Studies of the nuclear single-particle response function in a simple model

Abstract

An expansion for the single-particle response function for a collection of non-interacting fermions in a localized potential well is developed with particular emphasis on applications to nuclei (including Δ-hole excitations), computational techniques, and comparisons to an infinite Fermi gas. Ground states and excited systems can both be treated with this formalism, although the latter involves a significantly more difficult analysis. Also, a useful dispersion relation is obtained for the response function. Then, an accurate method is presented for evaluating bound state and continuum single-particle wave functions in momentum space, the representation in which one most naturally derives the appropriate single-particle normalization factors. However, it is argued that for calculating folding integrals of two singleparticle wave functions coordinate space may be superior to momentum space. Our main results show that for any reasonable description of light nuclei excited by pions, the continuum states must be included. Also, in these systems the overall response of the continuum states is dramatically dependent on the real part of the Δ-particle optical potential.