm). The concentration of complex nuclei was varied in several experiments. It was found, however, that the
extent, and, consequently, also the frequency of appearance, of the visible displacements is mainly a function of the
hydrogen density. One clear illustration of this is the following fact. At a hydrogen pressure of 23 atm, of 320
(A ? e)-decays in 49 cases (i.e., in 15% of the cases) gaps whose dimensions exceeded 0.5 mm were observed, while
the number of such gaps amounted to 50% at 5 atm hydrogen pressure, even though the concentration of complex
nuclei in the second experiment was almost triple that in the first experiment. The elastic scattering cross section
for pp + p pp + p was found from the expression
, 1Z-)
6- ' (2)
' rz..V (X, t-2t.,C,)
where is the mean velocity of the relative motion of pp and H2 (V = 2,7 ? 105 cm/sec); r2 is the root mean square of
the gaps computed from the distribution of the number of events over the gap lengths; N is the number of protons per
cubic centimeter; X0 + )qGz is the sum of the rates of free muon decay and jumping to carbon and oxygen nuclei at
*The energy of the hyperfine structure triplet level in the pp-mesic atom, with total spin F = 1 is 0.2 eV higher than
the energy of the singlet state with F = 0. The reverse transition (from singlet to triplet) is impossible then, on account
of the low value of the energy of the mesoatom's motion compared to the energy difference in the F = 0 and F =1 levels.
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a concentration C, determined in subsequent experiments (cf. section 5). The expression (2) takes cognizance of the
fact that, in real hydrogen, scattering occurs not on free protons, but on H2 molecules. The value of the cross section
o
+ '
determined with the aid of expression (2) on the basis of experimental data for 12, X and Cz, was found to
a
be (1.741) ? 10-19 cm2. A comparison reveals that this value is roughly 20 times greater than that predicted by
p
theory for the value of the scattering cross section of mesic atoms in the singlet state, which is a ?pi Ern co
[17]. This fact greatly complicates the situation and offers no direct proof (as might be anticipated on the basis of
muon depolarization data for liquid hydrogen) of the existence of fast transitions of pp-mesoatoms from the F = 1
state to the F = 0 state. Two avenues are open in interpreting the large value of the (pp + p)-scattering cross section:
either the F = 1 ?> F = 0 transitions actually proceed at a slower pace and then scattering in the triplet state (which,
as noted above, is considerable) introduces its contribution to the globally measured cross section, or else the true
parameters of the mesomolecular potentials determining the principal characteristics of the processes occurring in
the pp + p system will differ from those assumed in the theoretical treatment. In our later discussion, with the aim
of achieving a correct grasp of the experimental facts and drawing a more definite conclusion on the true rapidity of
the transitions occurring in the pp-mesic atom between the hyperfine structure states (determining the spin state of
the pp-mescatom), we will have to make a detailed analysis, based on,a large volume of statistical data, of the dis-
tribution pattern over the lengths of the ranges (gaps) of pp-mesoatoms in order to explain the possible existence in
these mesic atoms of two components with large and small values of -r2 corresponding to scattering in the singlet and
triplet states, on the one hand; on the other hand, we will have to carry out a combined theoretical analysis of the
most fundamental processes pertaining to the pp + p system, such as scattering, depolarization of p-mesons, forma-
tion of ppp-mesic molecules, etc., and we will have to find the parameters of the p-mesomolecular potentials satis-
fying these processes. The investigations of this problem at the Dubna Joint Institute for Nuclear Research progressed
in both the directions outlined.
3. Probability of Jumping of a p-Meson from a Proton to a Deuteron, and
Formation of ppp-Mesomolecules
When a slight deuterium admixture is present in hydrogen, the diffusing pp-mesoatom may pass close by a
deuteron. Owing to the fact that the K-level of the dp-mesoatom is situated 135 eV below the K-level of the pp-
mesoatom, jumping of the )1-meson from the proton to the deuterium,
d 41+ p , (3)
is highly favored. The difference in the binding energies of the p-meson on the K-shells of the corresponding meso-
atoms in process (3) goes over into the kinetic energy of the relative motion of the nuclei exchanging the p-meson.
The probability of process (3) is proportional to the concentration of deuterium but, as shown by theory, even at a
deuterium concentration of roughly 1% in hydrogen, the probability of this process begins to dominate over all other
rivals in this system of processes. It is evident from Fig. 2 that the dp system is the initial system for the formation
of ddp- and pdp-mesic molecules in which nuclear fusion is later realized. It is therefore obvious that an experi-
mental determination of the absolute probability of process (3) (the rate value which we designate by the symbol X d)
is of first-ranking significance.
If we remember that, as a result of the transition (3), the dp-mesic atom acquires a relatively high energy
(about 45 eV) and may range over a path of roughly 1 mm in liquid hydrogen,*then the attempt to find the value of
X d from liquid-hydrogen experiments with very slight deuterium admixtures will appear to be not at all hopeless.
However, the path turns out to be a closed one. This is chiefly due to the fact that process (3) suffers competition in
liquid hydrogen by the relatively intense process of formation of ppp-mesic molecules:
in +11 (hydrogen atom)
PP11+ e- ?
(4)**
It is precisely the mutual superposition of these processes which thwarts a direct experimental determination, in liquid
hydrogen, of the absolute probability of process (3) from the number of observed events featuring such gaps. The use
of a diffusion chamber offers tremendous advantages in such experiments, since the lower density of hydrogen renders
*L. Alvarez et al. [5], in liquid hydrogen bubble chamber experiments involving slight natural impurities of deuterium
(1 deuteron per 10,000 hydrogen atoms), observed gaps of precisely this dimension.
**In process (4), the binding energy of mesic molecules (approximately 100 eV) is imparted to the electron of the
hydrogen atom as a result of an electric dipole transition. In the ppp system, the catalysis reaction is extremely im-
probable under ordinary conditions [12].
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Fig. 4. Formation of dp-mesoatoms in gaseous hydro-
gen with deuterium impurity. Large gaps (8 - 10 mm)
from the end of the p--meson track to the beginning
of the decay-electron track are due to the range of
the dp-mesoatom, formed as a result of the transition
pp + d -+ dp + p. A point (Auger electron) is seen at
the beginning of the decay-electron track, in case b,
the formation of ppp-molecules far less likely, and the
gaps of interest to us, due to the range of dp-mesic atoms,
acquire dimensions tens of times larger than the dimen-
sions of those due to diffusion of pp-mesic atoms. We set
up an experiment at 23 atm hydrogen pressure and the
optimum deuterium concentration of 0.44% arrived at in
special experiments. In that experiment, about 800 events
were found, of which about half were conventional (p ?e)-
decay events, and the remaining showed apparent gaps
stretching from the end of the track of the muon brought
to rest to the beginning of the electron track, reaching 17
mm.* Two examples of such events are shown in Fig. 4.
The observation of large-gap events has made it possible
to reliably determine the probability of a muon jumping
from a proton to a deuteron. Under the conditions prevail-
ing in our experiments, the value found wasX'd = (1.51.3)
? 106 sec-1. On this basis, we obtain the value X d
= (1.21:1) ? 1010 sec-1 * * for the probability of the transi-
tion (3) reduced to the density of liquid hydrogen, and the
deuterium concentration Cd = 1. This value is in excellent
accord with theoretical values computed and reported in
[18, 14], equal to 1.3 ? 1010 sec-1. It has already been
noted that the transition process pp + d dp + p is charac-
terized by the highest probability among all the meso-
atomic processes occurring in hydrogen and deuterium. Its
cross section, computed on the basis of the known value of
the rate X d, is ?d = (4.2 ? 1.2) ? 10-18 cm2 at the tempera-
ture of liquid hydrogen.
A knowledge of the absolute value of the rate X d,
which, as we have indicated, plays an important part in p -
catalytic phenomena, is particularly valuable for the pre-
cise reason that the road is opened up for the determina-
tion of another important quantity, the probability of forma-
tion of the mesic molecule ppp in liquid hydrogen. This
last probability is very important to have on hand in order
to determine the relative fraction of muons experiencing
nuclear capture by a proton [process (1)] from the mesomolecule state. Let Xppp, for purposes of determination,
consist in the use of the ratio (X0 +X ppp)/Xd, the value of which has been determined and reported in several papers
[5, 19, 20] in studying the yield of the dp + p He3p + y reaction in liquid hydrogen. According to these papers,the
most accurate measurements are those carried out most recently by L. Lederman's group [20], a value of (1.06 ? 0.11)
? 10-4. The value which we found for X d leads, under these conditions, to the Xppp value of (0.8.11) ? 106 sec-1. It
must be stressed that the values we determined for rates X d and Xppp were confirmed in that paper [20], where the
work was carried out with much the same precision and accuracy, but by use of a completely different procedure
(measurement of the time dependence of the y -quantum yield from the dp + p He3p + y reaction at different deu-
terium concentrations, and using electronic techniques). Both our data and the data reported in [20] are in perfectly
satisfactory agreement with the theoretical values of these process rates, as computed by Ya. B. Zel'dovich and S. S.
Gershtein.
Armed with these experimental data, we are now in a position to state that, at the density of liquid hydrogen,
*Under the prevailing experimental conditions, the pp -mesic atoms display ranges from 0.25 mm to a maximum of
1.5 mm (cf. section 2).
**This means that the p-meson Jumps from the proton to the deuteron in a time 1/X d ? 0,8 ? 10-10 sec under condi-
tions where the number of hydrogen nuclei and deuterium nuclei are equal, and Cd = 1.
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only about 30% of the p -mesons (35% according to our data, and 25% according to the data reported in [20]) decays,
or is captured from the pp-mesoatom orbit, while the remaining fraction is captured from the ppp-system.
4. p -Meson Catalysis of the Nuclear Reactions d + d and p + d
Because of the high probability of the p-meson jumping from a proton to a deuteron, almost all the p -mesons
succeed in making the transition to the deuterons even when the concentration of deuterium in the hydrogen is very
low. In the same manner, in turn, as pp-mesic atoms approaching close to hydrogen atoms form the mesic molecule
ppp, dp-mesic atoms, as a result of the same mechanism, may succeed in forming pdp-mesic molecules, and even
ddp-mesic molecules, when the deuterium concentration is high. In these systems the nuclei of the deuterium atoms
or deuterium and hydrogen atoms approach to a distance on the order of the mesoatomic radius (-10-11 cm), with the
result that the width of the Coulomb barrier narrows down to a width far smaller than that found in conventional mole-
cules, where the distance separating the nuclei of the atoms is ?10-8 cm, Since the tunneling coefficient of the par-
ticles is strongly dependent on the width of the Coulomb barrier, the nuclear fusion reaction takes place at an appre-
ciably high probability in mesic molecules. This is precisely the gist of the catalytic action of negative muons in
fusion reactions involving light nuclei, which usually take place only when high energies (e.g. in thermonuclear re-
actions) are imparted to the participating particles.
Catalysis of the d + d Reaction. As is evident from Fig. 2, the ddp-mesic molecule may participate in two
types of nuclear reactions. In reactions of the first type, the p-meson is either liberated or proves to be bound in a
neutral system with a proton or triton, and may bring about a nuclear reaction again sometime in the future. A typi-
cal feature of the reactions of the second type is the bond linking the ti-meson to the helium nucleus. This type of
mesic atom is no longer electrically neutral, and is incapable of approaching to within a close distance of other nu-
clei and surrendering its ti-meson, or of causing a new nuclear fusion reaction. The p-meson caught in the He3 orbit
will either decay or, as has been demonstrated in experiments on muon capture in pure He3 carried out in our labora-
tory by B. Pontecorvo, R. M. Sulyaev et al. [21], has a very low probability of being absorbed by the He3 nucleus (as
a result of weak interaction) with the formation of H3 and a neutrino.* The capture of muons, resulting in the formation
of p-mesic atoms'of helium, constitutes one of the principal hindrances to the realization of a sustained nuclear chain
reaction between hydrogen isotopes by means of p-meson catalysis. The most probable reactions in the ddp-mesic
molecule are, according to theory, the first two reactions, so that the p-meson proves to be free. The other three re-
actions account for 2% of the events.
Only the first reaction,
ddiA I-Is
(5)
has been studied to date in our experiments.
The principal task before us is the determination of the probability of formation of ddp-mesic molecules (the
reaction rate X ddp). An experiment was carried out at a deuterium pressure of about 16 atm. Of 10,000 stoppages
of p-mesons, 27 cases of the reaction (5) were recorded. This reaction was easily identified from the range of the
proton or triton and from the presence of a decay-electron at the point where the triton-proton particle emerges. A
typical photograph showing such an event is seen in Fig, 5. Since, according to theoretical estimates, the probability
of the nuclear reaction in the ddp-mesic molecule exceeds by several orders of magnitude the probability of muon
decay, the nuclear reaction will take place in all the ddp-mesic molecules formed. This is the set of circumstances
which enabled us to determine the rate X ddp of interest from the observed yield of reaction (5). In so doing, we al-
lowed for the fact that the probability of the reaction ddp n + p- is equal to the probability of reaction (5).
The rate Xdo so calculated, reduced to liquid-deuterium density, is found to be
), I 4) 10' sec
Add (0, 4 4 ?
There are no other experimental data currently available in the literature on the value of the rate Xddp ex-
cept for the estimate X ddp > 0,1 ? 106 sec-1 obtained from liquid-deuterium bubble-chamber experiments [22].
