Barrier modification in sub-barrier fusion reactions using Wong formula with Skyrme forces in semiclassical formalism

TL;DR

This paper develops a semiclassical approach using Skyrme forces within the Wong formula to analyze sub-barrier fusion reactions, demonstrating that barrier modifications depend on the chosen Skyrme force and can fit experimental data without additional adjustments.

Contribution

It introduces a method to incorporate different Skyrme forces into the Wong formula via ETF, enabling better fitting of fusion data without extra barrier modifications.

Findings

Different Skyrme forces yield varying barrier characteristics.

The GSkI force fits $^{64}$Ni+$^{100}$Mo data exactly without modifications.

SIII force best fits $^{58,64}$Ni+$^{58,64}$Ni reactions.

Abstract

We obtain the nuclear proximity potential by using semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and use it in the extended $\ell$-summed Wong formula under frozen density approximation. This method has the advantage of allowing the use of different Skyrme forces, giving different barriers. Thus, for a given reaction, we could choose a Skyrme force with proper barrier characteristics, not-requiring extra ``barrier lowering" or ``barrier narrowing" for a best fit to data. For the $^{64}$Ni+$^{100}$Mo reaction, the $\ell$-summed Wong formula, with effects of deformations and orientations of nuclei included, fits the fusion-evaporation cross section data exactly for the force GSkI, requiring additional barrier modifications for forces SIII and SV. However, the same for other similar reactions, like $^{58,64}$Ni+$^{58,64}$Ni, fits the data best for SIII force. Hence, the barrier modification effects in $\ell$-summed Wong expression depends on the choice of Skyrme force in extended ETF method.