# 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{sup N-M}, the correlation potential {sigma}{sub 1}(r,r{sup '},E), and the screening of interaction between valence electrons by the core electrons {sigma}{sub 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{sup N} potential (the mean field produced by all electrons); {sigma}{sub 1}+{sigma}{sub 2} are added to the CI Hamiltonian to account for the core-valence correlations. We calculate {sigma}{sub 1} and {sigma}{sub 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 themore »

- Authors:

- School of Physics, University of New South Wales, Sydney 2052 (Australia)

- Publication Date:

- OSTI Identifier:
- 20982512

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.052504; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; CATIONS; CORRELATIONS; ELECTRON DENSITY; ELECTRONIC STRUCTURE; ELECTRONS; ENERGY LEVELS; GREEN FUNCTION; HAMILTONIANS; HARTREE-FOCK METHOD; INTERACTIONS; LANDE FACTOR; MANY-BODY PROBLEM; MEAN-FIELD THEORY; PERTURBATION THEORY; POTENTIALS; SCREENING; VALENCE; WAVE FUNCTIONS; XENON

### Citation Formats

```
Dzuba, V. A., and Flambaum, V. V.
```*Core-valence correlations for atoms with open shells*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.052504.

```
Dzuba, V. A., & Flambaum, V. V.
```*Core-valence correlations for atoms with open shells*. United States. doi:10.1103/PHYSREVA.75.052504.

```
Dzuba, V. A., and Flambaum, V. V. Tue .
"Core-valence correlations for atoms with open shells". United States.
doi:10.1103/PHYSREVA.75.052504.
```

```
@article{osti_20982512,
```

title = {Core-valence correlations for atoms with open shells},

author = {Dzuba, V. A. and Flambaum, V. V.},

abstractNote = {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{sup N-M}, the correlation potential {sigma}{sub 1}(r,r{sup '},E), and the screening of interaction between valence electrons by the core electrons {sigma}{sub 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{sup N} potential (the mean field produced by all electrons); {sigma}{sub 1}+{sigma}{sub 2} are added to the CI Hamiltonian to account for the core-valence correlations. We calculate {sigma}{sub 1} and {sigma}{sub 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 {sigma}{sub 1} and {sigma}{sub 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 Lande factors is demonstrated for all cases from Xe I to Xe VIII.},

doi = {10.1103/PHYSREVA.75.052504},

journal = {Physical Review. A},

number = 5,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}