# An Informal Overview of the Unitary Group Approach

## Abstract

The Unitary Groups Approach (UGA) is an elegant and conceptually unified approach to quantum structure calculations. It has been widely used in molecular structure calculations, and holds the promise of a single computational approach to structure calculations in a variety of different fields. We explore the possibility of extending the UGA to computations in atomic and nuclear structure as a simpler alternative to traditional Racah algebra-based approaches. We provide a simple introduction to the basic UGA and consider some of the issues in using the UGA with spin-dependent, multi-body Hamiltonians requiring multi-shell bases adapted to additional symmetries. While the UGA is perfectly capable of dealing with such problems, it is seen that the complexity rises dramatically, and the UGA is not at this time, a simpler alternative to Racah algebra-based approaches.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Louisiana State Univ., Baton Rouge, LA (United States). Dept. of Physics and Astronomy

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1258517

- Report Number(s):
- LLNL-TR-694837

TRN: US1601513

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; U GROUPS; ALGEBRA; HAMILTONIANS; CALCULATION METHODS; MOLECULAR STRUCTURE; NUCLEAR STRUCTURE; ELECTRONIC STRUCTURE; COMPARATIVE EVALUATIONS

### Citation Formats

```
Sonnad, V., Escher, J., Kruse, M., and Baker, R..
```*An Informal Overview of the Unitary Group Approach*. United States: N. p., 2016.
Web. doi:10.2172/1258517.

```
Sonnad, V., Escher, J., Kruse, M., & Baker, R..
```*An Informal Overview of the Unitary Group Approach*. United States. doi:10.2172/1258517.

```
Sonnad, V., Escher, J., Kruse, M., and Baker, R.. Mon .
"An Informal Overview of the Unitary Group Approach". United States.
doi:10.2172/1258517. https://www.osti.gov/servlets/purl/1258517.
```

```
@article{osti_1258517,
```

title = {An Informal Overview of the Unitary Group Approach},

author = {Sonnad, V. and Escher, J. and Kruse, M. and Baker, R.},

abstractNote = {The Unitary Groups Approach (UGA) is an elegant and conceptually unified approach to quantum structure calculations. It has been widely used in molecular structure calculations, and holds the promise of a single computational approach to structure calculations in a variety of different fields. We explore the possibility of extending the UGA to computations in atomic and nuclear structure as a simpler alternative to traditional Racah algebra-based approaches. We provide a simple introduction to the basic UGA and consider some of the issues in using the UGA with spin-dependent, multi-body Hamiltonians requiring multi-shell bases adapted to additional symmetries. While the UGA is perfectly capable of dealing with such problems, it is seen that the complexity rises dramatically, and the UGA is not at this time, a simpler alternative to Racah algebra-based approaches.},

doi = {10.2172/1258517},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Jun 13 00:00:00 EDT 2016},

month = {Mon Jun 13 00:00:00 EDT 2016}

}