Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

Abstract

While ample evidence for the so-called empirical parabolic law of the equation of state (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both nonrelativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and nonrelativistic free Fermi gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considering short-range correlations (SRCs) as well as nonlinear relativistic mean field models, we study effects of relativistic kinematics, dimensionality, interactions, and SRC on the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ in the FFG model depends strongly on the dimension $d$. While it is very small already in the normal three-dimensional space, it could be even smaller in spaces with reduced dimensions for subsystems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities, and/or symmetries. We also found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ could theoretically become very large only at the ultrarelativistic limit far above the density reachable in neutron stars. However, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affects significantly the density dependence of $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ compared to the relativistic FFG model prediction. The SRCs affect significantly not only the kinetic energy of symmetric nuclear matter but also the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ while the relativistic corrections are found negligible. Although we found no fundamental physics reason for the $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ to be very small especially at high densities, the results may help better understand the EOS of dense neutron-rich matter.