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

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.