NUCLEAR FORCES ABD THE THEORY OF THE MESON

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100030001-7
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 60
• Document Creation Date: December 22, 2016
• Document Release Date: June 1, 2012
• Sequence Number: 1
• Content Type: REPORT

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UsP1 KM ' Ftx N$LC, N? t, 19417 Y. L. Ginsburg
Iatreduotion
.e bend, the pith of the neson ee ebeerved is oesaio rsye, and ea
,+'- , the ether had, the meson theory of nuoloer re. Both of these
divieions of the theory era far from fsnished egad are still beige
`f.
worked out, in spite of great diffioulties. It is therefore
*Lstt~r* theta final. atatement eannet be ode en this wb~eet~ ?ur
I
bpurpese is merely to eluoidete its present state. (This ertiol? was
w ritteu Sept 1946)
n
At preeent the name meson or neeetron is given set only to the
very beav~- partiolec observed in cosmic rays, but oleo to the numerous
hypothetical partiolee whose waeeeo lie between the meeeee of the proton
and the electron. We shall ties the term "meson" to epecify when neoeseary
what sort of partiole (hypothetical or observed) ' is tinder discussion.
Mesone were discovered in cosmic rays in 1937 i7; the hard con
ponent6of oobraic rays at sea level or 1!a altitudes are baeioally oom~
posed of duet these partiolee. Moreover, at see level the meson hard
component amounts to about 70% e1 afl the particles in eosuio radiation0
finder lebore?
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The meson theory conprehenda ell preblend oonoerninr, on the
50X1 -HUM
50X1 -HUM
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no et ?ttng point.
o~ssukl~Pd
/.lo e4'c7'r'/ mp(stsJ tiafi ~
2. The mass of the mesL is approximate]. (m~ 200 m0
n\ ~
where mp le the mane of the electron. The most frequent
values of m lie between 150 mo and 250 mo. hence, in any
ace the overwhelming number of very heavy particles of
ooemio rare at sea level have, a maee elose to 200 mo; the
hypotheeie that the majority of particles have only, one value
for the mass does not seem contrary to exper tment,
3. 'The mee 14e % spontaneously, and the It fe h "
in the estem of+ aoord natee bed with it egp4,4 .' Li-
a
f~ r i I~ru~ f~l ~r :'
~ -
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tol9 condtttons, ae far eaAknowx, meeo a have not yet
been obtatned. The study ofe properties mesa
in r~osmtc ra71 is rendered dtffieult by many circumstances,
the first of which is that any large quekttty of soft particles
ie lacking in them. Oonsequently, in spite of intensive
experimental work, a whole series of basso characteristios
had not yet been established for the mea . Moreover,
it is even impossible to affirm that only one sort of very
heavy partiele?mo2); is the epr of a positive
i
meso~a; Z is the atomic number of the substen i
9s Set ton (in tsystem of
coordinates where the nucleus U
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o ert of aaturition. This means that tho
~
tiolee and hathe ~ p Y
energlr connected wigs a large nvcaber A of nuclear pertiolee m oressee
is proportion to A, not to 1R a a ha pc~-e ~ for inet'no e , in the oaeo of
A
tom of obu,rges. For this reason, the volume
CoulOIab interaction in a eye
of the nucleus is approximately oPortional to A , in contrast to the atom,
~'
whose dimensions are but 4ightll depeAdent upon Z.
The problem of the theor7 of nuclear f oreee obviously amounts to
the abovementioned quslitative properties of these forces and
expleini~
to establishing the relation between the various nuclear dimensions
measured experiment For quantitative proof of the theory, data may be
~
neutrons, and deuterons (oaloulation oft the
used which refer to protons,
of its extreme complexity, is not interesting
heavier mole i, because
'
from this standpoint). The following points are known by experiments
de on equals 2.1$ mev 7; the quadripole
the energy associated with a
.27 2 see ~ for example ~ 7);
-
moment of the deuteron Q .'"~ 2 .7 ? 1O cm
rotor-neutron and proton-proton scatterings
the constants cba,raoteri,sing P
in a broader son~e, the theory of nuclear forces
(see i5, Taken
also includes problems referring to separate protons and neutrons and
.
