Semiclassical treatment of the Dirac sea contribution for finite nuclei

Dirac sea corrections for bulk properties of finite nuclei are computed within a self-consistent scheme in the $\sigma$-$\omega$ model. The valence part is treated in the Hartree approximation whereas the sea contribution is evaluated semiclassically up to fourth order in $\hbar$. Numerically, we find a quick convergence of the semiclassical expansion; the fourth order contributing much less than one percent to the binding energy per nucleon.