Matching polynomial tails to the cut-off Woods-Saxon potential

TL;DR

This paper investigates how attaching Hermite polynomial tails to cut-off Woods-Saxon potentials affects the distribution of S-matrix poles, providing insights into resonance behavior and pole trajectories.

Contribution

It introduces a novel method of modifying cut-off Woods-Saxon potentials with Hermite polynomial tails to study pole distributions and resonance reflections.

Findings

Pole trajectories are accurately reproduced for real and imaginary parts.

Hermite polynomial tails influence the reflection points of resonant wave functions.

Modified potentials alter the distribution of S-matrix poles.

Abstract

Cutting off the tail of the Woods-Saxon and generalized Woods-Saxon potentials changes the distribution of the poles of the $S$-matrix considerably. Here we modify the tail of the cut-off Woods-Saxon (CWS) and cut-off generalized Woods-Saxon (CGWS) potentials by attaching Hermite polynomial tails to them beyond the cut. The tails reach the zero value more or less smoothly at the finite ranges of the potential. Reflections of the resonant wave functions can take place at different distances. The starting points of the pole trajectories have been reproduced not only for the real values and the moduli of the starting points but also for the imaginary parts.