THE MASS OF NEUTRAL MESONS

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• Collection: General CIA Records
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• Original Classification: C
• Document Page Count: 3
• Document Creation Date: December 22, 2016
• Document Release Date: October 19, 2011
• Sequence Number: 602
• Publication Date: June 11, 1951
• Content Type: REPORT

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CLASSIFICATION CONFIDENTIAL CONFIDENTIAL
CENTRAL INTELLIGENCE AGENCY REPORT
INFORMATION FROM
FOREIGN DOCUMENTS OR RADIO BROADCASTS CD NO.
SUBJECT
HOW
PUBLISHED
WHERE
PUBLISHED
DATE
PUBLISHED
LANGUAGE
Scientific - Nuclear physics, mesons
Per? ^,i.ical
Moscow
11 Jan 194?
DATE OF
INFORMATION
DATE DIST. // Jun 1951
NO. OF PAGES 3
SUPPLEMENT TO
REPORT NO.
THIS IS UNEVALUATED INFORMATION
TNIS DOCURINT CONTAINS INFORMATION AFFECTING THIS NATIONAL DEFENSE
OF KS UITID SATES WITHIN 50
U. ST C., ]NAND ]!T AS ANE VOID. T ITS TRANSMISSION O ESPIONAGE
1! FRO?
R TN! REVELATION TO A NISITES STTLAN. 1 RlFROOUCTION OF THIS FORE OISI PROHIBITED.
Doklady Akademii Nauk SSSR, Vol LXIV, No 2, 1949, pp 199-201.
THE MASS OF NEUTRAL 14 ONS
A. Sokolov and B. Kerimov
Sci-Res Inst of Phys
Moscow State U imeni Lomonosov
Submitted 20 Nov 1948 by Acad S. I. Vavilov
As is well known, the theory of scalar mesons leads to the following law
of interaction between two nucleofB., that is, between protons or neutrons:
U = - g2Rr-l.e-kdr, (1)
where g is the specific nuclear charge and ko is connected with the mass ?
of the meson by the relation. ko = 2 .wpe/h.
. Formula 1 cannot lead to the spin noncentral forces acting between the
nucleons. Along, with the scalar mesons, we can introduce also'pseuda.calar,
vector, and pseudoscalar mesons.
In the general case, by combining the various meson fields we obtain
the following static law of interaction between two nucleons:.
U ? (g2 + f2(~1c2) + f1, 10)(sT2v)) Oe k0r/r. (2)
As a rule, the constants g, f, f , ko are so selected that one obtains
the correct values for the energy of bond and for other quantities in the
deuteron problem or in the problem of the scattering of one nucleon on an-
other.
We shall show that we can arrive at a determination of these constants
by investigating the equilibrium of a system consisting of~ many nucleons.
(D. Ivanenko and V. Rodichev were the first to determine the mass of mesons
from the condition governing the equilibrium of two nucleons -- the. deuteron
problem. See their artier, is Zhurnal Eksperimental'noy i.Teoreticheskoy
Fiziki, Vol 9, 1939, p 526.)? For simplicity's sake, we shall limit ourselves
merely to neutral mesons.
CLASSIFICATION
a
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CO TILDENT3 r
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Then, rejecting dipole terms proportional to fj which cannot give a sta-
ble state, -.re find by employing the Hartree-Fock method that the energy of
the system of nucleons comprises the kinetic Va: T of the nucleons, .the
potential energy V?, and the exchange Disregarding surface effects fLnd also Coulomb repulsion, we obtain for
the kinetic energy: 4/3 5/3 2/3
T = (30/502)(3/410 ?(iA),(2/n) , (3)
where M-is the nucleon's mass, R is the radius of the system, A is the total
number of nucleons, and n is the maximum number of- particles which is able
to be located in a given energy state (in our case we have n u 4; namely, two
protons and two neutrons).
orgymall values of R
In a similar manner, the law of interaction for
leads to the following expression V? = 3g2A2/2k2R3. 1/3 (4)
Finally, for the exchange energy we have, when R ? (2/ko)(91rA/2n)
the following expression: 4/3
Va I(g2 + 3f 2) (91rA/2n) (n2/3 2R) + yin(g2 + 3f2)k0A. (5)
Tn the other extreme case, when R >> (2/ko)(91A/2n)l/3, we have:
Va = (0.75A2)(92 + 3f2)/ko2R3. (5
Introducing in the place cf R thegfollowing dimensionless quantity x:
R = r0A '?x,
we find for the total energy of the ystem of nucleons f"he value
E = A(ao - a1/x + a2/x2 + a3/x3), (6)
ao ko(g2 + 3f2), a1 - (3/w) ?(3/4)'(g` 3f`)/ro (7)
a2 = (3/m') 4/3.3h2/16OMro, a3 = 3g /2ko o?
Taking into consideration the conditions of equilibrium DE(x)/Dxl
and also the relation which must agree with empirical data on mays defect,
one observes approximately at the position of equilibrium the relations:
so - alt a2+a3 a2; ana hence so = 2a3, a2 = -(a1 - 3a3).
Hence, one can conclude that the mass of neutral mesons which leads
the equilibrium of a system of nucleons cannot exceed the value 130m, where
m is the mass of the electron.
In this. manner an investigation of a statistical model possessing well
known boundaries permits one to indicate the upper limit for the value of the
possible mass bf a neutral meson.
Calculations of the noncentral forces proportional to f2 and also calcu-
lations of surface effects or of the development of forces between protons
and neutrons can hardly be sufficient to change basically the theoretical,.-,side
- 2 -
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CQF~DEdT9l
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C-DF~F~DEDTIA1
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of the picture, although the limiting value of the meson's mass can be some-
what different. That is, considerations of these forces, basic ch were
reudisre-
garded in the previous derivations, can?hardly- change' picture.
in this connection interest has been recently-shown toward tie spon-
taneous decay of heavy-charged ir-mesons to charged u-mesons`htd neutral
mesons whose mass cannot exceed 115 # 30 m. This .decay?was- discovered by
Powell's group in thick photoemulsions. The decay of mesons was confirmed
also in the well known experiments of A. Alikbanov and A. A1ikumyan and
of others.) Recent photographs of Anderson and others also; show the decay
of mesons of cosmic rays with a mass of 200m to electrons and neutral
mesons whose mass cannot exceed 130m. It is possible that it is exact'.y
these neutral mesons that play an important role in nucleonic interactions.
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