Core-valence correlations for atoms with open shells

We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately constant. A constant potential does not change the core electron wave functions and Green's functions. Therefore, all operators describing interaction of $M$ valence electrons and $N-M$ core electrons (the core part of the Hartree-Fock Hamiltonian $V^{N-M}$, the correlation potential $\hat\Sigma_1({\bf r},{\bf r'},E)$ and the screening of interaction between valence electrons by the core electrons $\hat\Sigma_2$) may be calculated with all $M$ valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for $M>2$ prohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is calculated using orbitals in complete $V^{N}$ potential (the mean field produced by all electrons); $\hat\Sigma_1$ + $\hat\Sigma_2$ are added to the CI Hamiltonian to account for the core-valence correlations. We calculate $\hat\Sigma_1$ and $\hat\Sigma_2$ using many-body perturbation theory in which dominating classes of diagrams are included in all orders. We use neutral Xe I and all positive ions up to Xe VIII as a testing ground. We found that the core electron density for all these systems is practically the same. Therefore, we use the same $\hat\Sigma_1$ and $\hat\Sigma_2$ to build the CI Hamiltonian in all these systems ($M=1,2,3,4,5,6,7,8$). Good agreement with experiment for energy levels and Land\'{e} factors is demonstrated for all cases from Xe I to Xe VIII.