Hindrance in heavy-ion fusion for lighter systems of astrophysical interest

TL;DR

This paper introduces a simple Gaussian-based model to analyze heavy-ion fusion hindrance at sub-barrier energies, accurately fitting experimental data for lighter systems of astrophysical interest and outperforming more complex methods.

Contribution

A new simple diffused barrier formula is proposed for modeling sub-barrier heavy-ion fusion, providing accurate predictions and potential for extrapolation beyond measured data.

Findings

The model fits experimental data better than coupled channels calculations.

The parameters vary smoothly, enabling reliable extrapolation.

The approach is effective for lighter systems of astrophysical relevance.

Abstract

The hindrance in fusion of heavy-ion reactions crops up in the region of extreme sub-barrier energies. This phenomenon can be effectively analyzed using a simple diffused barrier formula derived assuming a Gaussian distribution of fusion barrier heights. Folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier, the fusion cross section is obtained. The energy dependence of the fusion cross section provides good description to the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Using this simple formula, an analysis has been presented from $^{16}$O + $^{18}$O to $^{12}$C + $^{198}$Pt, all of which were measured down to $<$ 10 $\mu$b. The agreement of the present analysis with the measured values is better than those calculated even from the sophisticated coupled channels calculations. The relatively smooth variation of the three parameters of this formula implies that it may be exploited to estimate the excitation function or to extrapolate cross sections for pairs of interacting nuclei which are yet to be measured. Possible extensions of the present methodology and its limitations have also been discussed.