Nuclear response for the Skyrme effective interaction with zero-range tensor terms. III. Neutron matter and neutrino propagation

The formalism of the linear response for the Skyrme energy density functional including tensor terms derived in Refs. [1,2] for nuclear matter is applied here to the case of pure neutron matter. As in Ref. [2] we present analytical results for the response function in all channels, the Landau parameters, and the odd-power sum rules. Special emphasis is given to the inverse energy weighted sum rule because it can be used to detect nonphysical instabilities. Typical examples are discussed and numerical results shown. Moreover, as a direct application, neutrino propagation in neutron matter is investigated through its neutrino mean-free path at zero temperature. This quantity turns out to be very sensitive to the tensor terms of the Skyrme energy density functional.