# New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms

## Abstract

A set of equations are presented for calculating atomic principal spectral lines and fine-structure energy splits for single and multi-electron atoms. Calculated results are presented and compared to the National Institute of Science and Technology database demonstrating very good accuracy. The equations do not require fitted parameters. The only experimental parameter required is the Ionization energy for the electron of interest. The equations have comparable accuracy and broader applicability than the single electron Dirac equation. Three Appendices discuss the origin of the new equations and present calculated results. New insights into the special relativistic nature of the Dirac equation and its relationship to the new equations are presented.

- Authors:

- National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States)
- National Energy Technology Lab. (NETL), Morgantown, WV (United States)

- Publication Date:

- Research Org.:
- National Energy Technology Lab. (NETL), Pittsburgh, PA, and Morgantown, WV (United States)

- Sponsoring Org.:
- USDOE Office of Fossil Energy (FE)

- OSTI Identifier:
- 1427018

- Report Number(s):
- NETL-PUB-21635

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING; Atomic Spectra; Multi-Electron Atom; Principal Spectral Line; Atomic Fine-Structure; Special Relativity; Dirac Equation

### Citation Formats

```
Surdoval, Wayne A., Berry, David A., and Shultz, Travis R.
```*New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms*. United States: N. p., 2018.
Web. doi:10.2172/1427018.

```
Surdoval, Wayne A., Berry, David A., & Shultz, Travis R.
```*New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms*. United States. doi:10.2172/1427018.

```
Surdoval, Wayne A., Berry, David A., and Shultz, Travis R. Fri .
"New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms". United States.
doi:10.2172/1427018. https://www.osti.gov/servlets/purl/1427018.
```

```
@article{osti_1427018,
```

title = {New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms},

author = {Surdoval, Wayne A. and Berry, David A. and Shultz, Travis R.},

abstractNote = {A set of equations are presented for calculating atomic principal spectral lines and fine-structure energy splits for single and multi-electron atoms. Calculated results are presented and compared to the National Institute of Science and Technology database demonstrating very good accuracy. The equations do not require fitted parameters. The only experimental parameter required is the Ionization energy for the electron of interest. The equations have comparable accuracy and broader applicability than the single electron Dirac equation. Three Appendices discuss the origin of the new equations and present calculated results. New insights into the special relativistic nature of the Dirac equation and its relationship to the new equations are presented.},

doi = {10.2172/1427018},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Mar 09 00:00:00 EST 2018},

month = {Fri Mar 09 00:00:00 EST 2018}

}