Sensitivity of the fusion cross section to the density dependence of the symmetry energy

TL;DR

This paper investigates how the density dependence of the symmetry energy influences nuclear fusion cross sections, using various theoretical models and focusing on the $^{48}$Ca+$^{48}$Ca system to inform the nuclear equation of state.

Contribution

It introduces a comparative analysis of fusion cross sections calculated with different energy density functionals and approaches, highlighting the sensitivity to symmetry energy parameters.

Findings

Preference for symmetry energy slope L≈50 MeV

Neutron-skin thickness of $^{48}$Ca estimated at 0.180-0.210 fm

Fusion cross sections slightly favor certain symmetry energy behaviors

Abstract

It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities\,\cite{balantekin2014}. In practice, we focus on $^{48}$Ca+$^{48}$Ca fusion. We employ three different approaches to calculate fusion cross-sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross-sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties. We find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm.