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 $\ensuremath{\nu}+n\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+p$ is evaluated within hot neutron matter under a strong magnetic field. We consider densities in the range $0.05\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}0.4\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, 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 nonrelativistic Hartree-Fock model using the LNS Skyrme interaction. The neutrino mean free path has a weak dependence on the temperature and, in the strong magnetic field region, it decreases for growing values of it. This contrasts with the scattering reaction $\ensuremath{\nu}+n\ensuremath{\rightarrow}{\ensuremath{\nu}}^{\ensuremath{'}}+{n}^{\ensuremath{'}}$, where the average mean free path is almost independent of the magnetic field and has a strong dependence on 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 $0.16\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$ and for a magnetic field strength of $B={10}^{17}$ G, the asymmetries in the mean free path are found to be $\ensuremath{\approx}9%$ and $\ensuremath{\approx}3.4%$ for temperatures of $T=15$ and 30 MeV, respectively. The same set of asymmetries for $B={10}^{18}$ G is $\ensuremath{\approx}58%$ and $\ensuremath{\approx}48%$.