Relativistic Hartree approach including both positive- and negative-energybound states

We develop a relativistic model to describe the bound states of positive en ergy and negative energy in finite nuclei at the same time. Instead of sear ching for the negative-energy solution of the nucleon's Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneous ly. The single-particle energies of negative-energy nucleons are obtained t hrough changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of t he meson fields are evaluated by means of the derivative expansion up to th e leading derivative order for the one-meson loop and one-nucleon loop. Aft er refitting the parameters of the model to the properties of spherical nuc lei, the results of positive-energy sector are similar to that calculated w ithin the commonly used relativistic mean field theory under the no-sea app roximation. However, the bound levels of negative-energy nucleons vary dras tically when the vacuum contributions are taken into account. It implies th at the negative-energy spectra deserve a sensitive probe to the effective i nteractions in addition to the positive-energy spectra.