Nucleon self-energy in the relativistic Brueckner approach

Abstract

The formalism of the relativistic (or Dirac-) Brueckner approach in infinite nuclear matter is described. As nucleon-nucleon interaction the one-boson exchange potentials Bonn A,B,C and for comparison the Walecka model are used. The T-matrix is determined from the Thompson equation and is projected onto five covariant amplitudes. By the restriction to positive energy states an ambiguity arises in the relativistic Brueckner approach which is discussed here in terms of the pseudo-scalar and the pseudo-vector projection. The influence of the coupling of the nucleon via the T-matrix as an effective two-nucleon interaction to the nuclear medium is expressed by the self-energy. In particular we investigate the scalar and vector components of the self-energy for the different one-boson exchange potentials and discuss their density and momentum dependence. We estimate the uncertainty of the self-energy due to the pseudo-scalar and the pseudo-vector choice. Usually the momentum dependence of the self-energy is thought to be weak, however, we find that this depends on the one-boson exchange potentials. For the Bonn potentials, in contrast to the $σω$-potential, the momentum dependence is strikingly strong above as well as below the Fermi surface. We compare with the results of other groups and study the effects on the equation of state and the nucleon optical potential.