  Most of the Skyrme interactions are known to predict spin or isospin
instabilities beyond the saturation density of nuclear matter which contradict
predictions based on realistic interactions. A modification of the standard
Skyrme interaction is proposed so that the ferromagnetic instability is
removed. The new terms are density dependent and modify only the spin p-h
interaction in the case of spin-saturated system. Consequences for the nuclear
response function and neutrino mean free path are shown. The overall effect of
the RPA correlations makes dense matter more transparent for neutrino
propagation by a factor of 2 to 10 depending of the density.
