NUCLEAR FORCES AND THE THEORY OF THE MESON

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100020106-2
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 41
• Document Creation Date: December 22, 2016
• Document Release Date: April 6, 2012
• Sequence Number: 106
• Publication Date: November 1, 1948
• Content Type: REPORT

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de on this subject; our
not be ma
natural that a final statement can
purpage is merely to elucidate its present state. {This article was
~
, r tten~ Sept 1946).
to the
eent the Qame meson or mesetron ie gi98n not only
t
pre
A
t~
rays, but also to the nun~eroua
heavy particles observed in cosmic
very
t
n
o
articles whose masses lie between the masses of the p o
rmthAtiQal p
h
y
7
SU
e
_
ce
and the electron. We shall use the term "meson" to specify when n
,~} t thetical or observed) is under discussion.
e~l~nt, sort ?f poi ~icle {jl~pO
diac?Tered in cosmic rays in 1937 /7; the bard coin.
Mesons were
en lode/ or lour altitudes are basically coin.
ponenttl~ of cosmic rays at s
rd
h
a
Moreover, at sea /errs/ the meson
,,.,a.d of just these particles.
tion
di
a
ra
component amounts to about 70% of all the particles in coamia.
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F'
Uspi KH i Fez 4',m, iv. x. "47 v. L. GiriebUrg
Introduction
' e
The meamn theory comprehends all probleme concerning, on th
~- - one hand, the path of the meson as ebeerved in cosmic rate , and em
, , the other hand y the meson theory of nuclear forces. Both of these
~
are far from finished and are still bed
r divisions of the theory
norked out, in spite of great d1TI1cw.'d. P ---
50X1-HUM
50X1 -HUM
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Cory conditions, ae far as known, mesons have not yet
been obtained. The study of bhe(~ropertiea mee ; ~
in cosmic rays ie rendered difficult by many Gircumatancee,
the first of which ie that any large quaiktity of soft particlee
is lacking in them. Ooneequently, in epite of inteneive
experimental work, a whole series of baeia rheracterietiee
had not yet been established for the mes p . Moreover,
it is even impossible to affirm that only one sort of very
heavy particle, ran be observed Ln cosmic raye,pr to say.
whether there are i very heavy particles with a single
value of th~;ny',r,..ri".;.M~^~r1
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 constants of betty-decay in various nuclei, which permit one on the basis
of certain hypotheses (see, for example, ,/) approximately to ascertain
the lifetime of a free neutron, which must finally be converted into
a proton plus an electron plus a neutrino. To this set of problems
4 must be referred the interaction of nuclear particles with mesons
(scattering, pair-production) and of mesons with light particles (decay
mesons).
Inasmuch as nuclear forces also act between uncharged neutrons, it
is generally considered obvious that these forces are absolutely separate
from electromagnetic forces. Such a viewpoint is not necessarily true,
since it is conceivable that nuclear forces are explained by the specific
properties of the motion of particles of spin 1 in an electric field
?J. However, the existence of non-electromagnetic reactions, evidenced
by the very fact of beta-decay and many other considerations, forces us
to think that nuclear forces cannot be reduced to electromagnetic
forces and that they are explained by the meson theory, as indicated
in the introduction.
The classic form of the meson theory is especially simple and
r ,I
, i,~ A r i .
~t~,llr!w. ; /
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graphic. It utilizes the concept of a non-quantized meson field.
Moreover, the detailed classic schome has not only an illustrative, but
a completely real importance, since in a static approximation, where
the state of nuclear particles is assumed to be unchanged, the results
of the classic and the quantum theories coincide , 7. The
situation here is the same as in electrodynamics where the Coulomb
w
2`'
interaction - ~,,,
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din?,`= o tained ae a result of examini`h exchanges . .
LJ. The use of 'static interaction is justified when non"-
. 2
static, teaction is disre-gaxded~ i&n
f/i
)A4
admieeible,pri the deuutjron theory (inasmuch as the velorttiee
of the proton and t~e ~s , ron in the the deutron are small as
with the velocity of light). r' Of course, for a more
complete and exact study of the problem of nuclear forces
it is necessary to utilize the theory of a quanb~r meson
field; but this refeks to t~ calculations of mesoten -dl*-
5~ t ~ tC' Y
f et3./ t nur;leat particles, etc.
