# Statistical Hauser-Feshbach Model Description of (n,α) Reaction Cross Sections for the Weak s-Process

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## Abstract

**:**

## 1. Introduction

## 2. Theory Framework

## 3. Results and Discussion

#### 3.1. $(n,\alpha )$ Reaction Cross Sections for s-Process Nuclei

#### 3.2. Astrophysically Relevant Neutron Energy Window for $(n,\alpha )$ Reactions

#### 3.3. Astrophysically Relevant Neutron Energy Range for $(n,\alpha )$ Reactions

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The $(n,\alpha )$ reaction cross section as a function of the incoming neutron energies for target nuclei as listed in the figure.

**Figure 2.**Comparison between the calculated and experimental $(n,\alpha )$ reaction cross sections for ${}^{17}$O, ${}^{26}$Al, ${}^{33}$S, ${}^{37}$Ar, and ${}^{41}$Ca. Model calculations include experimental nuclear masses and level densities from the Fermi gas model (TALYS-a) and nuclear masses and level densities from the Skyrme functional (TALYS-b). For comparison, results from the NON-SMOKER [8] TENDL-2019 [83], ENDF-B-VIII [84], JEFF-3.3 [9] and BROND-3.1 [85] data sets are also shown. The experimental data are taken from refs. [26,35,37,81,82].

**Figure 3.**The $(n,\alpha )$ reaction cross sections averaged over the Maxwell-Boltzmann distribution for the set of nuclei shown as a function of temperature.

**Figure 4.**The Maxwellian averaged cross sections (MACS) for $(n,\alpha )$ reaction for ${}^{22}$Na, ${}^{26}$Al, and ${}^{33}$S, ${}^{37}$Ar, and ${}^{39}$Ar as functions of temperature. The present results (TALYS-b) are compared to those from NON-SMOKER [8], ENDF-B-VII.1 [7], JEFF-3.1 [30], JENDL-4.0 [10], and ROSFOND-2008 [11].

**Figure 6.**The $(n,\alpha )$ reaction cross sections as a function of neutron energy $\sigma \left(E\right)$, and Maxwell-Boltzmann distribution ${f}_{D}\left(E\right)$ (in arbitrary units) for the range of temperatures $kT=$ 30–210 keV, shown for ${}^{41}$Ca, ${}^{59}$Ni, ${}^{65}$Zn, and ${}^{71}$Ge.

**Figure 7.**Relevant $(n,\alpha )$ reaction energy windows for the range of temperatures $kT=$ 30–210 keV described with the function ${f}_{I}\left(E\right)$ (in arbitrary units, see text) and the respective reaction cross sections for ${}^{17}$O,${}^{18}$F, ${}^{22}$Na, and ${}^{26}$Al target nuclei.

**Figure 8.**The same as Figure 7, but for ${}^{33}$S, ${}^{37}$Ar, ${}^{39}$Ar, and ${}^{40}$K target nuclei.

**Figure 9.**The same as Figure 7, but for ${}^{41}$Ca, ${}^{59}$Ni, ${}^{65}$Zn, and ${}^{71}$Ge target nuclei.

Nucleus | Q(MeV) |
---|---|

${}^{17}$O | 1.817 * |

${}^{18}$F | 6.418 * |

${}^{22}$Na | 1.952 * |

${}^{26}$Al | 2.462 |

${}^{33}$S | 3.870 |

${}^{37}$Ar | 3.264 |

${}^{39}$Ar | 3.060 |

${}^{40}$K | 2.973 |

${}^{41}$Ca | 6.101 |

${}^{59}$Ni | 5.711 |

${}^{65}$Zn | 6.223 |

${}^{71}$Ge | 5.704 |

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Küçüksucu, S.; Yiğit, M.; Paar, N.
Statistical Hauser-Feshbach Model Description of (*n*,*α*) Reaction Cross Sections for the Weak s-Process. *Universe* **2022**, *8*, 25.
https://doi.org/10.3390/universe8010025

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Küçüksucu S, Yiğit M, Paar N.
Statistical Hauser-Feshbach Model Description of (*n*,*α*) Reaction Cross Sections for the Weak s-Process. *Universe*. 2022; 8(1):25.
https://doi.org/10.3390/universe8010025

**Chicago/Turabian Style**

Küçüksucu, Sema, Mustafa Yiğit, and Nils Paar.
2022. "Statistical Hauser-Feshbach Model Description of (*n*,*α*) Reaction Cross Sections for the Weak s-Process" *Universe* 8, no. 1: 25.
https://doi.org/10.3390/universe8010025