Relativistic Calculation of Two-Body Correlations in Finite Nuclei

Abstract

0 and 'Ca are investigated in the framework of the relativistic Brueckner-Hartree-Fock method. The equations are solved by using the wave packet expansion method. The meson coupling parameters are adopted from the Bonn A potential. It is shown that the fourth-order calculation already gives fairly reproducing results. Applications of the relativistic quantum field theory to finite nuclei have beerr·: performed by many authors either in the Dirac-Hartree 0 or in the Dirac-Hartree-Fock approximation. 2 H> These models have reproduced some of the nuclear ground state properties, e.g., the magnitude of the spin-orbit splitting, using the effective values of the coupling constants for the lagrangian which contains sorhe kinds of mesons. However, in spite of the success, there remain some requirements-to be achieved. In the first place, when the parameters were adjusted so as to reproduce the bulk properties of nuclei, they lost fits to the nucleon-nucleon scattering data. Further­ more, these models ignored higher-order corrections which are not negligible in such a strongly interacting system. In order to meet the first requirement, one must determine the coupling constants from the nucleon-nucleon scattering data and deuteron properties and use them to reproduce the properties of nuclear matter and finite nuclei. The meson theoretical description of two-nucleon systems in free space has been better established recently: nucleon-nucleon scattering up to several hundreds of MeV and deuteron structure are well described by the meson exchange model (OBEP), where the Bethe'-'Salpeter equation with a three-dimensional reduction is solved. 5 >.s> Therefore it would be a reasonable next step to calculate the ladder-type correlations beyond the Hartree­ Fock approximation in finite nuclei. The generalization of the Brueckner equation to the relativistic framework for nuclear matter was performed by several authors 6 H> and the saturation properties have been reproduced quantitatively using the two-body interactions which reproduce the nucleon-nucleon scattering data and deuteron properties. The saturation mecha­ nism is essentially due to the strong density-dependence of the nucleon effective mass in nuclear medium. It decreases with density, supplying a strong increase of kinetic energies, and this repulsive relativistic effect shifts the Coester line to graze the experimental saturation point. As the result of this success, it is expected that this Dirac-Brueckner-Hartree-Fock (DBHF) scheme must reproduce fairly the bulk prop­ erties of finite nuclei. But, it has been supposed to be exceedingly difficult to solve