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 matter under a strong magnetic field. We consider densities in the range $0.04 leq ho leq 0.4$ fm$^{-3}$, 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 matter is described within the non--relativistic 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, $u + n o u´ + n´$ and $u + p o u´ + p´$, respectively; and the neutrino absorption reaction $u + n o e^{-} + p$. 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; while 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 with 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 $approx 21 %$ at saturation density for B$=10^{18}$~G, T$=15$~MeV and symmetric matter, while we have $approx -1 %$ for B$=10^{17}$~G and the same values of all the others conditions.