their interaction with other particles. In this experimental field,
values are known for the magnetic moment of a proton :c2 and a neutron
fit ,~, ~ : 2.791 and, '/ ? ?1.93,7a, nabere
T. reet~eotively equalin
direction contrary to that of the spin; that is, to proper meenaxa.aa
a
nea~tive.ei n of4 a magnetic moment signifies
? 2-o t this moment is in' a
th
~i-o
ton. ~
., - .' is the nuclear magneton and ~I is the mass or a pro
k
momen t of the neutron.) In addition, we know the
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 oonetante of bets-deoay in various nuolei, whioh permit one on the baeie
of certain hypotheses (eee, for exsmple, ,of f ) epprexi+ ste1yv to eeoertein
the lifetime of a free neutron, whioh must fins11y be converted into
a proton plus an electron plus a neutrino. To this set of probleme,
must be referred the interaotion of nuclear particle. with meeone
(eoattetriag, pair-produotion) and of meeone with light pertiolee (deoay
meeone).
Inasmuch ae nuclear foroee oleo act between uncharged neutrone, it
is general) y considered cbvioue that these foroee are abeolutely separate
from eleotrmmagnetic foroee 19uoh s viewpoint ie not neoeeearily true,
since it ie conceivable that nuclear foroee are explained by the epeoifio
properties of the motion of partiolea of spin 1 in an electric field
Ii??. However, the existence of non-electromagnetio reactions, evidenced
by the very foot of beta-decay and many other oonsideratione, foroee us
to think that nuclear forces cannot be reduced to eleotromagnetio
foraea and that they aro explained by the meson theory, as indicated
in the introduction.
The cleesic form of the meson theory is especially simple and
graphic. It utilieee the concept of a non-guanticed meson field.
Moreover, the detailed classic scheme has not only an illustrative, but
a completely real ', importenoe, einoe in a static approximation, where
the state of nuclear particles is assumed to be unchanged, the results
of the classic ad the quantum theories coincide 1, 1 7. The
situation here is the same as in eleotrodynamice where the Coulomb
2 ,~C. ~~ AA:' Z"
interaction -
J'
r
CJ?
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1
e
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~Ia the static ogee whioh interests wi .qation (2) ie aennrt.d
itaI~r* p and the d.aeity of the "seaos olurgs" egwle rS'(r -
share s'o i~ the position or tha r-u~len2' p.rtiole. Hence thA oquatte~-
for the field takes the toriiu
12 (19)
Since the poeition of a nuclear particle ie oflhide2'Sd fixed, it Ii
clear that it ie eonaidered sufficiently hear, and hence c*p.ble of
classical dv-ription. Let rote that in tho quuaat theory we have
ds
for the general case of a non-static scalar fields
where Duet be regarded ae au operator and where leis ie a Dirac
of ie connected with the fact that we
matrix. The emergence
oousider nuclear particles to be in conforaity with Dino to equation.
Let us note that on the right eide of equation (20) one more term ie
(
oDitted which contains derivative of +. u.functions and ie proportional
to a constant factor independent of g.)
The eolution of equation (19) ie ae follo~rss
l 1 ~, (21)
Utilizing the expreseion for the energy of the field, we can
ld and
fi
t
,
e
ing a
demonstrate ' that two nuclear particles crea
a,+~at tLS- 'i'
MM1MIIMIM~'VWtil4ir-I"r
situated at a dietance r, are attracted The scalar el a e a o
approxiaation is similar to Newton's field of gravitation, to which formal
traneitiom is made by setting )( equal'', to zero. Hence it ie clear that
rtiolee are attrao ed (eee
ale0 ilk the scalar theory of nuclear forces pa
remark below on the aesumption that a eoalar field is not charged.))