If we compare the value we found from experiment for thegobability of formation of ddp-mesic molecules
and the theoretically computed counterparts, then we find that X ddfi is approximately one order of magnitude greater
*According to experimental evidence [21], the probability of nuclear capture of the p -meson by the He3 nucleus is
(1.41 ? 0.14) ? 103 sec-1.
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Fig. 5. p--Catalyzed fusion of two deuterium nuclei.
When a dp-mesic atom collides with a deuteron, a
ddp-mesic molecule is formed, with an ensuing nu-
clear fusion reaction ddp --> T + p + p-. Almost all of
the energy of the reaction (-4 MeV) is carried off by
the tritium nucleus and the proton, flying off in op-
posite directions. Such a low energy is imparted to
the p--meson in the process (several kiloelectron-
volts, i.e., of the order of the binding energy of the
mesic atom) that the particle cannot travel any appre-
ciable distance from the point where the reaction took
place, and decays with the emission of a fast electron.
Fig. 6. Fusion reaction involving a proton and a deuter-
on; reaction catalyzed by a p--meson. After being
brought to rest, the p--meson formed the mesic atom
pp, and later a mesic atom dp. In the encounter be-
tween the dp-mesic atom and a proton, the pdp-mesic
molecule was formed, leading to the nuclear fusion re-
action pdp--.He3+ p-. 5.5-MeV energy were liberated
in the reaction; most of this energy (-5.3 MeV)was car-
ried off by the p--meson, so that the latter was re-
ejected. The gap stretching between the p--meson
tracks corresponds to the range of the neutral mesic
atom dp. The point at the start of the track traveled by
the eJectedp--meson is a track left by the He3 nucleus
which took a slight recoil (-0.2 MeV) in the reaction.
than Xth [12 14] It is worthwhile to point out, how-
ddp ?
ever, that the latter value was computed with no cog-
nizance taken of the existence in the ddp-mesic mole-
cule of a rotational level K = 1 and binding energy close
to zero [12]. It is possible that the presence of such a
level will result in resonance effects accompanying the
formation of the ddp-mesic molecules, as well as an in-
crease in the probability of the nuclear reaction in flight.
In future catalysis-reaction experiments in deuteri-
urn, the most interesting point to uncover will be whether
the rate of the reaction ddp He3 + n + p- actually dif-
fers little from the rate of reaction (5) which we studied,
as well as the determination of the sticking probability
of muons to helium nuclei.
Catalysis of the p + d Reaction. The catalysis of
(p + d)-reactions is, at the present time, a relatively
well-investigated process, when compared to the other
mesoatomic phenomena. It has been established [5, 23]
that two reactions proceeding in the mesic molecules
pdp are (cf. Fig. 2)
pdtt ? -1 [o" - (6)
and
pdix 1-te" .
(7)
The probability of a gamma quantum being emitted here
is approximately 15 times greater than the probability of
conversion of a p-meson. On being liberated in reaction
(7), the p-meson carries off 5.3-MeV energy, i.e., almost
all the energy of the reaction. The yield of nuclear re-
actions (6) and (7) is determined by the probabilities of
the processes; the probability Xpdp, of the formation of
the pdp-mesic molecule, and the probability of a nuclear
reaction occurring in that mesic molecule.
Since the probability of the mesic molecules form-
ing is proportional to the density of the hydrogen, while
the speed of the nuclear reaction in the mesic molecule
is independent of density, a comparison of the yields,
e.g., of reaction (7), at different hydrogen densities, af-
fords us an idea of the value of Xpdp. With this in mind,
we set up an experiment to determine the yield of reac-
tion (7) at a hydrogen pressure of about 20 atm under
conditions of almost complete saturation of process (3)
(Cd 5%). Of 12,000 muons stopped, only five eventsof
reaction (7) were detected, so identified by measuring
the momentum of the converted p-meson.
Figure 6 presents a photograph of one such event.
Results reported in [19], obtained in liquid-hydrogen bub-
ble-chamber experiments, were used to determine the
value of Xpdp, along with our own experimental data. It
was found that, at the density of liquid hydrogen,
(0, 5 _11(()): ) ? 10'1 sec -1.
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Recently, in experiments completed by two teams of American physicists {one of the teams [20] using a target
with liquid hydrogen and a slight admixture of deuterium measured the distribution in time of gamma photons from
reaction (6), while the other group [22] used a liquid-hydrogen bubble chamber with a high deuterium concentration
to determine the muon yield from reaction (7)}, values for the probability X pdp which differed by several times were
obtained, and were far in excess of the values we found. At the present time, it is difficult to account for such a con-
siderable discrepancy in the results. The problem calls for further study at several angles. There are grounds for sup-
posing that the reason lies in inaccurate interpretation of data directly obtained from experiments performed under
greatly disparate conditions. It may turn out that there exists some nontrivial density effect which has so far escaped
scrutiny, and which affects the determination of the probability of formation of pdp-mesic molecules in experiments
involving gaseous and liquid hydrogen and deuterium. On the other hand, an interpretation of the time distribution of
gamma photons from reaction (6), from which the authors of [20] determine the probability X pdp and the time of the
nuclear reaction in the pdp-mesic molecule, may prove to be ambiguous because of the existence of several nuclear
reaction times in various spin states of the mesic molecule [24].
We see, accordingly, that the protons and deuterons are bound by p-mesons into the mesic molecules ppp, pdp,
and ddp, with a probability comparable to the probability of muon decay. The relatively low probability of forma-
tion of mesic molecules, compared to the probability of process (3), is related to the mechanism, referred to above,
operating in the formation of the mesic molecules which has, as its result, the transmission of the excess energy to a
third particle, the atomic electron. In the transition process pp + d ?> dp + p, the energy is distributed between the
heavy particles, and the rate of this transition is therefore four orders of magnitude [-1/a2 ? (137)2] greater.
It must be noted that, in tritium-enriched hydrogen and deuterium, we may encounter formation of the mesic
molecules pTp, dTp, and TTp, and catalysis of the corresponding nuclear fusion reactions by the mesic molecules
formed. These processes are imperfectly studied at the present time, with meager experimental information available.
5. Jumping of Muons from Protons and Deuterons to Complex Nuclei
Probability of the Transitions X? and X SI. If nuclei of charge greater than two are present in hydrogen, then the
effective process at work will be the irreversible transition of muons from the hydrogen or deuterium orbit to the meso-
atomic orbits of these nuclei. Since there is always some oxygen and carbon impurity present in the hydrogen and
deuterium used in diffusion-chamber experiments, in proportions of approximately one impurity atom per 500 hydro-
gen atoms, we must have some knowledge of the probability of a muon jumping to the nuclei mentioned. This value
was determined for each experiment by comparing the number of stars produced by nuclear capture of a muon by oxy-
gen and carbon in the particular experiment to the number of such muon-produced stars in a specially setup experi-
ment where the transition of muons to those nuclei was close to 100%. The experiments showed that the probabilities
of muon transition from protons or deuterons to carbon nuclei or oxygen nuclei are relatively large. We found that,
within the limits of experimental error, these probabilities are the same for the nuclei of both elements, in the neigh-
borhood of 1.5 ? 1010 sec-1, i.e., X? ' 1.5 ? 1010 sec-1. If we take into account the results of recently completed
experiments on the observation of jumping of muons from protons and deuterons to Ne20 nuclei, with the resulting rate
XNe 1010 sec-1, it will apparently become possible to draw an inference of even more sweeping generality, viz.,
that the probabilities of muons jumping from hydrogen to light nuclei vary, but not drastically, from nucleus to nu-
cleus. Experimental X, values are found to be in satisfactory accord with theoretical data [25].
Auger Electrons. A theoretical paper has shown [25] that the high probability of a muon jumping from a proton
to nuclei of Z > 2 is due to the intersection of mesomolecular terms in the pZp system.* A detailed discussion of the
term diagram shows that the muon jumps most commonly to the mesoatomic levels of the carbon and oxygen nuclei
with principal quantum numbers n = 4 and n = 5, respectively. The upshot is that succeeding cascade transitions of
the mesic atoms to the ground state, at a transition rate close to 100%, must be accompanied by the escape of one or
several Auger electrons carrying away several kiloelectron-volts energy.
Our experiments support this theoretical inference, and are in agreement with the proposed transition mecha-
nism. Actually, in experiments using "pure" hydrogen, as well as in experiments using hydrogen with some deuterium
impurity, in about 60% of the (p ? e)-decay events where the starting point of the decay-electron track is separated
by a gap from the end of the muon track, a rather conspicuous "point," i.e., a clustering of droplets 0.3 to 0.6 mm
This mechanism accounts, in particular, for the low value of the experimentally observed cross section for Jumping
of muons to helium nuclei [26, 19]; there is no intersection of terms in helium mesic atoms.
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across, is observable at the start of the electron track (cf. Fig. 3, Fig. 4b). These are the tracks of the low-energy
Auger electrons. The frequency with which they appear and their associated energy (an idea of which may be de-
rived from the size of the tracks left behind) correspond to the values anticipated theoretically.
It is worthy of note that another explanation for these points, interpreting them as tracks of protons obtained in
the jumping of muons directly from hydrogen to the 1S state of the oxygen [or carbon mesic atom and carrying off
the entire energy associated with the transition (pi + 0 Ou + p)] has not been substantiated. Two reasons are ad-
vanced in explanation; first, theoretical estimates predict a very low rate for the transition of a u-meson directly in-
to the is state of the mesic atom of a complex nuclei nucleus; secondly, in the transition these protons would receive
an energy of about 100 keV, and would leave tracks of length about 1,5 mm under a chamber pressure of 5 atm. We
did observe points whose maximum dimensions fail to exceed 0.5 to 0.6 mm.
Summary
While the problem of hydrogen p-mesic atoms was first probed into theoretically as far back as about 15 years
ago, the intensification of experimental research on this topic does not date back past the recent half-decade, for
practical purposes. At the same time, we find this to be one of the most vigorously developing new fields in muon
physics in the recent period. One brilliant piece of evidence in support of this view is, for instance, the fact that
while only two or three experimental papers, including the well-known paper by L. Alvarez and colleagues reporting
the detection of ti-catalysis, were available in the literature at the start of our experiments on hydrogen mesic atoms
at the Dubna synchrocyclotron facilities, at the present time research on various aspects of this very problem is under
way at virtually all the large synchrocyclotrons throughout the world. It may be seen that, as a result of those experi-
ments performed at Dubna, the principal characteristics of the most important mesoatomic processes occurring in hy-
drogen and deuterium have been determined quantitatively; a number of phenomena are being studied first (e.g.,
scattering of pu-mesoatoms on protons). The values found for the probabilities of a ti-meson jumping to deuterium,
of formation of the mesic molecule ppu, and jumping to complex nuclei, are in excellent accord with calculations,
and provide confirmation of the correctness of the mechanisms invoked in theoretical treatments to explain the proc-
esses. Disagreement has cropped up in some instances between empirical results and data derived from theoretical
analysis (the larger experimental value of A. ddp), and the results of measurements performed in different laboratories
have been at variance in some cases. This is entirely to be expected in the study of new phenomena. However,there
is every reason for assuming that the further development of experiment and theory will make it possible to overcome
these difficulties, to probe still deeper into the secrets of the world of mesic atoms, and to reveal new characteristic
properties and regularities in this peculiar state of matter.
LITERATURE CITED
1. G. Charpak et al., Phys. Lett., 1, 16 (1962).
2. A. Citron et al., Phys. Lett., 1, 175 (1962).
3. Ya.B.Zel'dovich, DAN SSSR, 95, 493 (1954); Ya. B. Zel'dovich and A. D. Sakharov, ZhETF, 32, 947 (1957),
4. F. Frank, Nature, 160, 525 (1947).
5. L. Alvarez et al., Phys. Rev., 105 , 1127 (1957).
6. Ya. B. Zel'dovich and S. S. Gershtein, ZhETF., 35, 821 (1958).
7. H. Primakoff, Rev. Mod. Phys., 31, 802 (1959).
8. S. Weinberg, Phys. Rev. Lett_ 4, 575 (1960),
9, L. B. Egorov, A. E. Ignatenko, and D. Chultem, ZlifTF., 37, 1517 (1959).
10. V. P. Dzhelepov et al., ZhETF., 42, 439 (1962).
11, V. P. Gelepov et al., Intern. Conf. on High-Energy Physics, Geneva (CERN, 1962), p. 484.
12. Ya. B. Zel'dovich and S. S. Gershtein, Uspekhi fiz. nauk, '71, 581 (1960).
13. L. Wolfenstein, Proc. 1960 Ann. Intern. Conf. on High-Energy Physics, Rochester (Publ. Univ. Rochester, 1960)
p. 529.
14. S. Cohen, D. Judd, and R. Riddell, Phys. Rev., 119, 397 (1960).
15. S. S. Gershtein, ZhETF., 34, 463 (1958).
16. A. E. Ignatenko et al., ZhETF., 35, 894 (1958),
17. S. S. Gershtein, ZlifTF., 36, 1309 (1959).
18. V. B. Belyaev et al., ZhETF., 37, 1652 (1959).
19, M. Shiff, Nuovo Cimento, 22, 66 (1961).
20. E. Bleser et al., Phys. Rev. Lett., 8, 128 (1962).
21. I. Falomkin et al., Phys. Lett., 1, 318 (1962).
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22.
