Antibound poles in cutoff Woods-Saxon and in Salamon-Vertse potentials

TL;DR

This paper investigates how antibound poles of the S-matrix behave in cutoff Woods-Saxon and Salamon-Vertse potentials, revealing their dependence on potential parameters and the nature of their wave functions.

Contribution

It provides a detailed analysis of antibound pole trajectories and their dependence on cutoff radius in these potentials, including wave function characteristics.

Findings

Antibound pole positions depend on cutoff radius, especially for higher node numbers.

Starting points of pole trajectories correlate with the potential's range.

Wave functions are real below and imaginary above the coalescence point.

Abstract

The motion of l=0 antibound poles of the S-matrix with varying potential strength is calculated in a cutoff Woods-Saxon (WS) potential and in the Salamon-Vertse (SV) potential, which goes to zero smoothly at a finite distance. The pole position of the antibound states as well as of the resonances depend on the cutoff radius, especially for higher node numbers. The starting points (at potential zero) of the pole trajectories correlate well with the range of the potential. The normalized antibound radial wave functions on the imaginary k-axis below and above the coalescence point have been found to be real and imaginary, respectively.