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Asymmetry of the neutrino mean free path in partially spin polarized neutron matter within the Skyrme model

The asymmetry in the neutrino mean free path for the absorption reaction $ν+ n \rightarrow e^{-} + p$, is evaluated within hot neutron matter under a strong magnetic field. We consider densities in the range $0.05 \leq ρ\leq 0.4$ fm$^{-3}$, several temperatures up to 30 MeV and magnetic field strengths from $B=0$ up to $B=10^{18}$~G. Polarized neutron matter is described within the non--relativistic Hartree--Fock model using the LNS Skyrme interaction. The neutrino mean free path has a weak dependence with the temperature and in the strong magnetic field region, it decreases for growing values of it. This contrast with the scattering reaction $ν+ n \rightarrow ν' + n'$, where the average mean free path is almost independent of the magnetic field and has a strong dependence with the temperature. We have evaluated the asymmetry from both the absorption and scattering reactions. Our results shows that the total asymmetry depends on the magnetic field intensity, the density and the temperature. For a density of $0.16$ fm$^{-3}$ and for a magnetic field strength of B=$10^{17}$~G, the asymmetry in the mean free path is found to be, $\sim 9\%$ and $\sim 3.4\%$ for temperatures of T$=15$ and $30$ MeV, respectively. While the same set of asymmetries for B=$10^{18}$~G, is $\sim 58\%$ and $\sim 48\%$.