Skyrme interaction to second order in nuclear matter

Based on the phenomenological Skyrme interaction various density-dependent nuclear matter quantities are calculated up to second order in many-body perturbation theory. The spin-orbit term as well as two tensor terms contribute at second order to the energy per particle. The simultaneous calculation of the isotropic Fermi-liquid parameters provides a rigorous check through the validity of the Landau relations. It is found that published results for these second order contributions are incorrect in most cases. In particular, interference terms between s-wave and p-wave components of the interaction can contribute only to (isospin or spin) asymmetry energies. Even with nine adjustable parameters, one does not obtain a good description of the empirical nuclear matter saturation curve in the low density region 0 < rho < 2 rho(0). The reason for this feature is the too strong density-dependence rho(8/3) of several second-order contributions. The inclusion of the density-dependent term 1/6t(3)rho(1/6) is therefore indispensable for a realistic description of nuclear matter in the Skyrme framework.