Exchange Currents for the Time Component of Axial Currents: A = 2 Nuclear System as a Test Case

Progress of Theoretical Physics, Apr 1982

The exchange currents, due to one-soft-pion exchange, in the time component of the axial currents are investigated using the A = 2 unclear system as a test case. The possible importance of the tensor interaction is discussed.

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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-- 0 0 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. - 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)


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Satoshi Nozawa, Yasuharu Kohyama, Kuniharu Kubodera. Exchange Currents for the Time Component of Axial Currents: A = 2 Nuclear System as a Test Case, Progress of Theoretical Physics, 1982, pp. 1240-1243, 67/4, DOI: 10.1143/PTP.67.1240