Calculating broad neutron resonances in a cut-off Woods-Saxon potential

TL;DR

This paper investigates the behavior of neutron resonance poles in a cut-off Woods-Saxon potential, revealing how unphysical parameters influence resonance trajectories and pole interactions.

Contribution

It provides a detailed analysis of how the cut-off radius affects resonance pole positions and interactions in the Woods-Saxon potential.

Findings

Resonance pole distances are inversely proportional to the cut-off radius.

Pole interactions cause resonance trajectories to change shape and sometimes become antibound.

Sensitivity of pole behavior to the cut-off radius highlights limitations of the CWS potential.

Abstract

In a cut-off Woods-Saxon (CWS) potential with realistic depth $S$-matrix poles being far from the imaginary wave number axis form a sequence where the distances of the consecutive resonances are inversely proportional with the cut-off radius value, which is an unphysical parameter. Other poles lying closer to the imaginary wave number axis might have trajectories with irregular shapes as the depth of the potential increases. Poles being close repel each other, and their repulsion is responsible for the changes of the directions of the corresponding trajectories. The repulsion might cause that certain resonances become antibound and later resonances again when they collide on the imaginary axis. The interaction is extremely sensitive to the cut-off radius value, which is an apparent handicap of the CWS potential.