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The formalism of the linear response for the Skyrme energy density functionalincluding tensor terms derived in articles [1,2] for nuclear matter is appliedhere to the case of pure neutron matter. As in article [2] we presentanalytical results for the response function in all channels, the Landauparameters and the odd-power sum rules. Special emphasis is given to theinverse energy weighted sum rule because it can be used to detect non physicalinstabilities. Typical examples are discussed and numerical results shown.Moreover, as a direct application, neutrino propagation in neutron matter isinvestigated through its neutrino mean free path at zero temperature. Thisquantity turns out to be very sensitive to the tensor terms of the Skyrmeenergy density functional.

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