1
Our intention in what follows is merely to explain
we shall only go into detail on the classical theory mentioned
(quantizing the meson field M appled,to the theory of
In classic~terlninology,the explanation df fluclear forces
is connected with the fact that protons and neutrons are
the sources of certain fields (meson fields), which
~G A
act on other nuclear particles provide an interaction of
forces? if the field is scalar,,in the absence of sources it
conforms
taa o equation (~). The presence of forces means
that on the right side of the equation there must be a
function which plays the part of the density of a charge
or current in electrodynamics. In this latter case) for a
point..parti&le . the current density equals e S (r
where is the. delta-function 8dr 1 0 when
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can 5i aken from the classic s theory, ee is ueuall
y
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to a constant factor independent of g.)
The solut:on of equation (19) is 's follows :
xJti1iing the express ion f `,x- the energy of the field, we can
In the atatft caae which interests us, equation (2) is converted
~
the density of the "meson charge" equala g- (r ra
4:_ 0 aid
into!. ?
iahere ro is the position of the nuclear particle. Hence the equation
for the field takes the form:
Since the posit~aX1 of a nuclear particle ie~ considered fixed, it ie
aidered sufficiently heavy and hence capable of
clear that it i~ son
on Let us note that in the quantum theory we hzve
classical descri.pti
of bktEL is connected with the fact that we
matrix. The emergence
where ~p11- ~ir moat be regarded as an operator and where is a Dirac
for the general ease of a non-static scalar field:
(20)
r~
ax particles to be in conformity with Dirac 'a equation.
consider nude a
derivatives of 1kL..furLctions and is proportional
omitted which contains
(Let us note tlat on the right side of equation (20) one more term is
demonstrate q that two nuclear particles creating a field aria
? m 6R 444J ) A
r.U. r `.'
rr
rvw.~~dwrwnyw.n....,,.....,..?Y r
~at~V
e r, are attracted (The scalar field n a 8
situated at a distanc
approXimatic)n is Similar to Newton's field of gravitation, to which formal
i~ made by setting equalto zero. Hence it is clear that
t
ion
transi
so in the e'slar theory of nuclear forces particles are attracd (see
al
remark below the assumption that a scalar field is not charged.)
do
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The radius of the forco~, taco ti c1etir.from (22), is of the order
1. Since in tho quantum theory . me ? (see 1) , we thus obtain
x
a relation (1) between the radius of the forces and the mass of the
meson. It should be noted. that ~'e CUd not draw any distinctions between
protons and neutrons. This can be done only if the fielai
is not
charged, and,, consequently, the particles associatod with it are not
charged (neutral mesons or neutrettos). This subject will be taken
up later.
The interaction of (22) does not defend on the reciprocal orientation
of the spins of nuclear particles; this is contrary to the result of
experiment. In order to clarify the problem of nuclear forces' dependence
upon spin, let us examine the interaction of protons and neutrons with
a neutral vector field. Every theory in this instance is very closely
allied with conventional electrodynamics and becomes electrodynamic
~CX 4X ~ }4 X i ? X (i YX theory if 9 is assumed
to equal zero. (The c~.ose relation mentioned is associtated with the fact
that electrodynamics is also a theory of a vector field (the potential of
the field Ak is a four-dimensional vector)). To put this analogy in a
mare i;ual form, let us rewrite the equations for a vector fiel4 (9) in
another form, introducing the notation:
r? l9~ (23)
With this notation (23), equation (9) will take the following form:
,? l (24)
hen : 0, equations (24) will. be transformed into the usual Maxwell's
equations for a vacuum. This also holds true for equations (7) and (s),
which, in the new notation, become:
(25)
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,--? U h
field. having a "meson char e" and a meso n 6-.
rnent" Now in the general ease of the quantum theory k'
v
;
;;j
iv etead of (jj
owing equations~oceur:
1i~1
whereA jCt and are matrices of the Dirac, theory and (, A) j
a quantum field.
In the ste.tir r,r,ge wrirh interests us tOand A. are clae~I v I
Is as follows:
,Li9..7
can be treated classically. The s~lution~ of + stem (27)
magnitudes
Moreover:
In (27) both the fields and A and the ve for of the spin o
interacts*Jenergy of two identical nuclear partir,Iee v+ 4h
spins c and ~ , as ' fo,li e:$rom ~c e* e~ee`r r
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In electrodynami rs the energy of a parts rle w-a
charge e and a magnetic moment , situated in the field
(4 A), equals,e~ (pH), The form is the same for the
interarti energy in the case of a vector mee a fields ctivueh.`~ i
`o f
e eorresponde -w~ g and corresponds-wbh -ate, Hence the
Let us now aseume tJat nuclear partirlee reate a vector
 wlierE r is the radiiis-vector of one
to the others, The ihteraction
and also toy forges dependent on the orientation of
'h LQQyioi1s1y
e energies l ( 29) (reduee5
to forces dependent on the reciprocal orienton of the spins
the spins - n re& to r.
