Finite temperature RPA in symmetric nuclear matter with Skyrme interactions

We investigate the RPA response for thermally excited nuclear matter interacting through Skyrme interactions. Closed analytical expressions are obtained for the dynamic susceptibility in each spin-isopspin channel. We compute the strength as a function of energy, transferred momentum and temperature, and examine the evolution of collective states, when present. The energy weighted sum rules Mk, for k = -1, 1 and 3 are also shown to possess explicit expressions as functions of both momentum and temperature. It is seen that thermal effects on the susceptibility are as important as dynamical ones associated to momentum transfer, at least for temperatures as high as 20% of the Fermi energy. (orig.)