?RI:IMin
S~F,f;C,~vi
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car from (22), io of' the order
The radius of the foroar, at ~.~
A gnantt~ theos~ . (see ~ 1), 'we thus obtain
th
~. 8inae in
ss
x e radiuw of the fereee s1It the ma e! the
a relation (1) beto0en ~' green
did riot dram any dietinatione bo
upon. It ebould be noted that rro
done only if the rield ie not
tone and neutrons. This se~ be
the ~rt3ateo aeeoaiatod pith it aro n0
ohar ed~ ands oonaequent~', tb,
t
ttoe Thie eub~eat mill be taken
obareed (u
sutra/ mesons or Aeutre ) . up later.
22does not do 'cn or the reciproaa
The interaction of (l orientation
~ ~,
this ie oantrary to the ree't~t o
of the e~+ind of nuclear Fartialee; nce
toroee
ent. In order to olar~'y the problem of nuclear 1 depends
experin
on of Protana and neutrons rich
upon spin, let us examine the inter$Cti oloeely
? theory in this isaetance ie very
a neutral vector field. Ev rY raio
and
allied with Conventional eleotr0d71ami0e beoomee electr0C1Y1
theory if ~ ie ,a,aAUmed
d pith the fact
e relation mentioned ie aesooiate
to equal aero. (The oi,oe
e vector field (the ,potential of
atrvd smite is also a theory of
that ele Yn rn
T
%
veotor)) . To put' this analogy it- a
e field d ie a f?ur?dimeneionsl
th k
m uationg for a vector f~.el$ (9~ in
more ' ual form, let ua re-rrite the 4q
the notations
another form, introducing
With this no Cation (23) , equation (9) gill take
,~
-
bone (2L' Will be trsnpf ormed
'
LIa. e
1 the.URUNl BXWell
tC
~
When : 0, aqua
true for equations (7) and (8),
lds
also ho
one for a vacu~~ Thie egvati
,,,hieh, in the new notation, become:
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((4FIDENTJAL
as
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Let us now aeeumf teat aualear parttele reate a veator
field, having a "meeo ehwrge" g and a~mea j m
meat" No w1 is the general nose of the quantum theory. ,
ir+$tead of (25Y J the following equattone"oonurt
Wtl l' M ~I ~1~ vu trn off' h$ Dtr theory a z.
In the stRtt' naee w~inh interests use
*rmegnitudes ? Moreover
L19a1
In (27) both the field. 4? and A and. the ve/tor of the spin C^~
c~nn be treated olassioeal~r,
is U follower
1x92
The s'lution~ of b~totem (27)
In eleetro&ynamir?s the energy of a parti"le w&4-
charge a and a magnetic moment ! , situated in the field
(4 A), equa1s,ec1m-(p.H). The form is the sane for the
J. II
intera"ti energy in the eaie of a vebtor imeeo f ield~ nweh.
. , . .'I f v
e eorrespond.
interaeti* energy of two id,entidal nw 1ear partir,1es
'
:. f rom
epine 9? end t , ae fcll~are
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tr~l IAL
rm
~
",?
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WUeri is ths radiuii-veotor of one of the artioles irirMi~a~-
*he other- The tbterantion a energies (29) roda~es
t
o
~tlM r"
in
h
f
,
e sp
t
to forces dependent on the reoipronal orient on o
I Ii
cslassic Ili solution of (29).
Considering the Vectors as operators makes no ,hang. in the
dirt, r dt~
ie the proper of the partir1o).
c ? (shun l
end also to forces dependent on the orientation of
the spine to r.
The vectors end ~p- are mss !nS "Iuaet-mW1etta"
i
~ p
~
moment e of nurtl ear past i vle e.,end in the tuantum theory the
vecttora are operators ?the well-known Pault matrt~es (L'o
2
c'
with solar and vevtor fields. Two other oases, when the
are
fte1de a Peeudo$"a1er end pseudoveetor tape (see ?1,),
4 Cc1# ~ r d to the
iaIt be etudiade similar and redue
enar of interaottonlexpre$eed by a linear ~ombtnatton of
the terms , t1 and. U (see (). 'hue, the general ex-
Above we examined the interaettoa of nw 1ear partirlee
preeeton of the meso n theo for inter~rtii~i energy ~t11.
