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Effect of nucleon effective mass and symmetry energy on the neutrino mean free path in a neutron star

The Korea-IBS-Daegu-SKKU energy density functional (KIDS-EDF) models, constructed from the perturbative expansion of the energy density in nuclear matter, have been successfully and widely applied in describing the properties of finite nuclei and infinite nuclear matter. In the present work, we extend the applications of the KIDS-EDF models to investigate the implications of the nucleon effective mass and nuclear symmetry energy for the properties of neutron stars (NSs) and neutrino interaction with the NS constituent matter in the linear response approximation (LRA). At fixed neutrino energy and momentum transfer, we analyze the total differential cross section of neutrino, the neutrino mean free path (NMFP), and the NS mass-radius (M-R) relations. Remarkable results are given by the KIDS0-m*87 and SLy4 models, in which $M_n^* /M \lesssim 1$, and their NMFPs are quite higher in comparison with those obtained from the KIDS0, KIDS-A, and KIDS-B models, which result in $M_n^*/M \gtrsim 1$. For the KIDS0, KIDS-A, and KIDS-B models, we obtain $λ\lesssim R_{\textrm{NS}}$, indicating that these models could predict the slow NS cooling and neutrino trapping in NSs. In contrast, the KIDS0-m*87 and SLy4 models yield $λ\gtrsim R_{\textrm{NS}}$ and thus we expect faster NS cooling and a small possibility of neutrino trapping within NSs. We also calculate the NMFP as a function of the neutrino energy and the nuclear matter density and find that the NMFP decreases as the density and neutrino energy increase, which is consistent with the result obtained in the Brussels-Montreal Skyrme (BSk17 and BSk18) models at saturation density.