Nuclear response for the Skyrme effective interaction with zero-range tensor terms. II. Sum rules and instabilities

The formalism of linear response theory for Skyrme forces including tensor terms presented by Davesne et al. [Phys. Rev. C 80, 024314 (2009)] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the odd-power sum rules, with particular attention to the inverse energy weighted sum rule, M-1, as a tool to detect instabilities in Skyrme functionals.