J. Fetkoyich et al., Phys. Rev. Lett., 4, 570,(1960).
23.
A. Ashmore et al., Proc. Phys. Soc., 71,
161
(1958).
24.
S. S. Gershtein, ZhETF., 40, 698 (1961).
25.
S. S. Gershtein, ZhETF., 43, 706 (1962).
,
26.
0. A. Zaimidoroga et al., ZhETF., 41, 1804 (1961).
32
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to.
cover English translations appears at the back of this issue.
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LONGITUDINALLY POLARIZED PROTON BEAM
IN THE SIX-METER SYNCHROCYCLOTRON
M. G. Meshcheryakov, Yu. P. Kumekin, S. B. Nurushev,
and G. D. Stoletov
Translated from Atomnaya fnergiya, Vol. 14, No. 1,
pp. 38-40, January, 1963
Original article submitted October 16, 1962
Quantitative investigations of the spin dependence of the nuclear interaction at high energies are connected
with the performance of experiments on the scattering of protons on protons and neutrons in high-power accelerators.
The data thus obtained can be complete only if longitudinally polarized proton beams are used in experiments along
with unpolarized and transversely polarized beams [1].
The program of complete experiments on the scattering of protons on protons, which is carried out by means of
the six-meter synchrocyclotron of the Joint Institute of Nuclear Studies, includes experiments with the use of longi-
tudinally polarized proton beams. The present article describes an experiment where a longitudinally polarized beam
of protons with an energy of 612 MeV was obtained, and it also provides an analysis of its characteristic. The outline
of the experiment was proposed by S. B. Nurushev in 1959 [2]. In contrast to the well-known methods for producing
longitudinally polarized proton beams at lower energies [3,4], the polarizing scattering in our experiment took place
in the vertical plane outside the synchrocyclotron chamber. This made it possible to obtain a longitudinally polarized
beam in the horizontal plane, while the polarization vector could be directed parallel as well as antiparallel to the
proton pulse in the beam.
The experimental layout is shown in the figure. The unpolarized proton beam that was brought out of cham-
ber 1 of the synchrocyclotron was deflected upward at the angle zp = 2?. The magnetic field's horizontal component
that was necessary for this deflection was provided at the beginning of the extracted beam's channel in the region of
the accelerator's scattered magnetic field by means of special magnetic adapters 2. A detailed calculation of the
dimensions of the adapters and the determination of their optimum position relative to the synchrocyclotron magnet
are given in [2]. After collimation (collimator 3) and focusing by means of quadrupole lenses 4, the slightly upward
deflected primary beam entered the horizontal magnetic field of magnet 5, where the beam was deflected downward
through an angle of 8? in the vertical plane. The graphite diffuser 6, which served as the polarizer, was mounted at
the place where the beam intersected the median plane of the accelerator. The collimator 8 separated protons which
were scattered at the angle 0 = 6?, whose trajectories were in the horizontal plane. The scattering angle could be
changed by varying the deflection angles of the primary beam, which made it possible to regulate the degree of po-
larization of the secondary beam. The 0 = 6? value corresponds to the maximum of the product ?da(0)131(0), where
do dui
(A) is the differential cross section of the elastic scattering of protons on carbon nuclei, while P1(0) is the polariza-
tion in this process [5]. Thus, the optimum conditions for the performance of experiments on triple proton scattering
were secured.
Secondary protons whose polarization vector had the direction of the normal to the scattering plane entered the
vertical magnetic field of magnet 9 after leaving collimator 8. In order to intensity the magnetic field, magnet 9
was provided with additional adapters, which also secured partial focusing of the beam. Due to the presence of the
anomalous magnetic moment in the protons, the proton spin will precess in such a magnetic field with a velocity dif-
ferent from the velocity of changes in the direction of the proton pulse vector. In this, the precession angle x rela-
tive to the direction of the pulse vector is related to the beam's deflection angle co in the magnetic field by the ex-
pression
Ilp- ,
(13,
0-02
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Experimental layout for producing longitudinally polarized beams of protons with an energy of 612
? 9 MeV. a) Plan view; b) side view.
where pp is the proton magnetic moment in nuclear magnetons, and B is the proton velocity in units of the velocity
of light.
As a result of precession, there appears the longitudinal polarization component Piong = P1 sin x. For x = 90?,
the beam will have only the longitudinal polarization component. The given relationships make it possible to choose
such a deflection angle co as to obtain a completely longitudinally polarized beam for an initial energy of the primary
beam ri equal to 660 MeV.
The longitudinally polarized beam obtained as a result of deflection through the angle (p = 300 was focused by
means of quadrupole lenses 10 and was directed to the recording devices 16 and 17 through collimator 12. Ionization
chambers 7 and 13 served as monitors of the primary unpolarized beam and of the longitudinally polarized beam. For
the geometry shown in the figure, the polarization vector of the obtained beam was directed in opposition to the pro-
ton pulse. If the angle of primary deflection is made to be 0 = ?2?, and the unpolarized beam is then deflected up-
ward through an angle of 80 in magnet 5, the direction of longitudinal polarization will be reversed. In practice,
such an operation can be completed in 15-20 min. The flux density secured in the beam was equal to 2 ? 106 protons
per cm2 ? sec.
The energy of the longitudinally polarized beam was determined by measuring the proton ranges in copper (de-
vices 14 and 15); it was equal to Eiong = 612 ? 9 MeV. This value is in agreement with the primary-beam energy
E0 = 663 ? 7 MeV, which was measured by using the same method and allowing for the energy loss in the carbon po-
larizer, which had a thickness of 23 g/cm2. The energy Eiong = 612 ? 9 MeV, and the deflection angle eP = 30?, cor-
respond to the precession angle x = 89 ? 2.5?. In this, the degree Piong of longitudinal polarization is virtually equal
to the degree P1 of polarization that occurs in the scattering of the primary beam in polarizer 6. The .P1 value was
measured in a separate experiment, where the primary deviation of the beam and the scattering in polarizer 6 were
effected in the horizontal plane, while all the other geometric conditions remained unchanged. The value P1 = 0.43
? 0.03 which we obtained was in agreement with data from [5].
By analyzing secondary p + p-scattering by means of polarimeters 16 and 17, which consisted of polyethylene
diffusers and combined scintillation counters, it was found that the vertical and horizontal transverse polarization
components were absent in the longitudinally polarized beam. This was indicated by the fact that, within the limits
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of the measurement accuracy, which was ?0.02 with respect to absolute magnitude, no asymmetry in the distribu-
tion of protons repeatedly scattered at an angle of 21? was observed either in tile horizontal or in the vertical planes.
The determination of the spatial position of the trajectories of the primary and secondary beams, and the
choice of the best focusing conditions were performed with respect to self-recordings of transverse beam cross sections
along the entire channel and by measuring the beam intensities. At the location of polarizer 6, the beam cross sec-
tion had a circular shape with a diameter of 30 mm.
The density distribution of the proton flux in the longitudinally polarized beam between polarimeters 16 and
17 was investigated by means of a special device, which consisted of two scintillation counters and an EPP-09 auto-
matic electronic potentiometer. The scintillators had the shape of small cylinders with a diameter of 3 mm and a
length of 50 mm, and they were placed vertically and horizontally in the plane perpendicular to the direction of the
beam. The counters could be moved, one in the horizontal direction, and the other in the vertical direction. The
photomultiplier current for each counter was recorded on the strip chart of the EPP-09 potentiometer in dependence
on the counter position with respect to the beam axis. The horizontal and vertical scales were printed simultaneous-
ly. The curves thus obtained indicated that no significant asymmetry in the density distribution of protons in the
beam was present.
It should be noted that, simultaneously with the longitudinally polarized proton beam, the polarized beam of
neutrons which were generated as a result of the exchange interaction of protons in the carbon polarizer emerged
from the adjacent collimator 11. For neutrons emitted with an energy of 610 MeV, the precession angle xn in the
magnetic field of magnet 9 was approximately 950.
The authors hereby extend their thanks to L. P. Moskaleva for her help in measuring the intensity of the longi-
tudinally polarized proton beam.
LITERATURE CITED
1. L. Wolfenstein, Phys. Rev., 96, 1654 (1954).
2. S. B. Nurushev et al., OIYaI reprint, R-278 (1959).
3. J. Simons, Phys. Rev., 104, 416 (1956),
4, A. England et al., Phys. Rev., 124, 561 (1961).
5; L. S. Azhgirei and Huang Tieh-ch'iang, ZhgTF., 44, No. 1 (1963).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of this issue.
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ON THE THEORY OF ROTATIONAL SPECTRA*
A. Bohr, Institute for Theoretical Physics, University of Copenhagen, Copenhagen, Denmark
and B. R. Mottelson, NORDITA, Copenhagen, Denmark
Translated from Atomnaya gnergiya, Vol. 14, No. 1,
pp. 41-44, January, 1963
Original article submitted September 13, 1962
It is a great pleasure to contribute to this issue of "Atomic Energy" commemorating the scientific achievements
of the late Igor Vasilievitch Kurchatov. We would also like to take the opportunity to pay a special tribute to Acad-
emician Kurchatov's contributions to international scientific cooperation, which have meant so much for the fruitful
collaboration between members of our Institutes and physicists of the Institute for Atomic Energy in Moscow.
In the course of the last few years, a large body of empirical data on nuclear rotational spectra has been ac-
cumulated, as a result of great ingenuity and refinement in the experimental techniques.**
The rotational description implies, aS a first approximation, a number of simple relations between the states
in a given rotational band. Thus the energies vary as 1(1 + 1) (for K 1/2), and the transition intensities are propor-
tional to the square of a vector addition coefficient.***It is found that these relations are usually rather well satisfied,
often with an accuracy of the order of one percent.
The great accuracy of the experimental data, moreover, has permitted a quantitative study of the deviations
from the simple rotational rules, in a number of cases. For the interpretation of these data, one needs a systematic
scheme for enumerating the various correction terms implied by the rotational description. Such a scheme may be
based on a series expansion of the different matrix elements, as powers of the total angular momentum. The simple
rotational rules appear as the leading order terms in such an expansion. In the regions where the rotational descrip-
tion is most applicable, the series converges rapidly, and thus one obtains an accurate description in terms of a few
parameters. These parameters depend on the detailed structure of the rotating systems, but it is often possible on the
basis of simple models to estimate their relative orders of magnitude.
The details of the derivations and the more systematic enumeration of terms will be discussed in a forthcoming
publication; in the present note we shall confine ourselves to a few examples that seem to be of particular interest
in the analysis of the present data.
I. Energy Terms
The rotational energy may be considered a function of the components h. 12, and 13 of the angular momentum
in the intrinsic coordinate system. (The nuclear symmetry axis is the intrinsic 3-axis.) For a band with K = 0, the
axial symmetry implies that the energy must be a function of I + I and thus has the form
AI (1+1) H- B12 (I+1)2 C 13 (I?1)3; (1)
The publishers wish to express their appreciation to the authors for supplying a copy of their original manuscript.
**See, for example, the compilations by B. S. Djelepow and L. K. Peker, Decay Schemes of Radioactive Nuclei, Mos-
cow 1958; Nuclear Data Sheets, K. Way et al. Editors, Washington, D. C., and the analyses by B. R. Mottelson anc S.
G. Nilsson, Mat. Fys. Skr. Dan. Vid. Selsk. 1, No. 8 (1959), and by C. J. Gallagher, Jr., and V. G. Soloviev, Mat. Fys.
Skr. Dan. Vid. Selsk. 2, No. 2 (1962).
***We are here restricting ourselves to the case of nuclei with approximate axial symmetry. The effect of small
departures from axial symmetry in the nuclear shape is included in the higher order terms considered below. For a
nucleus with major deviations from axial symmetry, the power series considered here would converge poorly. One
should then develop an expansion based upon the appropriate rotational model.
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The empirical data have been found to fit this formula with good accuracy. The coefficient B is typically of order
-10-3 A, and C -3 X 10-6A.
For K * 0, one obtains, in addition to (1), terms resulting from the fact that the nuclear wave function is a sym-
metric combination of terms with Is = K. (The additional terms which are associated with a coupling between the
two parts of the wave functions may be thought of as resulting from fluctuations away from axial symmetry in the in-
trinsic structure.)
For the first few values of K, these terms have the form
+-
E' ( 1) 2 (i+-2) X [A1-1-]31/(/-1- 1)+ ...];
n=72
E'lc=1= (-1)141 I (I .4- 1) x B21 (I 1) .];
E'
K
3
) (/ +12_' (i -H
[B?H- Cy (I .1;
? (-1) (I ? 1) (1+2) x[1344- C 41- (I + 1) + .1.
The parameters are labelled by the index 2K, since they arise from operators proportional to (II + iI2)2K, which cou-
ple the K and -K components of the state.
