Sturmian representation of the optical model potential due to coupling to inelastic channels

Abstract

Eigenfunctions for a set of coupled equations with outgoing wave boundary conditions in each channel n, called Weinberg states, are used to construct a separable representation of the matrix Green's functions G/sub n/n'(r,r'). In terms of this representation, novel forms for the nonlocal optical potential in the elastic channel can be written, which take into account interchannel coupling to all orders. Expressions for the corrections to the distorted-wave Born approximation inelastic transition potentials are also given. Two expressions for the effective potential in the elastic channel are given. One involves the Weinberg eigenfunctions in the inelastic space. The other involves the Weinberg eigenfunctions for the complete (elastic plus inelastic) space. The former is more suitable for the evaluation of corrections to the distorted-wave Born approximation, the latter occurs naturally in the solution by the Sturmian method of the full set of coupled equations. Numerical approximations to the Weinberg states can be constructed by introducing auxiliary sets of Sturmian states, one set in each channel. By truncating the dimension of each set to the size M, one obtains separable approximations of rank M to the effective potentials. The procedure involves the diagonalization of a matrix of dimension (M x N)/sup 2/,more » where N denotes the number of channels included in the inelastic space.« less