Self-consistent reaction matrix calculation of the pion capture rate in finite nuclei

Abstract

Abstract The Hartree-Fock (HF) wave functions calculated from a realistic nucleon-nucleon interaction are used to study the two-nucleon emission process following π − capture in complex nuclei. In particular, we study the π(su−) absorption in the 12 C nucleus. The calculated angular distributions of the absorption rate and the branching ratios are compared with available experimental and theoretical results. In some cases, the agreement of our results with experiment is found to be much better than the results obtained by various other approaches which have been used to introduce the effect of short-range correlations in the wave function of the pion-capturing pair of nucleons. Calculations are also made with harmonic oscillator wave functions. In this case we study the corrections to the absorption rate due to various effects, in particular those arising from (i) short-range dynamical correlations, (ii) final state nucleon-nucleus scattering and (iii) final state nucleon-nucleon scattering. It is found that the pure harmonic oscillator model gives reasonably good results after including the contribution from low-lying excited states of the residual nucleus. The correction due to the first effect increases the absorption rate whereas the corrections due to the last two effects suppress the absorption for back-to-back emission of the nucleon pair. Further, it is noticed that the second correction is more important than the third one. The effect of these corrections on the branching ratio R = W (pn → nn)/ W (pp → pn) is studied in detail. Finally, it is pointed out that the Jastrow method of introducing short-range correlations is inadequate in explaining the angular distributions and branching ratio data simultaneously.