Relativistic mean-field approach in nuclear systems

A new scheme to study the properties of finite nuclei is proposed based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach starting from a realistic nucleon-nucleon interaction. The relativistic structure of the nucleon self-energies in nuclear matter depending on density, momentum, and isospin asymmetry is determined through a subtracted $T$-matrix technique. The scalar and vector potentials in nuclear matter are parametrized and extrapolated around the very low density region to provide the necessary basis for the finite nuclei calculation. The potentials of a single particle in finite nuclei are generated via a local density approximation (LDA). The surface effect of finite nuclei can be taken into account by an improved LDA. The bulk properties of nuclei can be determined in a self-consistent scheme, and the spherical nuclei $^{16}\mathrm{O},\phantom{\rule{0.16em}{0ex}}^{40,48}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}^{90}\mathrm{Zr},\phantom{\rule{0.16em}{0ex}}^{116,132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are sampled for validation. The results show that the calculated binding energies are coincident with the experimental data, and the predicted values for radii and spin-orbit splitting of single-particle energies are reasonably described with an underestimation of about 10%. Basic features of finite nuclei in this scheme are consistent with those of more sophisticated DBHF calculations.