A Foundation of the Derivative Scalar Coupling in the Relativistic Mean Field Theory

Abstract

The relativistic mean-field theories have achieved great successes in describing nuclear structure and scattering.HJ They are essentially based on the Walecka 6m model. It is characterized by the large negative scalar and positive vector potentials (or mean-fields). The former reduces the nucleon mass considerably. The effective nucleon mass M* is about half of the free mass M. This reduced nucleon mass in nuclear medium is the key ingredient in the relativistic models. It enlarges the lower components of the Dirac spinors, and so enhances the nuclear current and the spin-orbit strength. These results often produce the pronounced improvements in the theoretical predictions of nuclear structure and scattering at intermediate energies, as against the nonrelativistic models. However, the effective nucleon mass M* at saturation is rather small (m*=M*/M~0.55) as compared with the empirical values (m*~0.80-0.85l). Furthermore, the Walecka model yields much larger value of the incompressibility of nuclear matter (K ~ 550 MeV) than the empirical ones (K ~210-300 MeVl). (The introduction of the non-linear 6 self-coupling terms is able to bring K to a reasonable value.l) In the respect of these deficiencies, the derivative scalar coupling model by Zimanyi and MoszkowskiJ (ZM) has recently attracted great attentions.J-Il In this model, the coupling of the scalar-meson 6 to the nucleons ¢in the Walecka model is replaced as follows: