A microscopic theory of collisions between complex nuclei based on the generator coordinate method

Abstract

A formalism for multichannel collision between complex nuclei, based on the Kohn-Kato variational principle, is recalled. The formalism uses a trial function of a two-centre generator coordinate method (GCM) type, where the generator coordinate is the distance between the centres of two potentials. The only parameters that appear in the theory are those which describe the effective two-body interaction between nucleons. For the sake of consistency, the interaction is chosen so as to predict the structure of separate fragments in channels as well as the states of the compound system. The structure of fragments and the compound system appears through the form factor, which has an analytic form as a sum of products of a Gaussian function and a polynomial of generator coordinates. This special form enables one to calculate analytically some matrix elements which determine the K-matrix. No approximation such as the zero range force or the neglect of the Pauli principle is used. A method for calculating the analytic expression for form factors is developed which uses symbolic algebras on computers. In calculating collisions of p-shell nuclei it is assumed that fragments in the excited state can be described as a linear combination of determinants in the major shell. This enables one to eliminate completely the spurious centre-of-mass motion. In our calculations the elastic and one (or two) inelastic channel is included, the effect of the remaining channels is included by a second “pseudo”-inelastic channel. The channels are labeled by angular momenta of fragments and relative angular momentum.