Core-valence correlations for atoms with open shells

Abstract

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 ${\hat{\Sigma }}_1(\mathbf{r},{\mathbf{r}}^{\prime },E)$ 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 Landé factors is demonstrated for all cases from Xe I to Xe VIII.

13 pages, 5 figures

References in corpus (4)

• High-accuracy calculation of black-body radiation shift in ${}^{133}$Cs primary frequency standard
• Frequency shift of cesium clock transition due to blackbody radiation
• Frequency shift of hyperfine transitions due to blackbody radiation
• Calculation of energy levels and transition amplitudes for barium and radium

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• Relativistic corrections to transition frequencies of Fe I and search for variation of the fine structure constant
• Transition frequency shifts with fine structure constant variation for Fe II: Breit and core-valence correlation correction
• Coupled-cluster single-double calculations of the relativistic energy shifts in C IV, Na I, Mg II, Al III, Si IV, Ca II and Zn II