The leading terms in E' for K = 1/2 is the familiar "decoupling term", and usually A1 is of order A in (1). Sim-
ilarly, one expects B1 -B3 B. Although A2 appears as a coefficient of a second-order term in I, it is expected usual-
ly to be much smaller than A, as follows from a consideration of simple models, such as two particles coupled to an
axially symmetric rotor. Such models suggest that, apart from special situations involving degeneracies in the intrin-
sic motion, a more reasonable estimate is A2 ^, B. Similarly, one may expect in most cases B2 B4
While the expansion in I is expected to be valid for not too high values of I, there may occur, for large I, modi-
fications in the intrinsic structure which cannot be expressed by such a simple power series in I. An example is pro-
vided by the expected breakdown of the pairing correlation at the critical angular momentum
In situations where two near lying bands are strongly coupled, the usual expansion may not be appropriate. It
is then necessary to treat this particular coupling explicitly, while all other perturbations may be included in the
usual expansion of the various operators.****
E2 -Intensity Rules
For transition matrix elements, one can proceed in a similar manner as for the energy, taking due account of
the tensorial character of the operator. The most systematic evidence is available on E2 intensity rules.
E2-transitions within a band are expected to be rather accurately described by the leading order term [B(E2;
I1K I2K) < I K 20112K >2) which is obtained from the I-independent transition operator. The coupling between
rotational and intrinsic motion implies, as for the energy, I-dependent terms in the transition moment, but their effect
is relatively small, due to the collective character of the leading term. Usually, the leading order intensity rule is
therefore expected to be accurate to about a percent or better, The best available experiments have an accuracy of
5 - 10 percent, and so far no definite evidence for departure from the leading order intensity rule has been estab-
lished." ***
*We are indebted to 0. B. Nielsen for making available to us the results of his analysis of rotational energies in even-
even nuclei, to appear shortly.
**The existence of a term of the type B3 has recently been identified in the Coulomb excitation of Tb162 (A = 11.61
keV, B = -5.8 eV, B3 = 8.0 eV. (Diamond, Elbek, Stephens and Perlman, to be published).
?**B. R. Mottelson and J. Valatin, Phys. Rev. Letters 5, 511 (1960).
****For an example of this situation, see the spectrum of W183, discussed by A. Kerman, Mat. Fys. Medd. Dan. Vid.
Selsk. 30, No. 15 (1956).
* * * **Estimates of the expected correction terms to the intensity rules have also been made by P. Hemmer (private
communication. See M. C. Olesen and B. Elbek, Nucl. Phys. 15, 134 (1960), and B. Elbek (to appear).
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For K = 1/2 and K = 1, additional I-independent terms may occur, which couple the + K components in the
wave function. Thus, for K = 1/2, we obtain
ii (E2; 11K = )2- =
= 1165n Q0(11:- 201 /2 > qi( ?.1)1-1442(11? 41.2- 21 / 2 -2;1 > 2,
(3)
where Q0 is the usual intrinsic quadrupole moment, and qi (which is related to the wave function of the last odd par-
ticle) is of single-particle magnitude. Thus, the correction term in (3) may amount to as much as 10 percent. For
K = 1, the corresponding correction term is expected in most cases to be appreciably smaller.
E2-transitions between bands may be much more sensitive to higher order terms, partly because the leading
terms are smaller, and partly because certain of the admixed terms are proportional to the large collective matrix
element, Q0. We shall not attempt to enumerate all the correction terms, but confine ourselves to the leading order
terms involving Q. These may be regarded as resulting from a coupling of the two bands considered.
For A K = 1 (excluding K = 1/24--,K = 3/2), the leading order collective admixture gives rise to corrections
which have the same I-dependence as those obtained from an I-independent operator, and thus simply amount to a
renormalization of the intrinsic matrix element. In the case of K = 1/24- K = 3/2),a special term arises (associated
with the AK = 2 combination (K =- 1/24- = 3/2)), and one obtains
13 (E2;
?
1 1 .,K = ?) = [21/, ( -
9 - 2
3 \
1-.21. I /2 (M2 110 ( --I
involving the three intrinsic matrix elements M1, M2, and 02.
For AK = 2, the generalized intensity rule has the form
\
?/ ?
2 - 2/
1221 3 12
B (E2; J1K ?> 19K + 2) = [(11 12-F- 31) (11K22 I /2K -h 2)
H- 1)1 (11K 121 I [K H- 2)12.
For transitions between two different bands with the same K, the leading term containing the collective matrix ele-
ment, Q0, is of second order in I, as for AK = 2. To this approximation one obtains
(4)
(5)
B (E2; I I,K) = (I1K201 /2102,x {M0-- itro [I1 ( [1+ 1) ?12(12 + 1)])2-
(6)
(For K = 1/2--.1/2 and K = 14- -* 1, additional terms are present).*
The most systematically studied E2 intensities for transitions between bands are those between the ground-state
band in even-even nuclei (K = 0+) and the systematically occurring K =2+ bands (y--vibrations).. It is found that the
1
M2 term in (5) makes a significant correction to the observed intensities, typically of order 20 percent for the lowest
values of I. (Such an effect is produced by A -0.03 M2). The corrected intensity rule (5) is found to account for the
available experimental measurements on these intensities.**
*Correction terms of the type MI in (6) have also been considered by Z. Bochnacki (private communication).
* *0. B. Nielsen, Rutherford Jubilee Intern. Conf., 1961 (London, 1962).
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III. K-Forbidden Transitions
It is a characteristic feature of the intensity rules obtained from I-independent operators that the matrix ele-
ment vanishes for AK greater than the multipolarity X. Such K-forbidden transitions are indeed observed to be sig-
nificantly retarded (compared to "allowed" transitions) typically by a factor of 102 for each order of K-forbiddenness.
For the K-forbidden transitions, one may, however, write down the power series expansion in I in the same man-
ner as for the allowed transitions. The principal difference is that the leading order term already involves an I-de-
pendent transition operator, proportional to (II + i AK- X? To this order, the intensity rules take the form
B(?; I ----> I 21( ? AK) = M2AK (11K + AK - k;(I j-K)! (Ii+K+AK?k)!
?al I 21C AK)2 X (7)
The accuracy of (7) is expected to be governed by the same considerations as apply to the usual "allowed" transitions
discussed above. Thus, in cases where higher order terms involve relatively large intrinsic matrix elements, one may
expect a significant improvement by employing generalized intensity rules, similar to those discussed above for the
E2 case.*
In any discussion of intensity rules, it must be borne in mind that when the leading order intrinsic matrix ele-
ment is very small, the transition strength may be sensitive to small admixtures in the wave function and, therefore,
the power series expansion in I may appear to converge poorly. This seems to be the case for many of the low-energy
El transitions in odd-A nuclei, which are observed to be hindered by factors of the order of 103 x 106 comparedto
single-particle estimates; for these the leading order intensity rules are often found to fail by a large factor. The ap-
propriate intensity rule would depend on the mechanism responsible for the observed El-transition moment. So far,
there appears to be no adequate analysis of these effects.
The I-dependent terms in the energy and transition moments may be regarded as a result of the Coriolis force
acting on the intrinsic motion. The procedure outlined above provides a systematic enumeration of the various terms
which may occur to any given order in I. Such a description is phenomenological in the sense that the coefficient of
each term is left as an adjustable parameter. These coefficients may in turn be calculated from a knowledge of the
intrinsic nuclear structure. Thus, the I-independent terms may be obtained directly from the intrinsic states in a
static nuclear field; the higher order effects result from the rotation of the field and can be obtained in a manner
analogous to the estimate of the moment of inertia on the basis of the cranking model.
Part of this work was carried out during a visit to the California Institute of Technology, Pasadena, California.
We wish to thank members of the Physics Department for their generous hospitality.
*Recently, the M1 transitions from the K = 7/2+ band to the K =1/2+ band in Tm163have been found to have relative
intensities in agreement with (7) to within 155. (Private communication from P. Alexander and F. Boehm).
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ON DELAYED PROTONS
N. A. Vlasov
Translated from Atomnaya gnergiya, Vol. 14, No. 1,
pp. 45-47, January, 1963
Original article submitted September 27, 1962
It is known that there are radiators of delayed neutrons among the isotopes of light nuclei (Li9, N17, C16) and
fission fragments with excess neutrons. The emission of neutrons occurs after the 13-decay into excited levels with
the energy E* > Bn (Bn is the neutron binding energy in the final nucleus) and is, consequently, possible under the
condition that the decay energy E8 is greater than Bn.
Among the isotopes with excess protons, there may be such where the 8+-decay energy exceeds the proton
binding energy Bp in the final nucleus. In the decompositon of these nuclei into excited levels, delayed neutrons,
which until now have not been observed [1], may be emitted.
The possibility of producing and observing delayed neutrons
is indicated and estimated in the present communication.
Possible Radiators of Delayed Protons that are
Produced in the (He3, 2n) Reaction
Target
Product
Reaction
energy,
MeV
E 8 ,
MeV
Bp , period,
Mel/ isec
C,12
013
-16
17,1
1,94
0,01
016
Ne17
-22,3
13,4
0,60
0,05
Ne2o
Mg2I
-18,9
12,0
2,45
0,3
Nig24
Si25
-18,9
11,6
2,29
0,4
si2s
S23
-19,5
12,4
2,72
0,4
S32-
Ar33
-16,5
10,8
2,28
0,7
Ar"
Ca37
-13,5
11,2
1,86
-
Ca40
Ti47
-15,5
11,6
1,60
0,4
On the basis of the tables of nuclear masses which
were calculated by using semiempirical equations, for in-
stance in [2], one can indicate the regions containing pos-
sible radiators of delayed nucleons on an N(Z) diagram (N
is the number of neutrons, and Z is the number of .protons).
Such a diagram for light nuclei with even Z values from
10 to 30 is given in Fig. 1. The Ej3 > Bn > 0 band corre-
sponds to possible radiators of delayed neutrons and contains
7-15 isotopes for each element, while the E13 > Bp > 0
band corresponds to possible radiators of delayed protons
and contains four to six isotopes of each element. It is ob-
vious that, besides the known radiators of delayed neutrons,
it is possible that there are many radiators which have not yet been detected. Generally speaking, their production is
difficult due to the fact that neutrons are more readily emitted than protons in nuclear reactions. Thus, the latest of
the detected radiators of delayed neutrons, C16, was obtained [3] in the C14(t,p)C16 reaction, where both initial nuclei
are radioactive. It is simpler to produce nuclei with excess protons.
The probability that a proton will be emitted by an excited nucleus due to the Coulomb barrier is lower than the
probability that a rreutron with the same energy will be emitted. If the neutron width rn exceeds the radiation width
ry even when AE0 = E* - Bn > 50 keV, the condition rp > ry will be satisfied for considerably greater energy mar-
gins AEp = E* - B. Thus, for a copper nucleus, AEp 3 MeV, while AEp 7 MeV for a tin nucleus [4]. This is the
reason why the detection of delayed-proton radiators among the isotopes of heavy and even medium elements is not
very probable. However, the detection of such radiators among the isotopes of light elements is highly probable.
One of the simplest methods for producing nuclei with excess protons is the bombardment of certain targetswith
He3 nuclei, which are at the present time accelerated in some cyclotrons. The table lists the possible radiators of de-
layed protons that can be obtained in the (He3, 2n) reaction. The characteristics of the reactions and of the nuclei
were borrowed from [2, 5, 6].
For all the nuclear products enumerated in the table, Eis > 10 MeV, while the proton binding energy in the nu-
cleus formed after ,3 -decay is Bp Bp is suf-
ficiently high. The probability P(Bp) of the emission of a delayed proton can be estimated by means of the equation
which G. R. Kipin [7] used for estimating the probability of the emission of delayed neutrons:
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6'0
50
40
20
20
10
_
,
IN
....,,,
4.
P
,
,
6
1
er 7,
5n
OK
illilo
5
,--ob-
In.
10 12 14 18 18 20 22 24 26' 28 30 Z
Fig. 1. Regions which possibly contain radiators
of delayed nucleons in an N(Z) diagram for even
elements of light nuclei.
N8
...
r
ii.

6RIUIII
7
5

4,
ii
3
2
pt
illl.
8 P
I
It*
\MI
10
17
1 2 3
zi 5 6' 7 8
9
0,
0.
0,
0,
0
0,
0,
Li
0.
8
Fig. 2. Probability of the emission of a delayed
proton for the decay energy E3 = 11 MeV in de-
pendence on the effective binding energy B for
two values of the constant a in the level density
distribution. The arrows correspond to the
Ti -> Sc4I decay.
1,
(1) (E) (E) d E
I
P (B)
EI3
(1.) (E) Q (E) (-1 E
Here, (1.(E) is the dependence of the probability of 13-decay on
the energy, which can be given as = (E8 - E)5, and p(E)
=const e2VT? is the density of levels of the final nucleus
[8]. The width ratio r (under the conditions considered
Fp +]3,
here, Fn = 0) changes rather sharply with energy and, therefore,
it can be assumed that
FP = U for .E < B;,= Bp+ AE.:
P r V
r P ? 1 for E> B;?
p_
i.e., P(B) can be estimated by using not the physical magnitude
of the binding energy Bp, but a certain effective value Bi) that
exceeds Bp by AEp, which corresponds to the equality of widths
r = FY Then, the probability of decay to a level with the
P
energy E > B can be calculated by using the equation
Et3
(E.ti?E) e2 d E
P (B)
(E 13? E)5 e2 J/OEdE
0
Figure 2 shows the thus-calculated probability P(B) for
E3 = 11 MeV. The two curves correspond to the two values of
the constant a in the expression for the density of levels: al
= 3 MeV-1 (curve 1) and a2 = 1 MeV-I (curve 2). For small B
values, P(B) does not depend heavily on the a value. For the
case of the Ti' -> Sc4I decay, Blot 3 MeV, and P(3) = 0.60 ac-
cording to the one curve, and 13(3) = 0,83 according to the other
curve. The same curves can be used for estimating the proba-
bility of the escape of a proton with the energy Ep > E = B - Bp.
