# A Study on ^{19}F(*n,α*) Reaction Cross Section

## Authors

- First Online:

DOI: 10.1007/s10894-012-9587-4

- Cite this article as:
- Uğur, F.A., Tel, E. & Gökçe, A.A. J Fusion Energ (2013) 32: 414. doi:10.1007/s10894-012-9587-4

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## Abstract

In this study, cross sections of neutron induced reactions have been investigated for fluorine target nucleus. The calculations have been made on the excitation functions of ^{19}F (*n,α*), ^{19}F(*n,xα*) reactions. Fluorine (F) and its molten salt compounds (LiF) can serve as a coolant which can be used at high temperatures without reaching a high vapor pressure and also the molten salt compounds are also a good neutron moderator. In these calculations, the pre-equilibrium and equilibrium effects have been investigated. The pre-equilibrium calculations involve the full exciton model and the cascade exciton model. The equilibrium effects are calculated according to the Weisskopf–Ewing model. Also in the present work, reaction cross sections have calculated by using evaluated empirical formulas developed by Tel et al. at 14–15 MeV energy. The obtained results have been discussed and compared with the available experimental data.

### Keywords

Fluorine-19Alpha emission spectraCross-section## Introduction

The development of fusion reactor technology requires the knowledge of cross sections of fast neutron induced reactions. Particularly, the neutron cross section data around 14–15 MeV energy have a critical importance on fusion reactor technology for the calculation of neutron spectrum, activation, nuclear heating in the components and radiation damage of metals and alloy [1–3]. The neutron induced reaction cross section data around 14–15 MeV energy are especially required to estimation of the radiation damage effects on structural fusion materials, because these reactions can cause a process resulting in the radiation damage in the structural materials because of gas formation in the structural fusion materials used in the construction of the first walls and core of the reactor. So, the radiation damage seriously influences the structural integrity of fusion reactor. Especially, due to the (*n,α*) reactions, the mechanical and physical properties of structural fusion material could be adversely affected with the generation of helium gas bubbles and voids and hence swelling of the structure. [4, 5].

Certain light nuclei such as Li, Be, F (FLİBE) and its molten salt compounds (LiF, BeF_{2} and NaF) can be used as breeding and coolant materials in fusion reactors due to its low melting point and vapour pressure. The molten salts can serve as a coolant which can be used at high temperatures without reaching a high vapor pressure and also these compounds is also a good neutron moderator [6].

In this study, we have calculated the cross-section, by using Full Exciton Model (PCROSS), Equilibrium Model (PCROSS) and Cascade Exciton Model (*CEM*) reaction mechanisms for (*n,α*) reaction. And also alpha emission spectra were calculated by using the Full Exciton Model (PCROSS) and Equilibrium Model (PCROSS) for ^{19}F nucleus.

In the calculations, pre-equilibrium alpha emission spectra were calculated by using full exciton model with PCROSS code [7]. The obtained results have been discussed and compared with the available experimental data and found agreement with each other.

## Calculations of Nuclear Reactions

*n*excitons, W

_{l}is the total particle decay probability of the

*n*excitons state per unit time, E is the excitation energy of the compound nucleus, \( \lambda_{{}}^{ + } \) is the probability of transition \( n \to n + 2 \), and \( \lambda_{{}}^{ - } \)is the transition rate of \( n \to n - 2 \) transition. The use of master equation (1), which includes both the probabilities of transition to equilibrium \( \lambda_{{}}^{ + } \)(E,n) and the probabilities of return to less complex states \( \lambda^{ - } \)(E,n), enables us to calculate in a unified manner the pre-equilibrium and equilibrium emission spectrum in accordance with:

*a*,

*b*). \( {\text{W}}_{{\text{b}}} ({\text{E}},{\text{n}},\varepsilon _{{\text{b}}} ) \) is the emission probability of a particle of type

*b*with energy \( E_{b} \). The dimensionless depletion factor \( {\text{D}}_{\text{ab}} ({\text{E}}_{\text{inc}} ) \) accounts for reduced population of each state due to the particle emission from simpler states with smaller

*n*.

*CEM*combines necessary features of the exciton model with the intranuclear cascade model. The

*CEM*assumes that the nuclear reactions consist of three processes as intranuclear cascade, pre-equilibrium and equilibrium (or compound nucleus). Generally, these three processes may contribute to any experimentally measured quantity [10, 11].

*p*is a linear momentum a single particle state. The values

*N*respectively define the total particle number considered by the cascade, the pre-equilibrium and the equilibrium processes. The inelastic cross section \( \sigma_{in} \) is not taken from the experimental data or independent optical model calculations, but it is calculated within the cascade model itself.