take the forme
? /i3 U:o1U1.+ 02U2+ 03U3, (30)
??A 0 ere dertvativee.
where
Until now we have eoniidered the meenr field as '$lt
the eleotrou
11oh.r~harged; the t fisrcAewh a veetor field amore
m etic~ field on1r anountS to eying that the rest 'U
-M"
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since the reetM~e mass of a photon equals sero. We are study-
(ONFIDrNTL4L
' "gnaatwa esoa~1 field"--a meso r is equal to a ; o
in6 the c?utral field .i^arbb- bemuse of ibs grAater siapltetty
deeper oe*e#I &ttss.'i 'f the field is charged
(in this (ase, when it is quantified, ~eharged meeo ,ions corre-
epond i it), an expression of type (3o) is obtained also
for the Tories, but only in ease of the interaction of pro-
,
tone end neutrons. Bat for the nave of identieal nuclear particlee
(two proton. mid two neutrone) the interatt anerg t is equel
to cero in the ?pproximation under consideration. This re-
suit is Aompletely understandable from the viewrpoint of the
q 1t nttim scheme operating on the nonQept of an exchange of
l~
mesons bit%een nurwlear particles, sinne the proton is
ash napabie of emitting only a positive meso Psu, which
cen be absorbed by a neutron bust r,annot be absorbed by other
protons eto. Hence exange by one eharged meso~l In
b lw..n identirel nuclear particles oannot o4eu , ut an
occur between different nuclear particles. This explains
the character of1atera~tiener63r already mentioned.
U
Meanwhile, experimental data furnish evidence that
sa~eme developed here, this fact an only be explained by
proton-ptoton and proton-neutron foroes are of the same
order of magnitude, 1'!7'. Within the framework of the
e bo svoiA~l~iiliM assumption that ? neutretto eziets>
e?4xb I A.->
assuming that a neutral meeq,p (neutretto) exists. It ~o
only by theories rlr~inh oP er~t on the basis of ann exehenge
n ,
by paire of particles or excited charged states (see ? 3).
it
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it mu tube ibtaQ that the arguments in fator
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data do not contradict this assumption j.7!
cent experimental
Olarifioatton of the problem of the,euietence of neutrbbtos
is highly eeeential; the primary interest from this viewpoint
the stud of the "stare" in cosmic rays j,,7'.
obviously lies in
I laining nuclear dorces through exctengls y eertn
neutral mes s (?neutral" theory) ie not satiefaetory,
since in this way the
foroee end the behavior of charged mesone in , cosmi~
rays, as we1.14 as the
ins terent of nuclear partir1ee and charged ores oas also
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r
1
o
the neutrettoII1ed 'bY the al+usa whtrh leads to
nw 1ear fission, Tess rtatement$ fore'e us to sesame that
the nuclear fissions (altars") observed in cosmic rays mq
to a eoneideraible extent be produced by neutretto$. Pre-
of the ntatretto' $ extstenas b*I'Y a good ! wetit. But
in experintents .M, above a1, n ooemta ray uo definite
I ,
indiaations have U yet been obtained in Savor of the
of neatrettos. tf there ie really a nrutretto end b plays
an important pert in nucieear forces, its mue curt be of the
order of the mare of a nhaxBed mrro (this follows from (1))
~
end 1tec-:tnteae+etton with s iaucleuis must be reiativelY rtrong~
the(
whence it follows that in Berth' a atmosphere en appreoieble
number of formed, just as1 the Aase
e
neutrettor ~~
The reveres process should also be noted
chkrged mesQs
makes it poeeible to show - iT to etplain the enomaloue mag'
nett momente of a proton and a neutron (as we eaw above, there
momenta are not eq2R1 to a nuclear magneton for a proton or to
e neutron. This follows rom nire& s theory)l'1g,
cho for a ,
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I ?_v_ 7
one o her , r we might pat it that if the potential her s4ik
e ',tithe problem of the whole system
r 1 ,
of Stationery stags has no solution, To a oertain extent
this result is olassieal in tyrpe~ rinne in olassioal me"hanies
1 '
the potentials -2--TO) also 4j ,es to the fall of a par-
r
tirtle on t-e center (rer i~. it is easy to reanh this con-
,
nlurion by quantum menhenios, A particle cannot fall on the
center if ittr average kinetic energy in approsohing the venter
inosieai re rapidly than t~p average potenti
rl
, energy diminishes.
