# Covariances from light-element r-martix analyses

## Abstract

We review the method for obtaining covariance information for light-element reactions using R-matrix theory. The general LANL R-matrix analysis code EDA provides accurate covariances for the resonance parameters at a solution due to the search algorithm it uses to find a local minimum of the chi-square surface. This information is used, together with analytically calculated sensitivity derivatives, in the first-order error propagation equation to obtain cross-section covariances for all reactions included in the analysis. Examples are given of the covariances obtained from the EDA analyses for n-p scattering and for the n+{sup 6}Li reactions used in the latest light-element standard cross section evaluation. Also discussed is a method of defining 'pure theory' correlations that could be useful for extensions to higher energies and heavier systems.

- Authors:

- Los Alamos National Laboratory

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 960468

- Report Number(s):
- LA-UR-08-04932; LA-UR-08-4932

TRN: US1002046

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Conference

- Resource Relation:
- Conference: Workshop on Neutron Cross Section Covariances ; June 24, 2008 ; Port Jefferson

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73; ALGORITHMS; CORRELATIONS; CROSS SECTIONS; DATA COVARIANCES; EQUATIONS; ERRORS; EVALUATION; INFORMATION; LANL; NEUTRONS; R MATRIX; RESONANCE; SCATTERING; SENSITIVITY

### Citation Formats

```
Hale, Gerald.
```*Covariances from light-element r-martix analyses*. United States: N. p., 2008.
Web.

```
Hale, Gerald.
```*Covariances from light-element r-martix analyses*. United States.

```
Hale, Gerald. Tue .
"Covariances from light-element r-martix analyses". United States.
doi:. https://www.osti.gov/servlets/purl/960468.
```

```
@article{osti_960468,
```

title = {Covariances from light-element r-martix analyses},

author = {Hale, Gerald},

abstractNote = {We review the method for obtaining covariance information for light-element reactions using R-matrix theory. The general LANL R-matrix analysis code EDA provides accurate covariances for the resonance parameters at a solution due to the search algorithm it uses to find a local minimum of the chi-square surface. This information is used, together with analytically calculated sensitivity derivatives, in the first-order error propagation equation to obtain cross-section covariances for all reactions included in the analysis. Examples are given of the covariances obtained from the EDA analyses for n-p scattering and for the n+{sup 6}Li reactions used in the latest light-element standard cross section evaluation. Also discussed is a method of defining 'pure theory' correlations that could be useful for extensions to higher energies and heavier systems.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Jan 01 00:00:00 EST 2008},

month = {Tue Jan 01 00:00:00 EST 2008}

}