Fusion at deep subbarrier energies: potential inversion revisited

TL;DR

This paper uses the WKB approximation to invert fusion cross section data at deep subbarrier energies, revealing that the inter-nucleus potentials are significantly thicker than traditional models, impacting our understanding of heavy-ion fusion.

Contribution

It introduces a method to directly determine inter-nucleus potentials at deep subbarrier energies by inverting fusion data, highlighting the potential's increased thickness.

Findings

Inverted potentials are much thicker than phenomenological ones.

The method applies to $^{16}$O +$^{144}$Sm and $^{16}$O +$^{208}$Pb reactions.

Thick potentials influence fusion dynamics at deep subbarrier energies.

Abstract

For a single potential barrier, the barrier penetrability can be inverted based on the WKB approximation to yield the barrier thickness. We apply this method to heavy-ion fusion reactions at energies well below the Coulomb barrier and directly determine the inter-nucleus potential between the colliding nuclei. To this end, we assume that fusion cross sections at deep subbarrier energies are governed by the lowest barrier in the barrier distribution. The inverted inter-nucleus potentials for the $^{16}$O +$^{144}$Sm and $^{16}$O +$^{208}$Pb reactions show that they are much thicker than phenomenological potentials. We discuss a consequence of such thick potential by fitting the inverted potentials with the Bass function.