Exchange Currents for the Time Component of Axial Currents: A = 2 Nuclear System as a Test Case
- - A =
0
Nuclear System as a Test Case--
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Satoshi NOZAWA, Yasuharu KOHYAMA and Kuniharu KUBODERA Department of Physir:s, Faculty of Science and Technology Sophia University
,
Tokyo 102 (Received January 21, 1982)
The exchange currents, due to onesoft-pion exchange, in the time component of the axial currents are investigated using the A = 2 nuclear system as a test case. The possible importance of the tensor interaction is discussed.
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Although it is generally believed that ex
change currents (EC) should exist inside
nucleus, their identification is not a trivial
matter. ') This is partly due to the in
sufficiency of our knowledge on nuclear wave
functions. Another obstacle is that it is not
easy to derive unambiguously the effective
operators describing EC. A proposal'),3) was
made recently to separate from the entire EC
effect the part coming from the exchange of
one-soft-pion. The effective two-body cur
rent, denoted as ],,( l7r), corresponding to this
process can be derived in an essentially
model-independent way with the use of the
soft-pion theorem. The remaining part of
EC, in contrast, can be quite complicated and
its reliable treatment is yet to be found. We
may therefore expect that the cleanest test of
EC will be provided by those cases in which
],,(lJr) is the dominant EC effect. As for the
relative importance of ],,(l7r) as compared
with the impulse approximation (IA) current
],,(IA), a general argument shows the follow
ing.") (1) For ]" = V", the vector current,
V(1Jr)/V(IA) is large, whereas Vo(lJr)
IVo(IA) is small. (2) For ]"=A,,, the axial
current, Ao(1Jr )IAo(IA) is large, whereas
A(lJr)IA(IA) is small. (3) So far as the order
of-magnitude arguments are concerned,
V(lJr)IV(IA)~ Ao(lJr)IAo(IA), and thus a
remarkable parallelism between the roles of
V(lJr) and Ao(lJr) is expected. For V(lJr)
we know already two pieces of convincing
evidence. The first is the transition rate for
n+p .... y+d. The observed capture rate') is
about 10% larger than the IA value. The
inclusion of V(IJr) increases the IA value by
7%, eliminating most of the discrepancy.")
The second is the differential cross section
for e + d"" e' + n +p at small energy transfer
and at high momentum transfer. 6) The IA
fails totally in this case, whereas the addition
of V( lJr) changes the results drastically and
can explain all the essential features of the
data. 7) As for A o(IJr) a calculationS) based
on the Fermi gas model predicts Ao(lJr)
IAo( IA) ~ (40 - 60)%, an enormous effect.
One aspect to be noted, however, is that Ao is
in general smaller than A by a factor O( 1
1M), M being the nucleon mass. Thus the
identification of Ao( lJr) may be harder than
that of V(lJr). Nevertheless, we have
recently witnessed a remarkable accumula
tion of what may be considered as possible
evidence for Ao(lJr )."),9)_'5) The first case is
concerned with the mirror p'-decays in the A
= 12 triad. '0) The measurement of the elec
tron-nuclear spin angular correlation param
eter gives information on Ao, and hence on
Ao( IJr). The most recent calculations") in
dicate that the IA results disagree with ex
periment by 40%, and the addition of about
40% contribution of Ao( lJr) as estimated in
Ref. 3) is needed to explain the data. The
second, and more drastic, case concerns the
L1 T = 1, 0+ - 0- transition. Since there is a
strong suppression of the A contribution in
this case, the transition rate itself is very
sensitive to the possible existence of Ao( l7r).
The experimental data are available for
three cases: 16N(0-, T=1)-- 160(0+, T=O)
+ e- + Ve,12) ,(1- + l6O( 0+)-- 16N( 0-) + VI', 13) and
1BNe(0+, T=l)-- IB F(O-, T=O)+e++Ve. 14 )
The best existing calculations l5) show that
for each of the above three cases the theo
retical transition rate based on IA is by a
factor 3 to 4 too small whereas the inclusion
of A o( l7r) brings the theoretical value in good
agreement with the data. These impressive
results clearly indicate the importance of
Ao( l7r) as predicted in Ref. 3), but whether
they constitute really established evidence for
A o( l7r) is not easy to judge. The above
mentioned cases all deal with the complex
nuclei whose wave functions could be quite
complicated and might require a more sophis
ticated treatment than has been made previ
ously. We recall here that the evidence for
V(1ff) was satisfactorily firm because it in
volved the simple nuclear system with A = 2
in the wave function of which we have
reasonable confidence. This motivates us to
investigate in this short note whether and, if
any, how Ao( l7r) shows up in the A = 2 nu
clear system. Unfortunately, all relevant
experiments we could so far conceive are of
extremely difficult kind. The present study
is in this sense rather academic, but we con
sider it instructive to examine to what extent
the afore-mentioned parallelism between
V( Iff) and A o( l7r) materializes in the sim
plest possible nuclear system. Insights ob
tained thereby will hopefully shed some light
on the rela (...truncated)