# Positive Scattering Cross Sections using Constrained Least Squares

## Abstract

A method which creates a positive Legendre expansion from truncated Legendre cross section libraries is presented. The cross section moments of order two and greater are modified by a constrained least squares algorithm, subject to the constraints that the zeroth and first moments remain constant, and that the standard discrete ordinate scattering matrix is positive. A method using the maximum entropy representation of the cross section which reduces the error of these modified moments is also presented. These methods are implemented in PARTISN, and numerical results from a transport calculation using highly anisotropic scattering cross sections with the exponential discontinuous spatial scheme is presented.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (US)

- Sponsoring Org.:
- USDOE Office of Defense Programs (DP) (US)

- OSTI Identifier:
- 757426

- Report Number(s):
- LA-UR-99-1281

TRN: US0004417

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: M and C '99, Madrid (ES), 09/27/1999--09/30/1999; Other Information: PBD: 27 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CROSS SECTIONS; DISCRETE ORDINATE METHOD; SCATTERING; NUCLEAR DATA COLLECTIONS; LEAST SQUARE FIT; P CODES

### Citation Formats

```
Dahl, J.A., Ganapol, B.D., and Morel, J.E.
```*Positive Scattering Cross Sections using Constrained Least Squares*. United States: N. p., 1999.
Web.

```
Dahl, J.A., Ganapol, B.D., & Morel, J.E.
```*Positive Scattering Cross Sections using Constrained Least Squares*. United States.

```
Dahl, J.A., Ganapol, B.D., and Morel, J.E. Mon .
"Positive Scattering Cross Sections using Constrained Least Squares". United States.
doi:. https://www.osti.gov/servlets/purl/757426.
```

```
@article{osti_757426,
```

title = {Positive Scattering Cross Sections using Constrained Least Squares},

author = {Dahl, J.A. and Ganapol, B.D. and Morel, J.E.},

abstractNote = {A method which creates a positive Legendre expansion from truncated Legendre cross section libraries is presented. The cross section moments of order two and greater are modified by a constrained least squares algorithm, subject to the constraints that the zeroth and first moments remain constant, and that the standard discrete ordinate scattering matrix is positive. A method using the maximum entropy representation of the cross section which reduces the error of these modified moments is also presented. These methods are implemented in PARTISN, and numerical results from a transport calculation using highly anisotropic scattering cross sections with the exponential discontinuous spatial scheme is presented.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Sep 27 00:00:00 EDT 1999},

month = {Mon Sep 27 00:00:00 EDT 1999}

}

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