Transition from subbarrier to deep subbarrier regimes in heavy-ion fusion reactions

TL;DR

This paper investigates the transition point in heavy-ion fusion reactions where fusion hindrance occurs at deep subbarrier energies, using a potential model to analyze experimental data and define a threshold energy.

Contribution

It introduces a method to determine the threshold energy for deep subbarrier fusion hindrance by fitting experimental data with different Woods-Saxon potentials and compares it with empirical and theoretical models.

Findings

Threshold energies align with empirical systematics and KNS potential values.

Asymptotic energy shift decreases at deep subbarrier energies.

Fusion cross sections exhibit a constant energy shift at subbarrier energies.

Abstract

We analyze the recent experimental data of heavy-ion fusion cross sections available up to deep subbarrier energies in order to discuss the threshold incident energy for a deep subbarrier fusion hindrance phenomenon. To this end, we employ a one-dimensional potential model with a Woods-Saxon internuclear potential. Fitting the experimental data in two different energy regions with different Woods-Saxon potentials, we define the threshold energy as an intersect of the two fusion excitation functions. We show that the threshold energies so extracted are in good agreement with the empirical systematics as well as with the values of the Krappe-Nix-Sierk (KNS) potential at the touching point. We also discuss the asymptotic energy shift of fusion cross sections with respect to the potential model calculations, and show that it decreases with decreasing energies in the deep subbarrier region although it takes a constant value at subbarrier energies.