## Fast Neutrons Induced Empirical Cross Section Formulas

*C”*and “

*a”*are the fitting parameters determined from least-squares method for various nuclear reactions. The exponential term represents the escape of the reaction products from a compound nucleus. It has a strong s =

*(N*-

*Z)/A*dependence in Eq. (4). The non-elastic cross sections (\( \sigma_{ne} \)) have been measured intensely for many nuclides in the MeV range, enabling us to find out their variation with atomic mass. The neutron non-elastic cross section is calculated as follows,

Tel et al. suggested using these new experimental data to reproduce a new empirical formula of the cross sections of the (*n, p*), (*n, 2n*), (*n,* α), reactions at 14–15 MeV neutron incident energy [12, 13].

*s*is

*the*asymmetry parameter and defined as

*s*= (

*N*-

*Z*)

*/A.*

## Results and Discussions

^{19}F target nucleus. The pre-equilibrium calculations involve the full exciton model and the

*CEM*. The equilibrium effects are calculated according to the Weisskopf–Ewing model. The

*CEM*calculations have been made by using

*CEM03.01*computer code [10] in Figs. 1, 2, 3, 4, 5, 6, 7. The full exciton model calculations have been made by using

*PCROSS*computer code [7] in Figs. 1, 2, 3, 4, 5, 6, 7, 8. In the present study additionally, the (

*n,α*) reaction cross-sections have been calculated by using evaluated empirical formulas at 14.1 MeV neutron incident energy in Figs. 1 and 2.

*n,α*) reaction cross sections for

^{19}F have been calculated with the equilibrium, pre-equilibrium reaction models and Tel et al. formula in Figs. 1–2. The all model are higher than the experimental data for the

^{19}F(

*n,α*) reaction for incident neutron energy between 10 and 18 MeV in Fig. 1. When correction factor = 0.6 for Tel formula correspond to experimental data and when correction factor = 0.2 for the model calculation correspond to experimental data in Fig. 2. The all model calculations are lower than the experimental data for the

^{19}F(

*n,α*) reaction for incident neutron energy 2–10 MeV in Fig. 3. When correction factor = 5.0 for the model calculation correspond to experimental data. The all model calculations are very lower than the experimental data for the

^{19}F(

*n,α*) reaction for incident neutron energy 3–5 MeV in Fig. 4. When correction factor = 20.0 for the model calculation correspond to experimental data. The all model calculations are lower than the experimental data for the

^{19}F(

*n,α*) reaction in for incident neutron energy 2–10 MeV Fig. 5. When correction factor = 10.0 for the model calculation correspond to experimental data. The all model calculations are lower than the experimental data for the

^{19}F(

*n,α*) reaction in Fig. 6. When correction factor = 7.0 for the model calculation correspond to experimental data. The all model calculations are lower than the experimental data for the

^{19}F(

*n,α*) reaction in Fig. 7. When correction factor = 5.0 for the model calculation correspond to experimental data.

^{19}F target nucleus,

^{19}F target can emit alpha particle which has about 12–13 MeV kinetic energy in Fig. 8. And also In Fig. 8, when the neutron with kinetic energy 14.1 MeV hits

^{19}F, the experimental and theoretical cross-sections appear to give maximum value about emission proton energy 3–5 MeV.

## Summary and Conclusions

^{19}F nucleus has been investigated. The available experimental data in literature and the theoretical data obtained in this work are plotted in Figs. 1–8. The results can be summarized and concluded as follows:

- 1.
The all model are higher than the experimental data for the

^{19}F(*n,α*) reaction for incident neutron energy between 10 and 18 MeV. - 2.
When correction factor = 0.6 for Tel formula correspond to experimental data for the

^{19}F(*n,α*) reaction for incident neutron energy between 10 and 18 MeV. - 3.
The all model calculations are very lower than the experimental data for the

^{19}F(*n,α*) reaction for incident neutron energy 3–5 MeV. - 4.
The all model calculations are lower than the experimental data for the

^{19}F(*n,α*) reaction in for incident neutron energy 2–10 MeV. - 5.
If the neutron with 14.1 MeV energy hits to

^{19}F target nucleus,^{19}F target can emit alpha particle which has about 12–13 MeV kinetic energy - 6.
When the neutron with kinetic energy 14.1 MeV hits

^{19}F, the experimental and theoretical cross-sections appear to give maximum value about emission alpha energy 3–5 MeV.