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The neutrino mean free path in neutron matter under a strong magnetic fieldis evaluated for the inelastic scattering reaction and studied as a function ofthe neutron matter density in the range $0.05 \leq \rho \leq 0.4$ fm$^{-3}$ forseveral temperatures up to 30 MeV and magnetic field strengths B=0 G, $10^{18}$G and $2.5\times 10^{18}$ G. Polarized neutron matter is described within thenon--relativistic Brueckner--Hartree--Fock (BHF) approach using the Argonne V18nucleon-nucleon potential supplemented with the Urbana IX three-nucleon force.Explicit expressions of the cross section per unit volume for the scattering ofa neutrino with a spin up or spin down neutron are derived from the FermiGolden rule. Our results show that the mean free path depends strongly on theangle of the incoming neutrino, leading to an asymmetry in this quantity. Thisasymmetry depends on the magnetic field intensity and on the density, but it israther independent of the temperature. For a density of $0.16$ fm$^{-3}$ at atemperature T$=30$MeV, the asymmetry in the mean free path is found to be of$\sim 15\%$ for B=$10^{18}$G and $\sim 38\%$ for B=$2.5 \times 10^{18}$G.

Asymmetry of the neutrino mean free path in hot neutron matter under strong magnetic fields