A shell-model theory of complex collisions

Abstract

A microscopic theory of heavy-ion reactions is proposed based on the assumption that the set of antisymmetrizsd products of shell-model wave functions spans the complete Hilbert space of the system. The many-body Schrödinger equation and the equations given by the scattering theory of Ekstein are represented by the basis set, fully taking the Pauli principle into account. A set of coupled equations, which resembles that of the generator coordinate method, is obtained and reduced to a set of coupled integro-differential equations which leads to a simple physical picture for the scattering process of complex particles. The interactions between composite particles which have direct relations to the T-matrices for elastic, inelastic and rearrangement collisions are expressed in terms of shell-model 16O + 16O wave functions and the nucleon-nucleon interaction. A simple example is given for the local potential to lowest order.