For the other isotopes given in the table, the estimates are less
favorable. Finally, the actual probability can differ signifi-
cantly from the probability calculated on the basis of the sta-
tistical theory, since the density of levels is small for light nu-
clei. The above curves illustrate only the high probability of-detecting radiators of delayed protons among the enum-
erated and other similar isotopes of light elements.* 'None of the nuclear products given in the table has been ob-
tained until now. The cross sections of the (He3, 2n) reaction and of other reactions in which these nuclei could be
produced apparently are small in comparison with the cross sections of the simpler reactions that yield radioactive
isotopes and, therefore, it is rather difficult to detect them with respect to 3 - or y -activity. It is relatively simpler
to detect delayed protons, and their presence can be used for studying new nuclei with excess protons and nuclear re-
actions leading to their formation. From this point of view, the observation of delayed protons is of methodological
interest.
*V .I. Gol'danskii pointed out [9] that, in the 3 -decay of the predecessors of delayed protons, the superallowed transi-
tion would occur with the greatest probability and, on the basis of this, he estimated the probability of the emission
of delayed protons by certain nuclei.
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For the observation of delayed protons, it is necessary to have a pulse source of He3 nuclei, which are acceler-
ated to an energy in excess of 20 MeV (or a source of other particles, which are accelerated to higher energies), and
a proton detector, which is connected periodically during the intervals between radiation pulses.
LITERATURE CITED
1. V. L. Karnaukhov and N. I. Tarantin, ZhgTF., 39, 1106 (1960).
2. A. Cameron, Canad. J. Phys., 35, 1021 (1957); P. Seeger, Nucl. Phys., 25, 1 (1961).
3. S. Hinds et al., Phys. Rev. Lett., 6, 113 (1964
4. V. Weisskopf and D. Eying, Phys. Rev., 57, 472 (1940),
5. E. Almguist and D. Bromley, AECL, No. 950 (1959).
6. V. J. Goldansky, Nucl. Phys., 19, 482 (1960); A. I. Baz*, V. I. Gol'danskii, and Ya. Zel'dovich, Usp. Fiz. Nauk.,
72, 211 (1960).
7. G. R. Kipin, Atomnaya nergiya, 4, 3, 250 (1958); see also A. Pappas, Transactions of the Second International
Conference on the Peaceful Uses of Atomic Energy (Geneva, 1958). Selected Reports by Scientists from Abroad
[in Russian] (Atomizdat, Moscow, 1959), Vol. 2, p. 308.
8. J. Blatt and V. Weiskopf, Theoretical Nuclear Physics [Russian translation] (IL, Moscow, 1954).
9. V. L Gol'danskii, DAN SSSR, 146, 1309 (1960).
42
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of this issue.
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000600100001-7
THE ISOTOPE EFFECT IN ELASTIC SCATTERING
OF PROTONS ON NUCLEI
A. K. Val'ter and A. P. Klyucharev
Translated from Atomnaya Energiya, Vol. 14, No. 1,
pp. 48-56, January, 1963
Original article submitted September 13, 1962
Before proceeding to our exposition of the material, the authors would very much like to aknowledge, with
deepfelt appreciation, the crucial role played by the late Igor' Vasil'evich Kurchatov in the successful completion of
the investigation herein described.
Important contributions to the success of the project were made by the use of linear proton accelerators, the
use of targets containing various isotopes, and the processing of experimental data on high-speed electronic computers.
The late I. V. Kurchatov took a lively and indefatigable interest, backed up by effective and vigorous efforts
in the rapid development and implementation of linear accelerators at Khar'kov. We must acknowledge his valuable
contributions toward the production of an ample supply and variety of enriched materials. Finally, it was through the
approval and support of the late Igor' Vasil'evich that the electronic digital computer belonging to the Institute of
Atomic Energy of the USSR Academy of Sciences was made available to us (and which was, by the way, the first such
computer for our Institute) for the processing of experimental results.
Igor' Vasil'evich displayed an intense interest in the entire program since its inception in 1955. The last oc-
casion on which he took active part in the discussion of new results was in February 1960, less than a month before
his untimely demise.
The problem of elastic scattering of nucleons on atomic nuclei has attracted and continues to attract, at the
present time, the attention of many investigators. Over the past two decades, the arsenal of nuclear research tech-
niques has been strengthened by the addition of charged-particle accelerators, which have made it possible to obtain
intense beams of monoenergetic protons over a wide range of energies. This in turn has made it possible to carry out
a study in depth of the interactions of protons with atomic nuclei.
Until very recently, elastic scattering of protons on atomic nuclei was studied over a wide range of energies on
targets of natural isotope composition [1-10]. Results were obtained which contributed to the formulabion of several
general regularities present in the scattering picture. It was demonstrated, for example, that elastic scattering of pro-
tons on atomic nuclei at energies higher than the Coulomb potential barrier displays a diffraction character, and that
the position of the extreme points in the differential cross section as a function of scattering angle is determined by
the mass number of the scatterer at the specified energy and is shifted in the direction of smaller angles with in-
creased energy [11, 12]. This is clearly illustrated in Figs. la,lb for the energies 40 and 9.8 MeV, respectively, in
diagrams borrowed from references [13, 14].
The value of the differential cross section calc'ulated within the framework of the presently accepted optical
model is in satisfactory accord with the experimentally obtained value over a significant range of angles and energies
[15, 16]. The largest deviations of calculated values from experimental values is observed in the region of large
angles and increases, as a rule, as the mass number of the scatterer decreases. Except for the very lightest nuclei,
the angular distributions of elastically scattered protons at energies exceeding the Coulomb barrier are qualitatively
the same for all the elements in the periodic table. However, for neighboring elements in the Z = 24-29 region, the
scattering picture is markedly altered at lower energies. For example, Bromly and Wall [17], who studied elastic
scattering of protons of 5.25-MeV energy on copper nuclei (Z = 29), found that there are two peaks in the 40-50? and
130-140? regions, straddling a minimum (cf. Fig. lc) in the angular dependence of the ratio of the measured cross
section (9) to the Coulomb scattering cross section Rutherford
o(01 . At the same time, the nickel atom neighboring
0(U) Rutherford.
on copper (Z = 28 for nickel) yields a different scattering picture: the maximum is found at low angles, with the
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8
1,0
0,8
0,6
2,0
10
0,6
A4
0,2
1,8
1,6
7,4
1,2
1,0
0,8
0,6'
NCO
Ca"
Ni
Ni
1
0 .F.9 CO 90 120 150 180
0 , degrees
Fig. 1. Ratio of experimentally measured
scattering cross section 0(0) to the Coulomb
scattering cross section 0 (e)Rutherford as a
function of scattering angle.
minimum in the 80-90? region, and a continuous increase is evident
at large angles. Later on, Kondo et al. [18], studying elastic scatter-
ing of protons (5.7 MeV) on targets consisting of even-Z nuclei
(titanium, chromium, iron), demonstrated that the angular distribu-
tion of elastically scattered protons is similar to the distribution in
scattering on even nickel.
We infer from the findings of these experiments that the angu-
lar dependence of ) /0 (0)Rutherford differs qualitatively. for
even-Z nuclei and odd-Z nuclei at energies below the top of the
Coulomb potential barrier.
All of the investigations were conducted on targets of natural
isotopic composition, so that the differential scattering cross sec-
tions were averaged relative to cross sections of nuclei included in
the composition of the targets. Even-even nuclei predominate in
even-Z targets; targets with odd-Z nuclei in this region of the
periodic table consist of odd-even nuclei. The study of proton scat-
tering on targets of natural isotope composition therefore yields a
scattering pattern typical, or even or odd mass number of the target
nucleus. It is difficult to suppose that the parity of the mass number
would so affect the nature of the scattering.
Low-energy investigations thus turned out to be more sensitive
to the effect exerted by the individual properties of the nuclides on
the elastic scattering of protons.
A Study of Elastic Scattering of Protons on
Separated Isotopes
Elastic scattering of protons on separated isotopes at energies
5.4 MeV [19-20] and 19.6 MeV [21] was carried on using the linear
accelerators of the Khar'kov Physics and Engineering Institute of the
Academy of Sciences of the Ukrainian SSR, and at 6.8-MeV energy
[22] using the cyclotron at the Kiev Institute of Physics of the
Academy of Sciences of the Ukrainian SSR, the purpose of the in-
vestigation being a more detailed study of the scattering process.
Techniques were first elaborated for production of targets in
the form of thin free metal foil made of enriched isotopes. In the
process, workers were plagued with some difficulties related in the
first instance to the scanty supply of "raw material" available, and secondly to the fact that this raw material usually
involved a chemical compound rather than pure metal. Some of these techniques have been described in contribu-
tions by the authors and co-workers [23, 24].
The techniques worked out for studying the elastic scattering process are not highly involved, and we need not
be detained , therefore, in a reexamination of those techniques at this time. We shall confine our remarks to the point
that reliable discrimination of the particles due to inelastic processes is what counts here. The methods we employed
to record the protons were the scintillation counter method and the nuclear emulsion stack method, and relatively
small thicknesses of target material enabled us to single out and record groups of elastically scattered protons in our
work. The geometry of the experiment is shown in Fig. 2. The measured angular distributions of elastically scattered
protons are in agreement with theoretical results based on optical-model calculations run on an electronic computer.
Results of the Measurements
Calcium. Scattering was studied for two calcium isotopes (Ca 4? and Can) with doubly magic numbers 20 and 28.
Unfortunately, the calcium targets suffered partial oxidation during the experiment. We were therefore obliged to
limit our comparison to data obtained at large angles, where it might be possible to reliably distinguish groups of
protons scattered by calcium. But enough such data was found to infer a substantial difference in the angular distribu-
tions (Fig. 3). The solid-line curves in Fig. 3 were drawn through experimental data points; the broken curves
44
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a
Proton beam
Target
Photographic
---- ?C plates
----/ / \ \..
*/ I \ ?
\ ??DI'aphragm
-,--' A \ .\,
I oslIP\
Photographic
plates
Target
To integrator
Fig. 2. Scheme of the experiment: a) Using the nuclear emulsion technique; b) using
the scintillation counter technique.
3 correspond to the hypothetical low-angle variation of the
.5
angular distribution. The even-even Ca48 nucleus yields
\ ;?-?
II a scattering pattern typical for nuclei of odd mass number
3,0 iCa
M, while the even-even Ca48 nuclide also evinces an angu-
gZ1
lar dependence similar to the dependence for nuclei of
LO?liczNi
odd M (in the large-angle region a pronounced peak is
2,5 evident in the angular distribution).
Chromium. Cr52 and Cr" targets were bombarded
2,0 by 5.4 and 6.8 MeV protons. The angular dependence for
70%Ca41,307.C.(74 this case is shown in Fig. 4. Scattering on Cr52, which is
an even-even nuclide magic with respect to neutrons, is
similar to scattering on Ca44 at 5.4-MeV energy, while
/
is CO 48
the angular dependence for the even-odd nuclide Cr 53 is,
on the other hand, similar to the dependence for nuclei of
odd mass number. The data obtained at 6.8-MeV energy
only emphasize the difference in the elastic scattering of
protons by these nuclides, but the appearance of a hump in
the large-angle curve in the case Cr52 points to a tendency
for this difference to smooth out as the energy is increased.
The continuous curves indicate the angular distribution
computed on the basis of the optical model. It is not dif-
Fig. 3. Angular dependence of ratio a py a (120?) in
ficult to see that the best agreement between experimental
and theoretical data is observed for odd chromium, while
a sharp difference in the large-angle variation of the angular dependence is detected in the case of Cr52.
Nickel. Scattering was studied on the four nickel nuclides Ni58, Ni60, Ni,
and Ni84 at proton energies 5.4 and
6.8 MeV. The results obtained appear in Fig. 5. At 5.4-MeV energy, the angular distribution for the first three
nuclides is qualitatively the same, and similar to the angular relationships for Ca48 and Cr52. However, even in the
case of Ni, we find the scattering intensity at large angles to be markedly lower than the intensity for Ni58 and Ni60.
As for Ni, despite the even mass number, the angular dependence proved to be similar to that applying to the case
0 20 60
100
140 160
180
ecm, degrees
case of Ca48 and Ca48 at Ep = 5.45 MeV.
45
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13,
CD
CD
3,4
3,0 -
1 , 0
0,61-
1,2
1,0
0,8 -
0,6 -
0
Ep. 5,4- MeV
Cr52
L
Fig. 4. Angular
Thresholds of (p,n)-Reaction
SO 120
0 cm, degrees
160 0 80 120 16'0
0CM degrees
dependence of the o(0)/ 'Rutherford ratio for Cr52 and Cr53.
of odd nuclides. At 6.8-MeV proton energy, Ni58 and Ni"
much the same way as Cr52, while Ni62 presents the same
scattering pattern as an odd nuclide. The theoretically com-
puted curves are in excellent agreement with experimental
curves for Ni" at 5.4 MeV and for Ni62 at 6.8 MeV. A strik-
ing discrepancy is observed for the lighter nuclides, particu-
larly for Ni" at 5.4 MeV. At a higher energy, the optical
model reflects in a satisfactory manner the qualitative varia-
Nuclide
Threshold of
(p,n)-reaction, MeV
calc.
exptL
Ca4?
