PARAMETRIZATION OF The HALF SHELL t-MATRIX WHEN THE TWO BODY BOUND STATE IS DELINEATED

Abstract

Publisher Summary This chapter explores parametrization of the half shell T-matrix when the two-body bound state is delineated. The problem of parametrizing the half-shell function Φ( k , k ′) using the s-wave phase shifts δ( k ) and the bound state wavefunction r B as input data, was first considered by Haftel. His method required choosing a model potential V M , which admitted the same bound state as the actual potential and introduce a function Φ W ( k , k ′) described in the chapter. As regards the determination of Φ W ( k , k ′) itself, Haftel suggested that its symmetric part σ W ( k , k ′) be chosen arbitrarily. This chapter uses a separable potential V sep to be the model potential envisaged by Haftel. This choice is justified because such a separable potential would naturally admit the delineated bound state and has the advantage that being UPA to the exact (unknown) potential, it is expected to reproduce the halfshell function to a considerable extent, not leaving much to be bridged by arbitrary correcting terms.