Absorption and emission of neutrinos and antineutrinos in hot stellar matter with a strong magnetic field

We evaluated the cross section per unit volume for the absorption and emission of neutrinos and antineutrinos in hot stellar matter under the influence of a strong magnetic field. The system considered consists of neutrons, protons, electrons, and positrons in $\ensuremath{\beta}$-equilibrium and charge neutrality. Two different models for the equation of state (EoS) were employed: the first assumes noninteracting particles, while the second uses the Hartree-Fock approximation with the Skyrme interaction. The cross-section evaluation was performed self-consistently with the EoS. We analyzed densities up to $\ensuremath{\approx}2.5{\ensuremath{\rho}}_{0}$, where ${\ensuremath{\rho}}_{0}$ represents the nuclear saturation density, focusing on a system with a magnetic field intensity of $B={10}^{18}$ G and a temperature of $T=15$ MeV. Our results show that neutrino absorption is the dominant reaction. Furthermore, we found that the interplay between the EoS and the cross-section calculation is crucial. Due to the presence of the magnetic field, the cross section exhibits an asymmetric behavior depending on the direction of the (anti)neutrino absorbed or emitted relative to the magnetic field. This asymmetry favors the flux of (anti)neutrinos (anti)parallel to the magnetic field.