15,0
Ca'8
0,52
Ti"
8,0
Ti47
3,57
Ti"
4,90
Ti"
1,43
Ti5?
3,06
-7
V50
0,95
V51
1.53
1,56
Cr52
5.63
Cr53
1,83
Al 655
1,01
. 1,02
Fe"
5,4
Fe"
1,29
Feb'
3,08
1,87
Ni 58
10,48
Ni6"
7,17
Ni?2
4,77
4,7 ?
Ni"
2,45
2,5
Cu6"
4,2
4,2
Cu?5
2,13
(2,7)
Zn"
8,00
Z1166
5,97
6,05
Z11"8
3,81
3,4
46
Data
source
[28]
tion of the angular relationship for Ni52 and Ni613.
Cobalt, Copper, and Zinc. Scattering on cobalt, Cu65,
-
tering turned out to be similar to the case of scattering by
[281 such odd nuclides as cobalt and Cu65.
The curves computed for 5.4-MeV energy turned out
to be in excellent accord with empirically plotted curves for
Cu65 and Zn62, while a fairly pronounced large-angle dis-
crepancy was observed for Zn".
Zn", and Zn65 at 5.4-MeV proton energy was studied. The
angular relationship resulting is shown in Fig. 6. Despite the
fact that both zinc nuclides are of even mass number, scat-
[28- ]
[28]
[28] Angular scattering results for scattering on Cu63 and
[281 Cu65 at 6.8-MeV proton energy were measured and computed
[28- ] theoretically. The curves are similar (both nuclides having
1281 odd mass numbers) and exhibit satisfactory agreement with
the experimental curves both in general shape and in abso-
lute values (Fig. 7).
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4 C?
NI*"
1,2
1,0-
0,8
1,2
1,0
0,8
sos
Ni62
80 120 160
a
0CM ,degrees
-0 1,6
0,6'
1,8
7,6'
1,4
1,2
1,0
48
1,4
1,2
1,0
48
46.
N/62
if
0
80
120 180
0CM' degrees
Fig. 5. The same as Fig. 4, for nickel isotopes at Ep = 5.45 MeV (curve a), and Ep = 6.8 MeV
(curve b).
Discussion of the Results
The results mentioned above make it possible to draw several inferences on the nature of elastic scattering of
protons on atomic nuclei at low energies. It is evident, first of all, that the angular dependence of the ratio of the
measured cross section to the Coulomb scattering cross section is qualitatively different for nuclides of odd and of
even mass number, while the number of neutrons is close to a magic number in even nuclei.
The scattering picture is sharply altered when the number of nucleons in the nucleus is changed by one unit
(independently on the nucleon charge state). The parity of the mass number is accordingly of vital importance in
scattering. An odd nucleon strongly smears out the nuclear surface, apparently, and causes an appreciable increase
in the probability that an impinging particle will be absorbed in the surface layer of the nucleus. The same effect
is observed in nuclides far removed from the magic region, with even mass number and paired nucleons above the
closed nucleon shells.
However, an increase in absorption results in an increase in the scattering. In measuring the intensity of scat-
tered protons together with protons scattered elastically in the Coulomb field of the nucleus and in the field of the
nuclear forces, we inevitably come to record protons of the same energy and passing through the stage of the com-
pound nucleus, the (p,p)-process with capture. In our preliminary paper on the study of elastic scattering of 5.4-MeV
protons by some elements, which was published in 1956 [25], we expressed the conjecture that the high value of the
a (0 )/a (120?) ratio at large angles is related to the capture of the impinging proton by the target nucleus and the
formation of the compound nucleus N13 with the excitation energy in the resonance region. Greenless et al. [26],
47
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0
1,2
10
0,8
10
0,8
;2
1,0
0,8
0,6
zn?8
_
to
0 BO 120 160
9 civi,clegrees
Fig. 6. Same as in Fig. 4, for cobalt, Cu, Zn",
and Zn68 at Ep = 5.45 MeV.
40 30 120 180
Acm,degrees
Fig. 8. Same as in Fig. 4, for Co59 and Cu65 at
EP = 19.6 MeV: 0(?), Co59; ?(---), Cu.
48
,
0 1?.:7 60 120 160
61 c m,degrees
Fig. 7. Same as in Fig. 4, for copper nuclides at Ep
= 6.8 MeV.
detected a nonmonotonic energy dependence Of the angular
distribution of protons elastically scattered on magnesium,
and this may likewise be related to the formation of the com-
pound nucleus. At energies below the Coulomb barrier, the
probability of decay of the compound nucleus through the
elastic channel is always greater than the probability of de-
cay through inelastic channels for charged particles.
The (p,p)-process with capture will predominate if the
threshold of the (p,n)-reaction is greater than the energy of
the incident particle. Otherwise, a powerful competitor will
appear in the (pp)-process in\ the form of a reaction with
neutron yield. This imparts considerable interest to a com-
parison of the thresholds of (p,n)-reactions and the behavior
of the angular distribution of elastically scattered protons.
In the above table, we list values of the thresholds of
(p,n)-reactions computed from the values cited in [27] and
values found experimentally for the nuclides in the region we
studied. The inference we may make from the table is that
all nuclei of odd mass number have low thresholds, just as
neutron-enriched isotopes of even nuclei. Nuclides of even
mass number but of low N? Z difference have a high threshold,
as a rule. This is due to the binding energy of the last neutron
in the nucleus.
Let us compare these data with the results of measure-
ments of the angular distributions of elastically scattered pro-
tons. The maximum in the large-angle angular distribution
is given by all nuclides for which the threshold of the (p,n)-
reaction is lower than the energy of the primary protons: Ca",
Cr53, Ni64, Cu, and Zn68, but this does not apply to Ni62 and
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Zn". This maximum is not present in the case of Ni62
125 despite the fact that the threshold is below the energy of
the bombarding particles, but the value of the
o(0)/o(0)Rutherford
ratio in the large-angle region is
.00. .significantly lower than is the case for Ni58 and Ni.63 at
00 0 5.4-MeV energy. But even at 6.8-MeV energy, this nu-
clide scatters protons in the same manner as an odd nu-
cleus. It is possible that the probability of the (p,n)-re-
action for Ni62- close to the threshold is not high, and in-
t
creases appreciably as the energy is increased.
Consequently, the "anomalous" increase in the
ratio a(e)/("Rutherford in the large-angle region in
45
50 100 150
0 cm, degrees
Fig. 9. Same as in Fig. 4, for cadmium nuclides at Ep
= 19.6 MeV: 0, Cd111; X, Cd113; 0, cd116.
1,8
a)
-5 1,
a) 1,2
1,0
the case of nuclides of even mass number is due to a con-
siderable extent to elastic scattering of protons with the
formation of a compound nucleus. As the energy in-
creases, the role of the inelastic channels in the decay
of the compound nucleus is enhanced, in particular the
role of the (p,n) channel, when the energy of the primary
protons exceeds the (p,n) reaction threshold. Now this
leads to a decrease in the probability of decay of the
compound nucleus through the (p,p) channel with capture.
The preceding discussion implies clearly that the
theoretical treatment of the experimental results on
elastic scattering of protons on atomic nuclei, based on
the optical model with no allowance for competing proc-
esses, is valid only in those cases where the binding
energy of the neutron in the nucleus is not great and the
threshold of the (p,n)-reaction is small compared to the
? energy of the particle scattered.
0,E
Of course, a certain contribution to the attenuation
of the (p,p)-reaction is creditable to the inelastic chan-
t
0,6 nels bearing a yield of charged particles, for example
(P,p')-scattering. the value of which varies as the energy.
0,4 1
This may apparently account for the humps in the curves
of the angular distribution at large angles, in the case of
0,2 1
Zn" at 5.4 MeV, and in the case of Ni58 and NO? at 6.8
MeV.
0 40 80 120 160
0 cm, degrees
As the energy is increased, the relative contribution
of protons scattered with capture to the over-all intensity
of the (p,p)-process will decrease because of the growing
Fig. 10. Same as in Fig. 4, for tin nuclides at Er 19.6
MeV: Sni16; ? ---), Sn124.
probability of other inelastic channels open to the decay
(? ), (
of the compound nucleus, and the pattern of elastic scat-
tering will approach more and more closely a diffraction
pattern. The "isotope effect" in proton scattering at high energies exerts a much less prominent effect at high energies
than at low energies.
We studied elastic scattering of 19.6-MeV protons on the following separated isotopes: tritium, He3 and He4,
Li6 and Li7, N14, 016, cobalt, Cu63, Cu, Gen and GO, cam, Cd113 and Cdi16, sn116, sn117, sn118, sn119, sn120, sn122
and SnI24, pbarr, pb208, and bismuth [21].
The experimental and theoretically computed results for cobalt, Cu65, and various nuclides of cadmium and
tin appear in Figs. 8-10. The scattering in these cases is typically diffractive in nature. The optical model is in this
case a fully satisfactory description of the elastic scattering of protons on atomic nuclei. The discrepancies in the
low-angle region may be due to large experimental errors associated with certain difficulties encountered in low-angle
measurements,
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At low energies, the extent of agreement between experimental and theoretical data is also considerable for
those nuclides having a (p,n)-reaction threshold lower than the energy of the bombarding particles. For these nu-
clides, the smearing-out of the nuclear surface and the absorption width are greater than for nuclei of even mass num-
ber and are close to magic neutron number. This is in accord with the supposition we advanced earlier on the smear-
ing-out of the nuclear surface and the enhanced absorption of impinging particles by these nuclei. It is of course a
bit premature to draw any categorical inference from the data. An extended systematic study of the process of elastic
scattering of nucleons on separated energies at various energies will be required, with improved experimental ac-
curacy and with allowances for the contribution of the compound nucleus to the scattering picture.
LITERATURE CITED
1. E. Rhoderik, Proc. Roy. Soc., A201, 348 (1950).
2. R. Lelevier and D. Saxon, Phys. Rev., 87, 40 (1952).
3. L. Goldman, Phys. Rev., 89, 349 (1953).
4. B. Cohen and R. Neidigh, Phys. Rev., 93, 282 (1954).
5. L Dayton, Phys. Rev., 95, 754 (1954).
6. I. Dayton and Q. Schrank, Phys. Rev., 107, 1602 (1957).
7. I. Beyster, M. Wall, and E. Salmi, Phys. Rev., 104, 1319 (1956).
8. W. Waldorf and N. Wall, Phys. Rev., 107, 1602 (1957).
9. M. V. Pacetshnik, N. I. Putsherov, and M. A. Totsky, Comptes rendus du Congress Internationale de Physique
Nucleare (Paris, 1958), p. 598.
10. N. I. Pucherov, Ukrains'ki fiz. zh., 4, 313 (1959).
11. A. I. Akhiezer and L Ya. Pomeranchuk, Usp. fiz. nauk., 39, 153 (1949).
12. B. Kinsey and T. Stone, Phys. Rev., 103, 975 (1956).
13. M. Brussel and J. Williams, Phys. Rev., 114, 525 (1959).
14. H. Hinz, Phys. Rev., 106, 1201 (1957).
15, A. Glassgold, W. Cheston, M. Stein, and G. Erickson, Phys. Rev., 106, 1207 (1957).
16. A. Glassgold and P. Kellog, Phys. Rev., 107, 1372 (1957).
17. D. Bromly and N. Wall, Phys. Rev., 102, 1372 (1957).
18, M. Kondo et al., J. Phys. Soc. Japan, 13, 231 (1958).
19. A. P. Klyucharev and N. Ya. Rutkevich, ZhETF, 38, 286 (1960).
20. N. Ya. Rutkevich, V. Ya. Golovnya, A. K. Val'ter, A. P. Klyucharev, DAN SSSR, 130, 1008 (1960).
21. R. A. Vanetsian, A. P. Klyucharev, and E. D. Fedchenko, Atoonaya 6nergiya, 6, 661 (1959).
22. A. K. Val'ter et al., ZhETF., 38, 1419 (1960).
23. A. D. Bondar' et al., Pribory i tekhn. eksp., No. 3, 134 (1960).
24. A. D. Bondar' et al., Pribory i tekhn. eksp., No. 3, 137 (1960).
25. A. P. Klyucharev, L. L Bolotin, and V. A. Lutsik, ZhETF., 30, 573 (1956).
26. G. Greenless et al., Proc. Phys. Soc., A70, 331 (1957).
27. V. A. Kravtsov, Usp. fiz. nauk., 65, 451 (1958).
28. J. Blaser et al., Hely. phys. acta, 24, 3 (1951).
50
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of this issue.
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000600100001-7
COLLECTIVE INTERACTIONS AND THE PRODUCTION
OFA HIGH-TEMPERATURE PLASMA
E. K. Zavoiskii
Translated from Atomnaya Energiya,Vol. 14, No. 1,
pp. 57-65, January, 1963
Original article submitted October 15, 1962
Introduction
The problem of producing a high-temperature plasma and the problem of containing such a plasma cannot be
treated independently. It is difficult to think of a plasma confinement device that is not affected by the method
used to produce the plasma. Indeed, the plasma heating process determines directly confinement parameters such as
heating time, the time-rate-of-change of the electron and ion temperatures during the plasma production process,
the oscillation spectrum, the presence of trapped magnetic fields and impurities, plasma currents, etc. Because of
the complexity of the problem, however, at this stage we must consider methods of heating plasma separately from
methods of containing plasma. Below we shall be interested primarily in the plasma heating problem.
