The Effective DBHF Method for Finite Nuclei

Abstract：

A density dependent effective interaction in the relativistic Mean-Field (RMF) theory was adopted to reproduce the Dirac-Brueckner-Hartree-Fock (DBHF) results and applied to study the ground state properties of finite nuclei for both stable and unstable nuclei, especially Ca and Pb isotope chains. The coupling constants of σ and ω mesons are density dependent and parameterized by reproducing the scalar and vector potentials of the DBHF results at each density in the RMF approximation. In this way the RMF approach is equivalent to the relativistic DBHF method, which is usually called the density dependent RMF approach (DDRMF). Rearrangement self energies in the DDRMF were obtained by a variational derivatives of the vertices in the effective Lagrangian. It was found that the rearrangement terms in the DDRMF provide a repulsive potential in the Dirac equation. The single particle energy levels become less bound and the nuclear radius is expanded. In contrast the proper total binding energy was obtained by subtracting the rearrangement energy, which compensates the weak binding of the single particle states. As a result, the total binding energy is slightly increased. The ground state properties of stable nuclei, such as ¹⁶O,⁴⁰Ca,⁴⁸Ca,⁹⁰Zr, and ²⁰⁸Pb were studied. An improvement of including rearrangement term and good agreement with the experimental data were obtained. The similar effects were also found in the isotopes of Ca and Pb. It may conclude that the DDRHF is equivalent to the DBHF and an efficient method in the studying of finite nuclear properties. It can be used to describe very well the ground state properties not only stable, but also unstable nuclei without any free parameters.