Moreover, h. nqe*n c ~einetiR ene rgy of a pertih],ely situated in
-
T~#1 ' - tm nst
_-i-i1 r rore renter equge T ^ -k-~
~
diminishes more slowly 1
~
wly than -he fan is im-
possible; but if T7s - (C,~ 0)' a `lower level will
r ~
not exiet, einc,ee when the region tiax ue in which tie
7
particle is situated
grows smaller its energy converges * ,
Of c?ourse, this also ..r the
problem
of two bodies"' ewe know, with relative eoordinatee li
1 1/
L
e in ~ ~
e by virtue oi~#i ' pp }
Whence it is clear thi t, if the~rvv.rage potenti energy 44. r
rl amounts to the iii. problem of the motion of one par-
ti clr in
w~
i
True, if in (30) 03 0, the problem of the deutron-
It is also impossible to assume that 03 0 without
gore ado; Jeinoe in all variants of the theory with one type of orb
the conetant 03 ie' proportional to 02 L5I7, Aenoe, in
assuming that 03 . 0, we leave in (30) only the term O V , which
ll
does not slow spin dependence of the forces this is contrary
t9 experiment. Tm assume that 03 ffi 0 while eimultaneouely
fi R'~k.~e~l'S
'
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CONl~IDENiIAI
rstainin~ G2 Qr possible only on the hypothesis that
1M-&Wdr* 4Mp
there ere at lean two types of .recces. Buoh a variant
e
of the theory, in which both ventor and pseudosaalar a~e~e-erire~rs rtr
uii introduced, a~hisved a certain amount of oiroulation 53,
,L7 , In it the symmetrieale theory was employed and,ie
m as a result of it all four types of v"~''w~re were intro-
dunedt iteutrel(veetor and pseudosealar) and charged (veotor
and peeu~dosce1ar). The masses of veotor and peeudoecalar
partiA1es may differ j7. Aside from the fast that the intro-
duration of various types of '-eee4rees nausea a feeling of dis-
leads
satisfantion, the theory u to diffioulties w'hinh make
its sooner eo cclu .f the term with J- 1 merely an illusion.
/" r
First , the` type term is eliminated only irln a static
r3.w
approach sppea i with corresponding oomplier tions ski .v..
,
nonetatinA+ +r J527. Secondly, the theory leads to a ear-
y
tain result 4 direh~oontreint to experiment; name/r, -LIULk
-
it follows from the theory 53, 54 tithe
90?
on protons must be stronger at" t c angle
close to zero (in the eoordinate eyatem
of neutrons
than at ern angle
where the proton is
at first at seat). But in ex~eimentin th neutrons with
energies higher than 10 MeT, when the effect of asymmetry be-
moms marked, a reverse dependence ~,s ~beerved L557.
'
even
Third and lastly, if the indbaated method of a&iminating
the term with irr3 enewered the rpoee of the theory of nunlear
;) e
forces, it would not permi (Ciminati the other, no less
important diffi m ty" connected with the ftret one. T~ tart b 1 s
~-
that...ettt ~of the ? of ?~oa~- proton-neutron
leads us to the nonelusion that, if there is rhea r- asiLWw
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a " 4aae5magfletio" ~%oment f//I (see above) in a beev r particle, the etfeotive
roes seotion for scattering would grow with energy without 1t t.1.'
0
W which is inadaiseible. (gore aoourately, u31t dted growth of
orose section with energy' oontradiots the goueral position of the theory
only under certain sdditie2aal oonditione j7, whiob, however are
satisfied in the oseee of interest to ua.)
