The single-particle potential in a relativistic mean field model

The aim of this note is a discussion of the relevance and usefulness of a relativistic mean field model of the optical potential for nucleon-nucleus scattering. At first, the proper theoretical foundation and fundamentals of a relativistic quantum field theory are presented, as it forms the basis of a relativistic, self-consistent Hartree mean-field approximation. The relevance of such relativistic Hartree approximation in nuclear matter and for finite nuclei is discussed next. In order to make contact with the conventional non-relativistic Schroedinger phenomenology, the reduction of the Dirac equation to 2-component form was made, and the resultant effective Schroedinger equivalent potentials are discussed. The Hartree equation derived from a relativistic nuclear quantum field theory in the mean field approximation, and with the meson exchange parameters normalized to the bulk properties of nuclear systems, gives quantitative prediction of the charge and neutron density, r.m.s. radii and single particle levels of spherical nuclei which agreed with the experimental data. Finally, the problems of nuclear reaction calculation in the Dirac picture is presented with particular emphasis on the implication of the reduction of the relativistic reaction theory to the equivalent non-relativistic form. (Kato, T.)