# Resonance width for a particle-core coupling model with a square-well potential

## TL;DR

This paper derives a simple formula for the width of multi-channel resonance states using a deformed square-well potential, solving coupled-channels equations and analyzing partial widths in nuclear physics.

## Contribution

It introduces a new, straightforward formula for resonance widths in a particle-core coupling model with a square-well potential.

## Key findings

- Derived a formula for resonance widths in multi-channel systems.
- Applied the formula to a deformed nucleus and analyzed partial widths.
- Discussed the behavior of s-wave partial widths in the model.

## Abstract

We derive a simple formula for the width of a multi-channel resonance state. To this end, we use a deformed square-well potential and solve the coupled-channels equations. We obtain the $S$-matrix in the Breit-Wigner form, from which partial widths can be extracted. We apply the resultant formula to a deformed nucleus and discuss the behavior of partial width for an $s$-wave channel.