The one-loop effective potential in nuclear matter and nuclei

Abstract

Abstract The lowest-order quantum corrections to the Walecka model are approximated by the one-loop effective potential. The model is considered with and without scalar self-interactions. In contrast to previous work, quantum corrections from the nonlinear scalar self-interactions are included. The resulting equations of motion for the mesons and nucleons are solved self-consistently for nuclear matter and spherical nuclei. Comparison is made to linear mean-field results for several sets of cubic and quartic self-couplings; all sets are consistent with renormalizability and the existence of a stable mean field ground state. Because of these restrictions on the self-couplings, it is impossible to improve the nuclear systematics over those obtained without self-couplings or in the mean-field theory.