Neutrino scattering rates in the presence of hyperons from a Skyrme model in the RPA approximation

The contribution of -hyperons to neutrino scattering rates is calculated in the random phase approximation in a model where the interaction is described by a Skyrme potential. Finite temperature and neutrino trapping are taken into account in view of applications to the deleptonization stage of protoneutron star cooling. The hyperons can remove the problem of ferromagnetic instability common to (nearly) all Skyrme parametrizations of the nucleon-nucleon interaction. As a consequence, there is not any longer a pole at the transition in the neutrino-baryon cross-section. However there still remains an enhancement in this region. In the absence of ferromagnetism the mean free path in np matter is reduced compared to its value in np matter as a consequence of the presence of this additional degree of freedom. At high density the results are very sensitive to the choice of the - interaction.