# $S$ -matrix calculations of energy levels of sodiumlike ions

## Abstract

A recent S -matrix-based QED calculation of energy levels of the lithium isoelectronic sequence is extended to the general case of a valence electron outside an arbitrary filled core. Emphasis is placed on modifications of the lithiumlike formulas required because more than one core state is present, and an unusual feature of the two-photon exchange contribution involving autoionizing states is discussed. Here, the method is illustrated with a calculation of the energy levels of sodiumlike ions, with results for 3s _{1/2}, 3p _{1/2}, and 3p _{3/2} energies tabulated for the range Z = 30 – 100 . Comparison with experiment and other calculations is given, and prospects for extension of the method to ions with more complex electronic structure discussed.

- Authors:

- Univ. of Notre Dame, IN (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)

- OSTI Identifier:
- 1234599

- Alternate Identifier(s):
- OSTI ID: 1188515

- Report Number(s):
- LLNL-JRNL-670986

Journal ID: ISSN 1050-2947; PLRAAN

- Grant/Contract Number:
- AC52-07NA27344; PHY-1068065

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 6; Journal ID: ISSN 1050-2947

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS

### Citation Formats

```
Sapirstein, J., and Cheng, K. T. S -matrix calculations of energy levels of sodiumlike ions. United States: N. p., 2015.
Web. doi:10.1103/PhysRevA.91.062508.
```

```
Sapirstein, J., & Cheng, K. T. S -matrix calculations of energy levels of sodiumlike ions. United States. doi:10.1103/PhysRevA.91.062508.
```

```
Sapirstein, J., and Cheng, K. T. Wed .
"S -matrix calculations of energy levels of sodiumlike ions". United States. doi:10.1103/PhysRevA.91.062508. https://www.osti.gov/servlets/purl/1234599.
```

```
@article{osti_1234599,
```

title = {S -matrix calculations of energy levels of sodiumlike ions},

author = {Sapirstein, J. and Cheng, K. T.},

abstractNote = {A recent S -matrix-based QED calculation of energy levels of the lithium isoelectronic sequence is extended to the general case of a valence electron outside an arbitrary filled core. Emphasis is placed on modifications of the lithiumlike formulas required because more than one core state is present, and an unusual feature of the two-photon exchange contribution involving autoionizing states is discussed. Here, the method is illustrated with a calculation of the energy levels of sodiumlike ions, with results for 3s1/2, 3p1/2, and 3p3/2 energies tabulated for the range Z = 30 – 100 . Comparison with experiment and other calculations is given, and prospects for extension of the method to ions with more complex electronic structure discussed.},

doi = {10.1103/PhysRevA.91.062508},

journal = {Physical Review. A},

number = 6,

volume = 91,

place = {United States},

year = {2015},

month = {6}

}

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Web of Science

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