Sub-barrier fusion hindrance and absence of neutron transfer channels

TL;DR

This paper introduces a simple mathematical formula to analyze sub-barrier fusion cross sections, effectively describing experimental data and aiding extrapolation, while also exploring the impact of neutron transfer channels on fusion hindrance.

Contribution

A novel, straightforward Gaussian-based formula for sub-barrier fusion cross sections that matches experimental data and facilitates predictions for unmeasured systems.

Findings

The formula accurately fits existing fusion data.

Parameters vary smoothly, enabling reliable extrapolation.

Neutron transfer effects on fusion hindrance are discussed.

Abstract

The sub-barrier fusion hindrance has been observed in the domain of very low energies of astrophysical relevance. This phenomenon can be analyzed effectively using an uncomplicated straightforward elegant mathematical formula gleaned presuming diffused barrier with a Gaussian distribution. The mathematical formula for cross section of nuclear fusion reaction has been obtained by folding together a Gaussian function representing the fusion barrier height distribution and the expression for classical cross section of fusion assuming a fixed barrier. The variation of fusion cross section as a function of energy, thus obtained, describes well the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Employing this elegant formula, cross sections of interacting nuclei from $^{16}$O + $^{18}$O to $^{12}$C + $^{198}$Pt, all of which were measured down to $<$ 10 $\mu$b have been analyzed. The agreement of the present analysis with the measured values is comparable, if not better, than those calculated from more sophisticated calculations. The three parameters of this formula varies rather smoothly implying its usage in estimating the excitation function or extrapolating cross sections for pairs of interacting nuclei which are yet to be measured. Possible effects of neutron transfers on the hindrance in heavy-ion fusion have been explored.