A SEMICLASSICAL APPROACH TO RELATIVISTIC NUCLEAR MEAN FIELD-THEORY

Semiclassical relativistic particle and energy densities for a set of fermions submitted to a scalar field and to the time-like component of a four-vector field are derived in the Wigner-Kirkwood and Thomas-Fermi mean field theories, including gradient corrections up to order h{stroke}2. As a test of the validity of the semiclassical method, a simple case is studied, where the scalar potential and the zero component of the four-vector potential are identical and correspond to a harmonic oscillator. The semiclassical approach is then applied to the non-linear σ - ω model and the resulting variational equations are solved for finite nuclei and semi-infinite symmetric nuclear matter. In this case Hartree solutions are available and allow for an additional test of the reliability of the h{stroke}2 corrections. © 1993 Academic Press. All rights reserved.