The generator coordinate method for tertiary reactions of light composite nuclei

Abstract

A theory of nuclear reactions with three composite fragments in a final channel, based on a variational principle of Kohn type and the generatorcoordinate (GC) representation of the trial function, is proposed and tested numerically. The Hamiltonian operator is microscopic, and the GC basis enables the inclusion of any rearrangement channels. The trial function is totally antisymmetrized and exactly projected on the eigenstates of the angular momentum and parity operators. It consists of a correlation term and channel terms which have to be specified only in the regions not covered by the correlation term, in which a pair of fragments is not close together. The channel relative-motion wave functions, from which the GC representation of the channel terms is obtained, are calculated from an asymptotic series. The three-fragment part of the trial function is expanded in hyperspherical harmonics. In this paper we study primarily the convergence of the reaction parameters with respect to the GC basis applying the formalism to the reaction³He(³He,pp)⁴He without inclusion of the Coulomb interaction. The part of the rearrangement differential corss section corresponding to well-separated final fragments is compared to experimental data.