# Trajectories of the Poles of the S-Matrix and Resonance Scattering

## Abstract

An important advantage of the ZRP method is that it offers the possibility of obtaining in a uniform way the exact solution of both bound state and scattering problems. Transitions between states of the discrete spectrum and the continuum caused by various perturbations as well as resonance scattering will be discussed and their relation to the properties of the poles of the S-matrix in the complex k plane (or complex E). The relation between the poles of the S-matrix and resonance scattering is well known and described in many monographs (19,22,48). Here we shall only give a brief discussion of some important results of the general theory which are relevant to the problems considered in this monograph. Among these are the relation between various formulae for resonance scattering, the existence of second-order poles in the S-matrix, and the movement of these poles in the complex k plane caused by variation in the depth of the potential well.

## Keywords

Real Axis Imaginary Axis Coincidence Point Effective Range Separable Potential## Preview

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