Collective modes of infinite nuclear matter

In this paper we study the longitudinal collective vibrations of infinite nuclear matter in the long wavelength limit. We present an alternative method for solving the Landau equations which allows analytical expression for the response function, the odd sum rules and the strength of the modes. We solve the theory for a selection of Skyrme interactions and we also consider the properties of the ground state of the system specifically associated with the four collective states which exist in nuclear matter. The relationship between the quantum mechanical response function and the corresponding classical hydrodynamical quantity is explored and the approximate results obtained through sum rules are compared with the exact solutions of the RPA equations. Finally the Landau parameters obtained with the Skyrme forces are tested against the antisymmetry property of the foward particle-hole scattering amplitude on the Fermi surface and the enhancement factor in the photonuclear dipole sum rule