# Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies

## Abstract

Here, a model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of the scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenmüller [C. A. Engelbrecht and H. A. Weidenmüller, Phys. Rev. C 8, 859 (1973)]. The ensemble average of S -matrix elements in the diagonalized channel space is approximated by a model of Moldauer [P. A. Moldauer, Phys. Rev. C 12, 744 (1975)] using the newly parametrized channel degree-of-freedom ν _{a} to better describe the Gaussian orthogonal ensemble (GOE) reference calculations. The Moldauer approximation is confirmed by a Monte Carlo study using a randomly generated S matrix, as well as the GOE threefold integration formula. Lastly, the method proposed is applied to the 238U(n,n') cross-section calculation in the fast-energy range, showing an enhancement in the inelastic scattering cross sections.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- International Atomic Energy Agency, Vienna (Austria)
- CEA, DAM, DIF, Arpajon (France)

- Publication Date:

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

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1457256

- Alternate Identifier(s):
- OSTI ID: 1267546

- Report Number(s):
- LA-UR-15-26433

Journal ID: ISSN 2469-9985; PRVCAN

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 1; Journal ID: ISSN 2469-9985

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Kawano, Toshihiko, Capote, Roberto, Hilaire, S., and Chau Huu-Tai, P.
```*Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevC.94.014612.

```
Kawano, Toshihiko, Capote, Roberto, Hilaire, S., & Chau Huu-Tai, P.
```*Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies*. United States. doi:10.1103/PhysRevC.94.014612.

```
Kawano, Toshihiko, Capote, Roberto, Hilaire, S., and Chau Huu-Tai, P. Thu .
"Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies". United States.
doi:10.1103/PhysRevC.94.014612. https://www.osti.gov/servlets/purl/1457256.
```

```
@article{osti_1457256,
```

title = {Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies},

author = {Kawano, Toshihiko and Capote, Roberto and Hilaire, S. and Chau Huu-Tai, P.},

abstractNote = {Here, a model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of the scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenmüller [C. A. Engelbrecht and H. A. Weidenmüller, Phys. Rev. C 8, 859 (1973)]. The ensemble average of S -matrix elements in the diagonalized channel space is approximated by a model of Moldauer [P. A. Moldauer, Phys. Rev. C 12, 744 (1975)] using the newly parametrized channel degree-of-freedom νa to better describe the Gaussian orthogonal ensemble (GOE) reference calculations. The Moldauer approximation is confirmed by a Monte Carlo study using a randomly generated S matrix, as well as the GOE threefold integration formula. Lastly, the method proposed is applied to the 238U(n,n') cross-section calculation in the fast-energy range, showing an enhancement in the inelastic scattering cross sections.},

doi = {10.1103/PhysRevC.94.014612},

journal = {Physical Review C},

number = 1,

volume = 94,

place = {United States},

year = {Thu Jul 21 00:00:00 EDT 2016},

month = {Thu Jul 21 00:00:00 EDT 2016}

}

*Citation information provided by*

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Web of Science

Works referenced in this record:

##
Nuclear Ground-State Masses and Deformations

journal, March 1995

- Moller, P.; Nix, J. R.; Myers, W. D.
- Atomic Data and Nuclear Data Tables, Vol. 59, Issue 2, p. 185-381