It is now clear that the description of a plasma in terms of a system of charged particles that interact with each
other via binary Coulomb collisions is an inadequate one. Collective interactions play an extremely important role
in plasmas produced under actual experimental conditions. Among these interactions we think first of the interaction
of a beam of charged particles with a plasma, an interaction that has been studied in detail both theoretically and
experimentally. It has been found that a beam in the plasma rapidly loses the energy associated with the ordered
motion because of collective interactions. The possibility of using this effect for plasma heating seems to be worth
investigating. However, in actual experiments the beams are generally formed outside the plasma and for this reason
are characterized by low densities, as is the plasma into which they are injected. Obviously, charged particle beams
need not be injected into the plasma from outside; under certain conditions they are produced inside the plasma [1].
In this case a beam can generally excite plasma oscillations and have an important effect on the nature of the plasma
processes. This was first pointed out by R. Z. Sagdeev [2], who showed that the excitation of collective electron mo-
tions can explain the damping of shock waves in a collisionless plasma.
L. I. Rudakov has proposed that the dissipation of oscillation energy by virtue of this mechanism is possible not
only for the shock wave, but also for an ordinary wave, if the wave amplitude is sufficiently great.
Thus, the important problem of studying collective processes in a plasma can be reduced to the search for con-
ditions under which charged particle beams capable of exciting plasma oscillations can be produced by electomag-
netic fields. If an effective method for transferring the energy of an external electromagnetic field to a flux of
charged particles can be found, this would represent a solution to the problem of heating a collisionless plasma with
a high degree of efficiency.
Obviously the importance of collective processes in a plasma is not limited to this one aspect of the problem;
as far as obtaining a high-temperature plasma is concerned, however, these effects are evidently the most important
so long as plasma stability is not considered.
The problem of heating a plasma by randomizing the energy of ordered motion through collective processes
has certain wider ramifications. Let us assume that strong external electromagnetic fields cause rapid ordered plasma
motion which, in turn, leads to the appearance of an instability on a scale which is much smaller than the character-
istic dimensions (for example, the radius of the plasma column). If the growth time of these instabilities and the
time during which the external electromagnetic fields are applied are both small, and if the oscillations arising as a
result of the instability relax quickly to a thermal level, then this process will result in the thermalization of the
ordered velocity without having a noticeable effect on plasma loss from the trap. The plasma temperature that can
be achieved under these conditions is determined by the ordered velocity of the ions, i.e., the magnitude of the ex-
ternal fields, The difference between this method of heating and that described above, which is based on the
51
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development of beam-type instabilities, lies in the difference in the nature of the mechanisms producing the insta-
bilities in the plasma; in turn, these differences lead to important differences in the space and time scales of the in-
stabilities.
Conditions for the Excitation of Electron Plasma Oscillations
The interaction of a beam of charged particles with a plasma has been studied in detail both theoretically and
experimentally, and has been described by many authors. Although most of the experiments have been carried out
with the beams injected into the plasma from outside, the criteria for excitation of collective oscillations are approxi-
mately the same as for the case in which the beams are produced in the plasma by external electromagnetic fields.
The excitation of oscillations requires that ve, the ordered velocity of the electrons with respect to the ions, be
-2Te
greater than the thermal velocity veTV
= ? . Under these conditions, Langmuir oscillations are excited in the
m
2 47rne2
plasma in a time of order T_.-,., -\/- , where too . , with wavelengths of order ve/wo. The energy of the
too m m
plasma oscillations is thermalized at the same time. If the plasma is located in an external magnetic field H and
coo >> coeH, where cod; = ?eH , the magnetic field has little or no effect on the development of the instabilities.
mc
Using these general considerations, we now consider the concrete problem of exciting electrostatic oscillations
in a plasma by means of external electromagnetic fields [3]. Assume that the plasma column is located in a longi-
tudinal magnetic field described by
H= H H _e?c" sin cot. (1.)
The electron current density in the plasma is then
c
? ev,pn -ft
au
4-a r ,
(2)
where r is the distance from the axis of the column. Using Eq. (2), we find criteria for the appearance of a collective
electron friction
H2 cog
87tn?T, > I k 12 C2
(3)
I1 dH
?=
where k = ? is the wave vector, which depends on the plasma density n, the magnetic field H, and the
orientation of the field with respect to H...,. If H,... is parallel to H, then when H?,/H kzvII , we ob-
tain results which, to within a numberical factor, agree with those given above [(11), (17), (18)1. Thus, in making a
qualitative comparison of the theory and experimental results, we can use the results of calculations obtained in which
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2
10
8
6'
2
6'
2
01
6
x X
X
X X
X .
X
X >--
Tx
X
/
L
X
r
I
gli
x
.
i1---;
;
r
,
I
,
2 4 6 810
JD mA
2
4
Fig. 2. The signal received by the rod antenna at
frequency 11 = 2.2 Mc as a function of N [E = 160
key; Icon= ?1.5 kA; Iinj = 0.5-110 mA; p = (1-6)
? 10-7 mm Hg; Uc = 0].
electrical component of the field exhibits a sharp rise.
the ion distribution function is assumed to be a -function if
the relation > 10 is satisfied in Ogra, where T1 is
the mean kinetic temperature of the transverse ion motion.
Experimental Results
Earlier measurements of the electric fields at the cyclo-
tron frequencies of molecular and atomic ions carried out in
Ogra by means of a spectrum analyzer [6] showed a nontrivial
dependence of the amplitude of the high-frequency field on
the density of fast particles [7]. The intensity of the field at
the H ion cyclotron frequency as a function of density ex-
hibited a rise for injection currents linj 3 10 mA as com-
pared with currents 10 mA; on the other hand, there was no
singularity in the dependence of the total density of fast ions
or the density of atomic ions on current in this region.
In order to interpret the nature of the field oscillations
at the cyclotron frequencies, we carried out a number of spe-
cial experiments. Using a loop antenna located in the central
region of the Ogra chamber, we measured the magnetic com-
ponent of the field. The dependence of the magnetic field at
the cyclotron frequency for the molecular ions (11 = 2.2 Mc)
on the density of fast ions N (in relative units) is shown in
Fig. 1. In this same mode of operation we obtain the depend-
ence on N of the signal measured by a rod antenna (Fig. 2),It
is evident from these figures that the magnetic component of
the high-frequency field increases in approximate proportion
to the density over the entire range of variation. However,
at injection currents greater than approximately 10 mA, the
This may indicate that at some critical value of N the elec-
tric component of the field in the plasma becomes greater than the magnetic component, i.e., in addition to the elec-
tromagnetic wave, there are electric fields (the so-called longitudinal oscillations) associated with oscillations of the
plasma density. The linear growth of magnetic field with increasing density indicates the bunching of ions.. It is
known that the radiation produced by charges moving in a circle is proportional to the charge density if the charges
are phased (coherent radiation).
We now estimate the magnetic field produced by ions moving in a circle in free space. The magnetic field
due to a single particle is
CO) 0
H I' sinll ? o
di, ,
where wH and p H are, respectively, the gyration frequency and the radius of the circle traversed by the charge e; R
is the distance from the center of the circle to the point of observation; 0 is the angle between the axis of rotation
and the line connecting the center of the circle to the point of observation. If (pH = 1.4 ? 107 sec-1, pH = 25 cm,
R = 102 cm, 0 = 7 /2, the field due to a single Hif ion is
H 1 0-15 gauss.
In incoherent radiation due to many particles, frec--1-iTt-, where Nt is the total number of radiated particles.
If Nt = 1014 (the number of Er2F ions in Ogra), I= 10-8 gauss. The measured values of magnetic field for ion densi-
ties of approximately 107 cm-3 are found to lie in the range 5 ? 10-5 to 8 ? 10-4 gauss, which is four or five orders of
magnitude greater than the value obtained by the estimate given above, which applies for free space. Actually, the
ions move in a volume enclosed by metal. Hence, in computing the magnitude of the oscillating electromagnetic
field produced by the ions, one should take account of the actual boundary conditions. The solution of this problem
would involve considerable mathematical difficulty; on the other hand, the measured values of the field differ from
the estimate given above by several orders of magnitude, and it would be difficult to attribute the effect to the boun-
dary conditions alone. For this reason, these calculations were not carried out. The large discrepancy can be
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1
I
i
i
1
I
A
X
%
%
)(
4 %
..
.1,
1
I
I
I
I
/
/
0
%
N
\I
Vx
\
\
\
0,5
1
1,5
2 2510
l/z,cm/set
Fig. 3. The distribution of H2+ ions over longitudinal
velocity measured in the central region; solid line,
= 100 mA; broken line, I = 2 mA.
11, mV
6
1
8
6'
4
2
0,1
8
6'
0,0
11)
o
X (It
p t
x
i
X
x Pro/
cr-i
.
0
>.
rm....5(
X
/
X
X
x
o
x
I
-X
x
8 0
1
2
4
6'
81
4 6810
iinj mA
Fig. 4.
The signal picked up by the rod antenna as
a function of the injected current [E = 160 keV; Icon
= ?1.5 kA;. p = (0.8-3) ? 10-7 mm Hg; Uc = 0]. 0 ,
f = 2.2 Mc; X, f2 = 4.4 Mc.
explained qualitatively if one assumes that the ions form
bunches and radiate coherently. The current of molecu-
lar ions injected into Ogra does not have frequency com-
ponents beyond 0.8 Mc. Furthermore, it is possible to
operate the ion source so that the current spectrum con-
tains no frequencies above 2 Mc. However, it is found
that even under these conditions the antennas record sig-
nals at the frequency f2 = 4.4 Mc. In order to understand
how molecular ions in Ogra can form bunches, and to ex-
plain the observed dependence of high-frequency electric
and magnetic fields on ion density, we must postulate
some mechanism which is responsible for the excitation of
intense oscillations at the ion-cyclotron frequency. Such
a mechanism is the cyclotron instability described above.
As far as the anisotropy of the plasma formed by injection
of the molecular ion beam in Ogra is concerned, we have
qualitative information regarding the ion distribution for
1-121- measured over longitudinal velocity vz by Yu. A.
Kucheryaev and D. A. Panov, who used a collimated radial
probe located in the central portion of Ogra (Fig. 3). If
we assume that the transverse ion temperature T1 is equal
to the kinetic energy Mv21./2 while the longitudinal tempera-
ture Til is equal to the half-width of the spread in longi-
tudinal ion velocity, then for 1-1 with Iinj = 100 mA, we
find Ti/Tir 26. This means that the cyclotron insta-
bility can develop in Ogra if (11) is satisfied.
+ .
Since the cyclotron frequency for H2 ions f =2.2
Mc, the inequality in (11) is satisfied at an electron density
ne > 6 ? 104 cm-3. To examine the existence of instability
boundaries of the plasma in Ogra, measurements were made
of the electric fields, at small injection currents (Fig. 4).
In this case, with Iinj = 0.1 rnA and a chamber pressure p
= 1 ? 107 mm Hg, the plasma density is approximately 105
cm-3 [8].Measurements at frequencies ft--? 2.2 Mc and f2
= 4,4 Mc indicate that when the current is increased from
0.1 mA there is first a strong increase in the signal at the
fundamental frequency fl, and then at the proton cyclo-
tron frequency f2. An especially sharp rise is observed at
the frequency f2 when the current is changed from 0.2 to
0.3 mA, in which case the signal increases by approximate-
ly a factor of 6. In spite of the large spread in the experi-
mental points (Fig. 4), it is evident that after the initial
growth of the signal there is little change, although the
plasma density continues to increase in linear fashion. Then
the field increases again, but at a smaller rate.
In Fig. 5 we show a typical oscillogram of the signal spectrum observed on the rod antenna. Similar spectra
can be observed by connecting to the analyzer any other pickup unit located in Ogra. The magnitude of the electric
field can be estimated by means of a method suggested by D. A. Panov. In particular, if we regard the antenna as a
metal surface on which there is induced a charge with surface density 0, the electric field component normal to the
surface is E = 41r0, where 0 = U/wHSR (here U is the voltage measured in the experiment across a resistance R;
is the field frequency; S is the surface area). In the case of the rod antenna we have E = 5 ? 102U. For the observed
values of the signal U = 0.1 V. we find E = 50 V/ cm (Linj RS 120 mA, p RI 3 ? 10-7 mm Hg). This value is more than
two orders of magnitude greater than the electric field E = H = 0.24V/ cm obtained by meausrements with the rod
antenna. Thus, the estimate of the electric field given above supports the conclusion based on the experimental
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Phase Velocities and Wavelengths (Grid Potential Uc = 0)
Antenna
rnA number
= 1 , kA
con
I con= --o,t kA
degrees
X, m
. ,
to cm/sec
Aso,
degrees
X, m
49'
os cm/sec;
80 13-16
13-1
5-19
45
30
170,
94
24
1,4
54
54
3,1
6-1 12
>27
5-12 100
5,4
50 13-6 0-180
?_>-13
0-90
>12 >27
13-1
0-60
>12 >27
6-1 12 >27
12 >27
5-12 120
2 4,5
.190
9 4,5
13-6 90?45
8-94 1.854
13-1 60
12
97
30 24 54
1-6 ?
