Analysis of Chiral Mean-Field Models for Nuclei

Abstract

An analysis of nuclear properties based on a relativistic energy functional containing Dirac nucleons and classical scalar and vector meson fields is discussed. Density functional theory implies that this energy functional can include many-body effects that go beyond the simple Hartree approximation. Using basic ideas from effective field theory, a systematic truncation scheme is developed for the energy functional, which is based on an expansion in powers of the meson fields and their gradients. Chiral models are analyzed by considering specific lagrangians that realize the spontaneously broken chiral symmetry of QCD in different ways and by studying them at the Hartree level. Models that include a light scalar meson playing a dual role as the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon interaction, and which include a "Mexican-hat" potential, fail to reproduce basic ground-state properties of nuclei. In contrast, chiral models with a nonlinear realization of the symmetry are shown to contain the full flexibility inherent in the general energy functional and can therefore successfully describe nuclei.