Abstract
Background: The study of the nuclear equation of state (EOS) and the behavior of nuclear matter under extreme conditions is crucial to our understanding of many nuclear and astrophysical phenomena. Nuclear reactions serve as one of the means for studying the EOS. Purpose: 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 [A. B. Balantekin et al., Mod. Phys. Lett. A 29, 1430010 (2014)]. In practice, we focus on 48Ca+48Ca fusion. Method: 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. Results: The folding-potential model provides a reasonable first estimate of cross sections. DC-TDHF, which includes dynamical polarization, reduces the fusion barriers and delivers much better cross sections. Full TDHF near the barrier agrees nicely with DC-TDHF. Most of the Skyrme forces which we used deliver, on the average, fusion cross sections in good agreement with the data. Trying to read off a trend in the results, we find a slight preferenceforforceswhichdeliveraslopeofsymmetryenergyofL ≈ 50MeVthatcorrespondstoaneutron-skin thickness of 48Ca of Rskin = (0.180–0.210) fm. Conclusions: Fusion reactions in the barrier and sub-barrier region can be a tool to study the EOS and the neutron skin of nuclei. The success of the approach will depend on reduced experimental uncertainties of fusion data as well as the development of fusion theories that closely couple to the microscopic structure and dynamics.