Thie very real difficulty, which we shall aoanider further under
I :ie not elimizaated by introducing two t9pee of meaone, beosuee either
type of meson may be eoattered independentll7 of the other; and because
9thth c a ^ A) , this eoattering will iacreaee without limit witb
energy, Hence , the noombinatiortP"t trios/" theory of
Rosenfeld /?j, 9ohwinger/51/ and others is uneat ief a ctorp for a number
of reaeone.
Anot~er group of vsriante of the theory of nuclear forces was based
on outt5ig " an inadmieeible potential of type 1/t~. This meane that
"
the expreeaion for the potential 4/r3 ie considered true only up
3
to some eoattering of roe when r4,, this potential. ie "out"; that
ie it ie replaced by some other potential whicb dose not contain an
insdmieeible feature, fcr example, by the potential U ^ a covet. (
when r r) ? The "cutting" operation hue a foxrmal character 4 it ie non-
~ o
relativietic and can be justified only because a complete and exact
theory leads automatically to eome change, or cutting in the potential
(or even a deeper change in the entire ordinary eyateai o4' the intro-
duction of nuclear forces) (eee jand 3)? Cormeoted with "cutting"
ie the introduetion
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H
of a nea eoaetaat r? or, more aoou1'Itel7, a dew funotien `~~rheA
r < re. At first glance it night seen that eith sA srbitrs ohoioe
or 11(r) any results might be obtain?d, However, thin is not t ruo, since
the value of ro should not exceed the radius of nuclear forces ___?
aao
and the tort o! the punotion U(r) on ar~y reasonable hypotheeee has no
very pest effect on the results After the "cutting" and com-
pariaon of the oslculstiopis pith experimentsi data, it ie possible to
exclude..dbrts in theoretical possibilities. Thus the " euny~etrioaln
theory with oertsin vector (charged and neutral) meeone , 77 proves
unutiefsctory, einoe to Obtain oorreotly the level of a deuteron and
the arose section for neutron proton scattering it is neoeeeary to
aeeinre that re ' b? and that the prinoipal sign of the quadripole
Sao
moment of a deuteron proves incorrect, but its value ie sprroximately
10 times greater than the value observed, (The quadripole moment of a
deuteron hie a positive eign LZQJ, which oorreeponde to the elongated
oiger-shaped form of the deuteron ) On the contrary, the "neutral"
vector theory ie in good agreement with data on deuterone5J. However,
as already indicated, utilisation of aome neutral meeone is uneatiefaotory.
Bee des, it is obviously entirely poeeible in this scheme to introduce
additional and relatively weak proton-neutron interaction with a charged
meson. A similar variant of the "urieymmetriosl" th ttr (vector neutrettos
plus charged mesone), although known to us, waa not verified. A similar,
but in some respects simpler end more attractive variant of the "un-
eyatmetrical" theory
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 ww, aLr
diffinu1ty under eoneideration obviots11TUb 15J
(in L117? f2/A0.01, but in the "e1mmetrica1" theory, for
1 ?~
iaetarnne, f2/( ,O.].). In additioa, of course, eves the
ti
rec~proc~ally coordinated cutting of ezprisgione for the
potentie~1 at d hs*WSi4eti is a very slight su~cAees and
for the moat part, only shifts the problems center of
grRvity to the field of the "cutting" operations. with in
4' .,
based on the etudy of non-etatie foreee~ the' relativistic
viouely die"useed, there is another to Bing poeeibliy L3-
1
the general ~rnmerk of the theory of nuclear forces, pre-
a neutral mee jk ie considered scalarA a rhargedmPieudo-
f.AR
efferte. Thie theory is ~!6IWnmetricaland in it as in 1332
Vm' 0 in (30) equale Q the !! f r3"difficulty disappears
I v 4M-
that it ie abeeht in the ~relativietic approximation,. ' Since
eealw. The eeeential difference ie that the interaction of
a paeudosralar meeo amt a proton?neutron ie co
In the relativistic approximation, however, the charged
meson ronditione an interaction which appears to be very
important. In ite qualitstive aspect Tatum' a theory agrees
1AL
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section. Bush a .t1 5oint mey be considered admissible
n
if *ka "euttingN co'sentions is necsesary for wave lengths
less than the radtus of "cutting", for a potentis1
mer n ^ i'
o
ra#;1rA*,, that is for energies g me
~
This doe. not take place in the "ehargel" and "sym-
metridal" theories and the nroes section appears to be
w
larger than that observed when !iaa2 5~, 7, In, Hul-
h nunetr c l" theory, in view of the comparative
thene s " Y
2"\1 weess of the interaction with 'charged partiales~'\he
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Ai we s w in Md 2, the theory of the meeo and
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with the basin experimsntal data. xt is .loo tho only
scheme of the tarp. under discussion aVtbh has no serious
interned ddiflinultie$, suoh u "nuttinI" the potential and e,Jt..mI
section It meet not be forgotten thatj.ntity and
&neurAoy of the Leta now at hsnd on . system of two aunlesr
, '
partials .re such that azy- theory of nuale.r fortes feass
. serious quanti.ttYe test, Tor this reason, until quanti-
tat the a e1AU1 at ions have been made,?itht+h ks. net ys
a more detailed tondideration of Temm's theory
b pxemture.
