Relativistic shell model. I. Calculation of the Migdal parameters

A recently developed relativistic many-body theory which has been used to explain the saturation properties of nuclear matter is applied to the study of the interaction between relativistic quasiparticles. Specifically, we calculate the scattering amplitude for two quasiparticles at the Fermi surface. From a calculation of the forward scattering amplitude we may extract the Landau-Migdal parameters of the interaction. We compare our results with the parameters determined in extensive phenomenological studies of the properties of finite nuclei. In the relativistic theory the Landau-Migdal parameter F0 exhibits a very strong density dependence. Recently, phenomenological studies have indicated that this parameter is about ten times larger in the less dense regions of the nuclear surface than in the interior of a large nucleus. From our work we see that this large reduction of F0 with increasing density (found in phenomenological studies) may be a relativistic effect closely related to the mechanism giving rise to nuclear saturation in the relativistic theory. In addition, if we contrast the results of the relativistic model with those of the nonrelativistic model, we find that the parameter F1 is a larger (negative) number in the relativistic theory. (In turn this implies that the effective mass parameter, m*, is somewhat smaller.) The parameters F and m* exhibit a stronger density dependence in the relativistic theory. The physical basis for the increased magnitude of F1 in the relativistic analysis and the strong density dependence of F0 is discussed