Neutrino mean free path for proto–neutron star matter within the Skyrme model

Abstract

The neutrino mean free path is evaluated in hot proto--neutron star matter under a strong magnetic field. We consider densities in the range $0.04\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}0.4\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, several proton fractions from symmetric matter up to pure neutron matter, temperatures up to 30 MeV, and two magnetic field strengths $B={10}^{17}$ and ${10}^{18}$ G. Polarized proto--neutron star matter is described within the nonrelativistic Hartree-Fock model using the LNS Skyrme interaction, where the proper treatment for instabilities for low densities and temperatures is implemented. Under the same conditions, the degree of polarization of protons is stronger than the one for neutrons. For the neutrino mean free path we consider three reactions: the neutrino-neutron and neutrino-proton scattering, $\ensuremath{\nu}+n\ensuremath{\rightarrow}{\ensuremath{\nu}}^{\ensuremath{'}}+{n}^{\ensuremath{'}}$ and $\ensuremath{\nu}+p\ensuremath{\rightarrow}{\ensuremath{\nu}}^{\ensuremath{'}}+{p}^{\ensuremath{'}}$, respectively, and the neutrino absorption reaction $\ensuremath{\nu}+n\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+p$. The magnetic field induces an asymmetry in the mean free path which favors the flux of neutrinos parallel to the magnetic field in the case of neutron scattering and the absorption reaction, whereas it is antiparallel in the case of proton scattering. For most of the conditions the absorption reaction is the dominant one. The dependence of the neutrino mean free path on the magnetic field, the temperature, and the proton fraction is different for each reaction. As a representative case of our results, the asymmetry in the mean free path is $\ensuremath{\approx}21%$ at saturation density for $B={10}^{18}$ G, $T=15$ MeV, and symmetric matter, while we have $\ensuremath{\approx}\ensuremath{-}1%$ for $B={10}^{17}$ G and the same values of all the other conditions.