r _ .
y?slae th. tIli8ri83 ~.110adY ?rminedr based on
ns in regard to exchange one mes I~Ni W'
integral spin, an effort has been made to a onstrabt "pair"
theories. In them a proton end neutron are ?xc~hanged th ar o-ri'tL
EOl-;t'Y a pair of parttrlee of different aigne whet
s i,n and 4 mass of the order of 200 m0 L?, 61, ka*
Bch theories, also involving difficw~ltiee, woul, d in or
9
opinion only be( Ome i~ ntereetin~if the meeo spin in
bl
b
e.
a
coemin rays ?qua3J i'. At present it is more pro
that the meaoNNM1n spin is an integer and that
an electron and neutron fly off. A definitbve, experimental
olarifkeation of the problem is extremely important.
There Si'. also "patr" theoriee working on the
?x~hange a pair of particles t~4a. integral spin t eee,
for exantple, L1J ). Theis ~heue~;bern,no~~i~te~ceabiag~ re~
eulte along theee lines.
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With dStPiovltiae or the eeoand olaaa~ on the other hands 4s'.
the very first aon?sere a pproxi^
*stion of the perturbation theory leads to inaorreet results (a1ietite4
gzorti of the oroea 'eetion) . Moreover, either there ie n' eolut be for
the problem of the motion of pertiolee in a Coulomb field (~ 1) or ee}"'
" miscible" 1/t3-type potential mekee ite appearance.
Anal is shows that the spreoranoe of "difficulties of the second
class" ie oozteoted witb the preaenee of a mwgnetia ("quaeimagnetia" )
moment in a particle or with the fiat that scattered partiolea are
ohsrged77 . We ear in 8 1 that the oroea eection for light oc&tterire~
o~
particle of epin } increaeee without limit if this particle baa a
"true" ma etic etoment, - o (ace (U)). The inoreaee in the oroea
eection for light ecatteri by a particle of apin 1 is also conrieoted
with the preoenoe in it of a magnetic moment in a relativirtio apprcxi-
mation 1Z, f.7. Furthermore, the inctrease in croon section for meson
aoattering by a proton-neutron takes place if the heavy particle has a
"qUaeimagnetie" moment, described by a term exactly like the tenet with
in 14 . The fail of particles of spine 1 aria and 1
,u1
toward a Coulomb center is oleo }produced by the presence of a "true"
magnetic moment, by virtue of rhich the df fective potential appears to
have the form -1 . (V1e speak of a "true" ~aagnetie moment as diatirguiehed
r~
from the magnetic moment of a Dirac electron, which does not appear in
an extremely relativistic approximation). Finally, the appearance of
this potential, -1 ' in the theory of nuclesr forces is
r~
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 CONFIDE! 'r
ooriaeotod with the "quaeiragnetion noment. Thir ie already eWioua from
tbi loot that the ?aergy Of iuter~otian of tea nIkgnetio momeabe /U 1
and ,U 2 in nagnstostatia? oqurls:
Been to be of a clansical nature U, 67737. Let ue treat this
(31) if it be aeeumed that'( 0; that ie, m . A, whiab exactly aorree-
gonda to oonvereion to electrodynamics.