24 >54
5-12 100-120
2,4-2,0
5,4-4,5
(50 4 9
90 13-6 0-90
>12
>27
45-180
>13
13-1
30-120
1-6
12 >26
5-12 60
4
9
60-70
4-3,4 9-7,6
II) 13-6 90?30
9-18
20-40
180
13
13-1 60
12
27
190
6 13
1-6 30
19
97
30-90 4-12 9--27
5-12 0; 60
none; 4
none;9
60 9
5 13-6 270
4 9
180 6 13
1-6 70
5,1 11
_
5-12 60
4 9
0 none none
results that longitudinal density waves are excited in Ogra. In order to determine the spectral composition of these
waves, we have carried out experiments with a series of foil antennas (13 elements in all) located along the axis and
in the azimuthal direction (Fig. 6). The antennas are copper sheets 1 cm in radius located at a distance of 6 cm
from the chamber walls. The signal from each antenna is transmitted from the measuring instrument by means of a
matched cable. In these experiments we measured the distribution of electric field in the plasma along the axis and
in the azimuthal direction, and recorded the phase shifts between two antennas, at the frequency fi = 2.2 Mc. The
experiment showed that in Ogra there are both traveling and standing density waves; the amplitudes and wavelengths
depend upon the mode of operation (injection current, pressure, grid voltage 18]). In the azimuthal direction the
waves travel in the same direction as the fast ions. It is evident from Fig. 7 that the signal on antenna 12 leads the
signal on antenna 5. The direction of propagation of the wave along the axis is not unique and depends upon the in-
jection current and the pressure. In certain modes of operation it is possible to observe two wave groups; one travels
toward the center and the other away from the center (Fig. 8). Thus, there are waves that propagate at an angle with
respect to the external magnetic field Ho .The observed phase shifts indicate the existence of a complicated wave pat-
tern in the plasma which changes with time.
The phase shifts were measured by means of a two-beam oscilloscope DO-1 to which the signals at 2.2 Mc
from the two antennas are applied through g narrow band amplifier. The oscilloscope is triggered by one of the sig-
nals (in the table and in the figures the number of this antenna is indicated at the beginning).
On the screen of the oscilloscope one can see the stationary pattern of two sinusoidal signals shifted in phase
with respect to each other. If the phase shift changes with time a sine wave remains on one pattern (the signal trigger-
ing the oscilloscope), while the other pattern becomes smeared, indicating the superposition on one frame of many
single-shot measurements of phase shift. This result indicates the existence of a whole spectrum of waves at the cy-
clotron frequency.
The measured phase shifts and the computed wave lenths and phase velocities are given in the table. The wave-
length is computed from the relation X = ?x, where A40 is the phase shift; x is the distance between the antennas,
Acp
and it is assumed that the wave propagates in one direction. To compute X and the phase velocity vco when Aco 60?,
in general it is necessary to take account of the existence of two traveling waves moving in opposite directions.
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?,1? 1 ?
2 2 4
7 7
f,1Mc
Fig. 5. Oscillogram showing the spectrum of the
electric field (E = 160 key; Icon = ?0.1 kA; Iinj
= 100 mA; p = 3.5 ? 10-7 mm Hg; Uc =.0).
iiiimansmimminssal
laninaumworamigneova
1 6:41 ? ?IZ m
MIR., NI
krtii0 I '
*14
Fig. 7. Oscillogram showing the phase shift be-
tween signals at antennas numbers 12 and 5 (the
upper beam corresponds to No. 12, the lower to No.
5): E = 160 keV; Icon = ?1.5 kA; Iinj = 20 mA; p
= 1.5 ? 10-7 mm Hg; Uc = 0.
gt?
? la. ,
cm
1-2
,,
a
-3
PE
m25,50
1-4 11-05-75-8
5-95-10,5-145-12
I
10016
12
24
36 :48166
Direction of
ion
rotatio
Center of
chamber
207c
Fig. 6. Location of the foil antennas in Ogra.
Fig. 8. Oscillogram showing the phase shift between
signals at antennas numbers 6 and 13 (the upper beam
corresponds to No. 6, the lower to No. 13): E = 160
key; Icon = ?1.5 kA ; Iini = 20 mA; p = 1.5 ? 10-7
mm Hg; Uc = 0.
In spite of the large spread of experimental points
and poor accuracy in the phase-shift measurements (20?),
using the table we can establish certain features of these
phenomena. First of all, as the current is reduced the
length of the wave propagating along the axis is reduced
from approximately 24 to 4-6 m, while the wavelength
in the azimuthal direction increases from 1.4 to 4 m (at small currents the azimuthal phase shift cannot be detected).
In other words, as the plasma density increases, waves with greater obliqueness (kx/kz 0) are excited, in qualitative
agreement with Eq. (19) which, strictly speaking, applies to an infinite plasma.
Second, to within the experimental errors the observed azimuthal wavelengths are found to be approximately
an integral fraction of the circumference (1 = 4 m) at the radius at which the antennas are located. As the injection
current is changed the wavelength changes in discrete steps.
Third, from the table and the oscillogram (cf. for example Fig. 8), it follows that as the current is increased
one not only excited individual waves, as at small currents, but a whole spectrum of waves with different phase velo-
cities.
The measurements of the amplitude of the electric fields along the axis and in the azimuthal direction show
that standing waves also occur in Ogra (Fig. 9). With an injection current of 5 mA, the wavelengths of these waves
along the axis is smaller than at 50 mA, as for the wavelengths of the traveling waves. The electric field in most
modes of operation does not vary greatly in azimuth (within 20%), i.e., we have primarily traveling waves. When a
positive potential is applied to the grids located in the mirrors the magnitude and wavelength of traveling and stand-
ing waves are both reduced.
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U , m
10
3
+
, .
.
4
5
7,5
5
2,
0
Center of
chamber
100
200
300
Z, cm
Fig. 9. Distribution of electric field along
the axis of the chamber at frequency f1
= 2.2 Mc [E = 160 keV; Icon = ?0.1 kA; p
= (1.6-2) ? 10-7 mm Hg; Uc = 0] for the
following values of Iinj, mA: 1) 50; 2) 30;
3) 20; 4) 10; 5) 5,
Conclusions
The experimental results reported here indicate that a cyclo-
tron instability can and does develop in Ogra. Furthermore, at the
present time, as far as we know there is no other possible explanation
for the anomalous magnitude and the dependence of electric field (at
the cyclotron frequency) on plasma density observed experimentally.
The presence of density waves with different phase velocities can
cause electron heating and electron loss. In this regard, the fact that
the electrons can interact with the electric waves seems to be indi-
cated by experiments with an electron beam carried out by Yu. A.
Kucheryaev and D. A. Panov [9]; these experiments indicate that an
electron beam passing through a plasma along the magnetic field
loses or gains energy by virtue of interaction with waves at the cyclo-
tron frequencies corresponding to HiF and 14: ions.
On the one hand, the effect of the cyclotron instability can
cause ions to form bunches as a result of nonlinear effects, and these
can lead to a more effective interaction, with the dissipation and ex-
change of energy. On the other hand, the existence of electric fields
perpendicular to the magnetic field can cause ion drift across the
magnetic field when the phase velocity of these waves is approximate-
ly equal to the ion velocity. As is evident from the table, this situa-
tion can arise in certain modes of operation. For a more detailed ex-
planation of the effect of the cyclotron instability on ion loss and
electron loss, it will be necessary to carry out further investigations.
The author wishes to take this opportunity to thank I. N. Golovin for
his continued interest in this work and for a number of valuable com-
ments offered in discussions of the experimental results, E. P. Velik-
hov for help in carrying out the calculations, and A. N. Karkhov and
V. F. Nefedov for help in carrying out the measurements with Ogra. Fruitful discussions of the experiments and the
results of the calculations with colleagues working with Ogra were very helpful in determining the physical pattern of
these effects,
LITERATURE CITED
1. A. A. Vedenov and R. Z. Sagdeev, Collection: Plasma Physics and the Problem of a Controlled Thermonuclear
Reaction [in Russian] (lad. AN SSSR, Moscow, 1958), Vol. 3, p. 278.
2. R. Z. Sagdeev and V. D. Shafranov, ZhETF, 39, 181 (1960).
3. A. V. Timofeev, ZhETF., 39, 397 (1960).
4. E. Harris, Phys. Rev. Lett., 2, 2, 34 (1959).
5. K. N. Stepanov and A. B. Kitsenko, ZhTF., 31, 167 (1961).
6. A. N. Karkhov, PTE, No. 5, 115 (1961).
7. A. E. Bazhanova, V. T. Kariukhin, A. Karkhov, and V. I. Pistunovich, Report No. 212, International Conference
on Plasma Physics and Controlled Nuclear Fusion, Salzburg, 1961.
8. G. F. Bogdanov, L N. Golovin, Yu. A. Kucheryaev, and D. A. Panov, Report No. 210, International Conference
on Plasma Physics and Controlled Nuclear Fusion, Salzburg, 1961.
9. U. A. Kucheryaev and D. A. Panov, J. Nucl. Energy, Part C (in press).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to.
cover English translations appears at the back of this issue.
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SCREW AND FLUTE INSTABILITIES IN A LOW-PRESSURE PLASMA*
B. Lehnert
Royal Institute of Technology, Stockholm
Translated from Atomnaya Energiya, Vol. 14, No. 1,
pp. 82-91, January, 1963
Original article submitted October 4, 1962
1. Introduction
Under certain conditions, a plasma can be confined in a magnetic field in the directions across the field lines.
In the particular situation where the plasma pressure is small compared to the magnetic energy density, the magnetic
field is only slightly affected by the plasma and will become close to a vacuum field. Any transverse plasma motion
which produces noticeable distortions of the field would then increase the field energy far beyond the energy content
of the plasma. Such a motion therefore becomes energetically impossible.
However, even in a low-pressure situation there exist other types of motion by which the plasma may escape
the confinement. For these types the particles drift across the field in a way to leave the latter unchanged at the
same time, i.e., without producing any electromagnetic induction effects. The mechanism which makes this possible
is due to an electric field and an associated transverse drift which arise from a charge separation in the plasma.
There are two ways in which this can be established in a plasma of nonuniform density. First, a separation oc-
curs when the density distributions of ions and electrons drift at different speeds across the magnetic field, at the same
time as there is a transverse density gradient in the plasma. Such conditions prevail in the "flute" instability phe-
nomenon first discussed by Rosenbluth and Longmire [1].
Secondly, a charge separation will also occur when the ion and electron distributions move at different speeds
along the magnetic field. Then, there should also exist a density gradient, both in the longitudinal and in the trans-
verse directions. An example of this is given by a "screw"-shaped disturbance which may become unstable on ac-
count of the longitudinal motion. This phenomenon has been analyzed in detail by Kadomtsev and Nedospasov [2].
Further discussions on the corresponding instability mechanism are due to Hoh and Lehnert [ 3] and Kadomtsev [4].
The purpose of the present paper is to treat some simple cases which demonstrate the close connection between
the screw and flute instability phenomena. The paper also gives a survey of different mechanisms which influence
the space charge formation, such as drift motions from gravitation and centrifugal fields and from the magnetic gradi-
ents, effects of magnetic compression and Coriolis force, and finite Larmor radius effects. A short discussion on the
influence of viscosity is also included.
2. Starting Points
The present analysis is based on the following conditions:
1. A plasma is originally assumed to be in a stationary, unperturbed state where it is confined by a static mag-
netic field B.
2. Possibly, a stationary gravitation field g = ?V clIg will be present, and the plasma may rotate around an axis
of symmetry at the constant and homogeneous angular velocity O. We limit the discussion to such configurations
where .g is perpendicular and fi is parallel to B.
3, The angular velocity la is much smaller than the gyro frequencies toi = eB /mi and We = eB/ me of ions and
electrons (mi is the ion mass and me is the electron mass).
4. In the unperturbed state the plasma is uniform in the direction along the magnetic field lines. The surfaces
of constant density and of constant particle energy are perpendicular to to the centrifugal force arising from 0, and
to VB in the cases to be discussed.
5. The center of mass of the plasma is at rest in a frame which follows the unperturbed motion. Ohmic
*This paper is presented by Academician Kh. Al'fven (translated from the English).
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dissipation is very small and can be neglected as far as the motion of small perburations of the equilibrium state are
concerned.
6. Superimpose small perturbations on the stationary state. The densities ni and ne, and the velocities v i and
ye, of ions and electrons will then be changed from their unperturbed values, nio = neo = N, and vio and v eo. The
perturbations become 1 = ni ?N, e = ne ? N, = vi ? v in and Ve = ye ? veo. Analogously, the pressure tensors
are Trio and ire? in the unperturbed state, and ri = ?rip and Ire = Ireo + ire in the perturbed state. Finally, the elec-
tric field changes from its unperturbed value E0 to E = E0 + t. The perturbations are small enough for corresponding
nonlinear effects to be neglected.
7. The gyro periods 27r/wi and 27r/we are assumed to be much shorter than the characteristic times during
which the perturbations change appreciably. Likewise, the Larmor radii ai and ae of ions and electrons should be
much smaller than the characteristic lengths L c of the perturbations.
8. The particle density is high enough for the plasma to become electrically quasi-neutral in the sense that
1 ? rie 1