Finite-nucleus treatment of the response to σμτλprobes and pion-like excitations

Abstract

Presents an exact finite-nucleus treatment of the response to spin-isospin-sensitive probes. Since linear momentum is not a good quantum number here, the author adopts a formalism suggested by Toki and Weise (1980) which incorporates an expansion in partial waves of good nuclear total angular momentum. The author starts from the pion self-energy Pi , which is non-local in momentum space. Iterations of this quantity lead to the response function R, obtained by solving a matrix integral equation exactly (using numerical methods). R is used to renormalise the matrix element of a spin-isospin ( sigma mu tau lambda ) probe and find large effects for intermediate and large momenta (q>mpi ). These effects are unimportant for very low momenta. He also finds very important effects of the non-locality in momentum space. The formalism is applied to the JP=1+, T=1 level in 12C. The results are compared with approximations in current use: the infinite nuclear matter approximation, the local density approximation and the approximations of Toki and Weise. All these approximations are found to be unsatisfactory, especially for q to 0 and near the critical momentum region (q approximately (2-3)mpi ).