# Data Covariances from R-Matrix Analyses of Light Nuclei

## Abstract

After first reviewing the parametric description of light-element reactions in multichannel systems using R-matrix theory and features of the general LANL R-matrix analysis code EDA, we describe how its chi-square minimization procedure gives parameter covariances. This information is used, together with analytically calculated sensitivity derivatives, to obtain cross section covariances for all reactions included in the analysis by first-order error propagation. Examples are given of the covariances obtained for systems with few resonances ({sup 5}He) and with many resonances ({sup 13}C ). We discuss the prevalent problem of this method leading to cross section uncertainty estimates that are unreasonably small for large data sets. The answer to this problem appears to be using parameter confidence intervals in place of standard errors.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22436777

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Nuclear Data Sheets; Journal Volume: 123; Conference: International workshop on nuclear data covariances, Santa Fe, NM (United States), 28 Apr - 1 May 2014; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CARBON 13; CROSS SECTIONS; DATA COVARIANCES; HELIUM 5; LANL; MINIMIZATION; R MATRIX

### Citation Formats

```
Hale, G.M., E-mail: ghale@lanl.gov, and Paris, M.W.
```*Data Covariances from R-Matrix Analyses of Light Nuclei*. United States: N. p., 2015.
Web. doi:10.1016/J.NDS.2014.12.029.

```
Hale, G.M., E-mail: ghale@lanl.gov, & Paris, M.W.
```*Data Covariances from R-Matrix Analyses of Light Nuclei*. United States. doi:10.1016/J.NDS.2014.12.029.

```
Hale, G.M., E-mail: ghale@lanl.gov, and Paris, M.W. Thu .
"Data Covariances from R-Matrix Analyses of Light Nuclei". United States.
doi:10.1016/J.NDS.2014.12.029.
```

```
@article{osti_22436777,
```

title = {Data Covariances from R-Matrix Analyses of Light Nuclei},

author = {Hale, G.M., E-mail: ghale@lanl.gov and Paris, M.W.},

abstractNote = {After first reviewing the parametric description of light-element reactions in multichannel systems using R-matrix theory and features of the general LANL R-matrix analysis code EDA, we describe how its chi-square minimization procedure gives parameter covariances. This information is used, together with analytically calculated sensitivity derivatives, to obtain cross section covariances for all reactions included in the analysis by first-order error propagation. Examples are given of the covariances obtained for systems with few resonances ({sup 5}He) and with many resonances ({sup 13}C ). We discuss the prevalent problem of this method leading to cross section uncertainty estimates that are unreasonably small for large data sets. The answer to this problem appears to be using parameter confidence intervals in place of standard errors.},

doi = {10.1016/J.NDS.2014.12.029},

journal = {Nuclear Data Sheets},

number = ,

volume = 123,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}