Structure of residual interaction in spherical nuclei

The effect of residual interaction between nucleons (quasiparticles) on shell oscillations of the masses of spherical nuclei is considered. The singularity of the ground state energy of the system in the vicinity of nucleon magic numbers is analyzed for various types of the dependence of residual interaction on orbital momentum of the quasiparticle. It is shown that only the perturbation band width of the Fermi distribution due to residual interaction which is proportional to the square of the angular momentum vector is consistent with the character of the magic cusps. The coupling constants between the quasiparticles are determined on the basis of the available data. The constant decreases rapidly with increase of nuclear radius. Possible consequences pertaining to the energy spectrum of infinite nuclear matter are discussed.