"Diffioultiea of the second claem", to which reference has alread7
been made, also arise during the scattering of charged meeone, of the
vector type for instance, not 'by the moment, but by the "quasielectric"
charge of a heavy partiole. In this event the unlimited increase in
eroee eeotione ie eauaed by a decreaae in the number of intermediate
etatee during acattering. The latter is connected with the fact that
a proton can only give off a positive meeon, while the neutron can eject
only a negative meson g, 69/.
At least the main "difficulties of the second class", connected
with the presence of a magnetic (or "quaeimagnetic") moment, are easily
other. The "unpermieeib1e" potential U in (29) ie into
where r ie the radiue-veotor of one of the particles relative to tho
As we know, the olassic non.-relativistic equation of motion for
moment ies
magnetic moment.
problem in more detain beginning with the scattering of light by a
where 8 ie the angular momentunn of particle and
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 Declassified in Part - Sanitized Copy Approved for Release 2012/06/01 : CIA-RDP82-00039R000100030001-7
,,1/i$ its m~gnetio moment ebich ie natally oonaidsrad aqua/ to S 8,
where $ 1e a oot-st~nt.
After exkmiJniag the aerttering o~ light and ~~stii+ing that the
itie1dHeqi10e we alw3.7 3'iad ,`3J tit the elfe+otive
or.ee eeotion !or this rroosae equsles
~; 2 (33)
that is to eay, it inoreasee without limit with the T. fregUenoyq o
,
t' exactly ae in quantum eelc1aticsne hg thmet-bod of the per-
r ,
turbation theory. The source of etch a eituation is readily under-
stood. If the field H it (32) is asetmed to ec~uai the outer field of a
fal] inH Rave, then the claeeioal calculation, mentioned above, bntirely
cerreseonde with the quantum mechanical calculation in the f iret non-
zero eppreximatioo- of the perturbatic'n theory. Meanwhile, in the eetee
of (32), the field H must demote the whole field, equal to the aum of
the field outside and the proper field of the magnetio moment. Cal-
oulation of the proper field ahowa that, if H in (32) denotes the
outer field , it is necessary to write this same equation in the
but
forms
I + 'J L (34)
is the effective radius of a particle of momemt , S (by the
where ro
elaaeiaal eleotronie theory, it to impoeeible to examine a point par-
ticle ainoe for point articles the second term on the right side of
becomes infinite just as it does with regard to the electro-
formula (34)
magnetic mace of a poixit charge).
(ONFJDENrl
G~ 6
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 Declassified in Part - Sanitized Copy Approved for Release 2012/06/01 : CIA-RDP82-00039R000100030001-7
The final term to (34 ), an anala of force
of radial frtAtion, dieturbe the iss.eam+ of the equation
and we sho11 not examiae it. mquation (34) M!ven without the
'/tra a 4 ri' final term involtes a~eention whicb,._ frequencies, takes
~
~
the form of X33) but is nonstant ? frequencies
Moreover, if for the sake of agreement, it be aseumed that
e~
9t 4 .. nd r I, the condition requiring smallness
mc2 o mead
frequenoee means that
-, 'v .. _ pd.uor tng o
e equenc f !stet be eonlidered large ~ W the tnverse r-J
I
(ty~me2). In this wey the proper field of a
magnetic moment is naloulated wording to the olaaeieal
c
theory for ~ei~imjnating ?diffic~ult~r of the second e
connected with of light 'that moment,
The energ~r of interaction of two magnetic moments takes
the form of (31 he 1jr3 type, it is clear from ! that
in the elaeaical theory the motion of a pair of magnetie
moments will be limited; their fafl, one on another, will
of nu' only if no energy acyss~1 is aa1c fated except the
potential energy and the k444d energy of orbital motion.
When the action of the proper field is disregarded there is
energy dependent on r. But a oe