The (π, 2π) reaction and spin-isospin strength distribution in nuclei

Abstract

We study pion production on nuclei within the distorted wave impulse approximation (DWIA) and using the local density approximation (LDA) for the treatment of possible nuclear spin-isospin mode enhancements. The scattering amplitude input is based on a one-nucleon mechanism since two-nucleon processes are here estimatedito be relatively unimportant. For discrete nuclear levels, we study differential and total (angle-integrated) cross sections for various pion-like levels ( J P = 0 −, 1 +, 2 −,…; T = 1); these are also compared with non-pion-like excitations. The cross sections for discrete excitations are quite small. The inclusive cross sections, achieved by summing over all nuclear states, are considerably larger, of the order of 0.1–10 mb. We use the Fermi gas model to test the importance of the quasi-free peak for various incident pion momenta k, and to study the closure approximation for summing over nuclear levels when calculating inclusive cross sections. It is found that for k of the order of about twice the Fermi momentum most of the quasi-free peak region contributes to the nuclear excitations, and the use of closure is justified and practical. All cases are studied as a function of g', the Migdal spin-isospin parameter, and it is found that the dependence upon this parameter may range from changes of an order of magnitude to a factor of two over the range 0.4 ⩽ g' ⩽ 0.7.