Origin of a maximum of astrophysical $S$ factor in heavy-ion fusion reactions at deep subbarrier energies

TL;DR

This paper explains the maximum observed in the astrophysical $S$ factor during heavy-ion fusion at deep subbarrier energies by fitting fusion data with two potentials, revealing insights into the fusion hindrance phenomenon.

Contribution

It introduces a two-potential fitting approach to explain the $S$ factor maximum and clarifies its relation to fusion hindrance at deep subbarrier energies.

Findings

The $S$ factor maximum correlates with a threshold energy for fusion hindrance.

Two-potential fits reveal different logarithmic slopes at energies below and above the threshold.

The $S$ factor remains a useful analysis tool despite its strong energy dependence in heavy-ion systems.

Abstract

The hindrance phenomenon of heavy-ion fusion cross sections at deep subbarrier energies often accompanies a maximum of an astrophysical $S$ factor at a threshold energy for fusion hindrance. We argue that this phenomenon can naturally be explained when the fusion excitation function is fitted with two potentials, with a larger (smaller) logarithmic slope at energies lower (higher) than the threshold energy. This analysis clearly suggests that the astrophysical $S$ factor provides a convenient tool to analyze the deep subbarrier hindrance phenomenon, even though the $S$ factor may have a strong energy dependence for heavy-ion systems unlike that for astrophysical reactions.