# Potential model for nuclear astrophysical fusion reactions with a square-well potential

## TL;DR

This paper explains why a shallow square-well potential effectively models nuclear astrophysical fusion reactions, contrasting it with the deeper Woods-Saxon potential, by analyzing boundary effects and absorption radius implications.

## Contribution

It clarifies the physical reason behind the shallow potential requirement in square-well models for fitting fusion data, linking boundary behavior to potential depth.

## Key findings

- Square-well potential requires a large absorption radius.
- Shallow potential suppresses wave function in absorption region.
- Boundary effects explain the effectiveness of square-well models.

## Abstract

The potential model for nuclear astrophysical reactions requires a considerably shallow nuclear potential when a square-well potential is employed to fit experimental data. We discuss the origin of this apparently different behavior from that obtained with a smooth Woods-Saxon potential, for which a deep potential is often employed. We argue that due to the sharp change of the potential at the boundary the radius parameter tends to be large in the square-well model, which results in a large absorption radius. The wave function then needs to be suppressed in the absorption region, which can eventually be achieved by using a shallow potential. We thus clarify the reason why the square-well potential has been able to reproduce a large amount of fusion data.