The vectors viand =cz are mea9' n? "quae1-magnetic'f
moments of nuclear particles, and in the quantum theory the
L*
vectors are operators-the well-known Pauli matrices
is the proper of the particle).
Considering the ectors as operators makes no change in the
classic, solution of (29).
Above we examined the interaction of nuclear particles
with scalar and vector fields. Two other eases, when the
axe o
fields( a peeudosca1ar and pseudovector type (see ?i)a
can be studied similar and reduced to the
enery of interaction~expreseed by a linear combination of
the terms U1, U2 and U. (see us, tie general ex-
pression of the meeo ri theo for interar i energy gi11,
take the forms
It) U = O U1' 02U2+ 03U3, (30)
, C
where C
and C
are derivatives.
l
2
3
Until now we have conaid.eIed the mesot n field ae
h'~.charged; the t fiua C Aeueh a ve,etor field the electro-
magnetic field only arnountg to eaying that the reet 'w
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 0
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spond. d44q it), an expression of type (30) is obtained also
for the fortaes, but only in case of the interar,tion of pro-
tons And neutrons, Bat for the rase of identic''al nuclear particles
(two protons and two neutrons) the interactienergy is equal
to zero in the approximation under consideration. This re-
suit le completely understandable f~ om the viewpoint of the
quantdm echeme operating on the ronrept of an exchange of
mesons between nuclear particles, since the proton is
r'. .'\
en}x capable of emitting only a positive meson, which
urn n.i F'.
ran be absorbed by a neutron but cannot be absorbed by other
protons, etc, Hence exjange by one charged meson
..,,...,....., ~ by one charged meson
t~
.. men i dent i c
al nuel ear parts cl es /cannot
w.u
.lA
o
ux
jrn can
l
"quAntumrmc~so ~bn# field" -a meso p . is a uRl; to m -'4
,,, ,
8i.rtre the re 't mass of a photon equals zero, We are study-
in k; the central field because of its greater simplicity
( , a i.
tJl?uriiJ.
deeper Cene{der&tlonsti if the field is charged
; ow..,,
(in this rase, when it is quantized,"ncharged meso ons eorre-
occur between different nuclear particles. This explains
..~ 4;.:ii
the Character ofX3nteraetise energy already mentioned,
Meanwhile, experimental data furnish evidence that
w
proton-proton and, proton-neutron forces are of the same
order of magnitude, LT Within the frpmework of the
srjeme developed here, this fact Can only be explained by
assuming
that f~ neutral mesoi n (neutretto) exists, It r?(
'di .
ti .~ ~ e'~', ~t f) (, , .) 1 L_
to avoid 4e assumption that a neutretto exists
j
only by theories ~ ' + , operrtpo.n thhtu is of nn ~~xrht~n~~;e
by pairs of particles or exr~i.tecl (~l,?~r(}
9~in..w, ,ne~P.!41) It rriu ; t be , n d ril I f,
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 M ^-(rj i..
0, one ano her, Qr we might put it that/if the potential has a
?) '
?
.
t t
_ ?, .~ie
( &
A ~ .s..r. -,
ooath,~ 1.LL-, the problem of the whole system
of stationary stat.s has no solution. To a certain extent
this result is classical in t3.pe) since in classical mechanics
1
the potentials -p----~(
w..
r -~
o) also dues to the fall of a par-
.. ,
title on the renter (see it is easy to reach this con-
elusion by quantum mechanics, A paxtirie cannot fall on the
center if ilts average kinetic energy in approaching the r.,erter
increase) more rapidly then t o average potential energy diminishes,
.
of a partible situated in
Moreover, the average kinetic energyy
re~i0n i C,'\,r c:/
,.,a,..._..., . rF
aa:rd from the center equals T
f~ ue r
(. ? P ra
S f "/e~ sei' r1 n c/ rl" J?l'?l (~ f
sinr.i; by virtue ofd ;
A 1
Whence it is clear thr;t, if the