Beyond ${\rho }^{2/3}$ Scaling: Microscopic Origins and Multimessengers of High-Density Nuclear Symmetry Energy

Abstract

Nuclear symmetry energy $E_{\mathrm{sym}}(\rho )$ encoding the cost to make nuclear matter more neutron rich has been the most uncertain component of the EOS of dense neutron-rich nucleonic matter. It affects significantly the radii, tidal deformations, cooling rates and frequencies of various oscillation modes of isolated neutron stars as well as the strain amplitude and frequencies of gravitational waves from their mergers, besides its many effects on structures of nuclei as well as the dynamics and observables of their collisions. Siemens (1970s) observed that $E_{\mathrm{sym}}(\rho )$ scales as $(\rho /{\rho }_0{)}^{2/3}$ near the saturation density ${\rho }_0$ of nuclear matter, since both the kinetic part and the potential contribution (quadratic in momentum) exhibit this dependence. The scaling holds if: (1) the nucleon isoscalar potential is quadratic in momentum, and (2) the isovector interaction is weakly density dependent. After examining many empirical evidences and understanding theoretical findings in the literature we conclude that: (1) Siemens' ${\rho }^{2/3}$ scaling is robust and serves as a valuable benchmark for both nuclear theories and experiments up to $2{\rho }_0$ but breaks down at higher densities, (2) Experimental and theoretical findings about $E_{\mathrm{sym}}(\rho )$ up to $2{\rho }_0$ are broadly consistent, but uncertainties remain large for its curvature $K_{\mathrm{sym}}$ and higher-order parameters, (3) Above $2{\rho }_0$, uncertainties grow due to poorly constrained spin-isospin dependent tensor and three-body forces as well as the resulting nucleon short-range correlations. Looking forward, combining multimessengers from both observations of neutron stars and terrestrial heavy-ion reaction experiments is the most promising path to finally constraining precisely the high-density $E_{\mathrm{sym}}(\rho )$ and the EOS of supradense neutron-rich matter.

Comments: Accepted version of a 53-page invited contribution to the Euro. Phys. Jour. Special Topic on "High-density nuclear matter". This article is dedicated to the memory of Prof. Philip J. Siemens (1943-2023)