Journal of Fusion Energy

, Volume 32, Issue 3, pp 414–418

A Study on 19F(n,α) Reaction Cross Section

Authors

  • F. A. Uğur
    • Department of Physics, Faculty of Arts and ScienceOsmaniye Korkut Ata University
    • Department of Physics, Faculty of Arts and ScienceOsmaniye Korkut Ata University
  • A. A. Gökçe
    • Department of Physics, Faculty of Arts and ScienceÇukurova University
Original Research

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 19F (n,α), 19F(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 [13]. 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, BeF2 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 19F 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

The mechanism of a nuclear reaction depends on the energy of incident particle. It is known that in the energy region below 10 MeV, compound nuclear processes dominate. The exciton pre-equilibrium model for nuclear reactions is a phenomenological model based on phase space arguments. The equilibration in energy of a composite nucleus is followed in terms of the creation and destruction of pairs of particle and hole degrees of freedom. Exciton model is based on the solution of the master equation in the form [8, 9]. Integrating the master equation over time, we can write as
$$ \begin{aligned} - {\text{q}}({\text{n}},{\text{t}} = 0) & = \lambda^{ + } ({\text{E}},{\text{n}} + 2)\tau ({\text{n}} + 2) + \lambda^{ - } ({\text{E}},{\text{n}} - 2)\tau ({\text{n}} - 2) \\ & \quad - \left[ {\lambda^{ + } ({\text{E}},{\text{n}}) + \lambda^{ - } ({\text{E}},{\text{n}}) + {\text{W}}_{l} ({\text{E}},{\text{n}})} \right]\tau ({\text{n}}) \\ \end{aligned} $$
(1)
where q (n, t = 0) is the initial condition, \( \tau (n) \) is the time during which the system remains in a state of n excitons, Wl 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:
$$ \frac{{{\text{d}}\sigma _{{{\text{ab}}}} }}{{{\text{d}}\varepsilon _{{\text{b}}} }}(\varepsilon _{{\text{b}}} ) = \varepsilon _{{{\text{ab}}}}^{{\text{r}}} ({\text{E}}_{{{\text{inc}}}} ){\text{D}}_{{{\text{ab}}}} ({\text{E}}_{{{\text{inc}}}} )\sum\limits_{{\text{n}}} {{\text{W}}_{{\text{b}}} ({\text{E}},{\text{n}},\varepsilon _{{\text{b}}} )\tau ({\text{n}})} $$
(2)
where \( {{\upsigma}}_{\text{ab}}^{\text{r}} ({\text{E}}_{\text{inc}} ) \) is cross section of the reaction (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.
The 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].
$$ \sigma \left( p \right)dp = \sigma_{in} \left[ {N^{cas} \left( p \right) + N^{prq} \left( p \right)} \right.\left. { + N^{eq} \left( p \right)} \right]dp, $$
(3)
here 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

The empirical cross sections of nuclear reactions induced by fast neutrons can be approximately written in the following form,
$$ \sigma (n,x) = C\sigma_{ne} \exp \left[ {as} \right] $$
(4)
here \( \sigma_{ne} \) is the neutron non-elastic cross section, and the coefficients “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,
$$ \sigma_{ne} = \pi r_{0}^{2} (A^{1/3} + 1)^{2} $$
(5)
where, \( r_{0} = 1.2 \times 10^{ - 13} \)cm.

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].

Tel formula for (n,α) reactions at 14–15 MeV [13];
$$ \begin{array}{*{20}c} {{\text{odd-Z}},{\text{ even-N}}} \hfill & {\sigma _{{{\text{n}},\alpha }} = 1793(A^{{1/3}} + 1)^{2} \exp [ - 34.04s]} \hfill \\ {{\text{even-Z}},\,{\text{even-N}}} \hfill & {\sigma _{{{\text{n}},\alpha }} = 1443(A^{{1/3}} + 1)^{2} \exp [ - 32.17s]} \hfill \\ {{\text{even-Z}},{\text{odd-N}}} \hfill & {\sigma _{{{\text{n}},\alpha }} = 1941(A^{{1/3}} + 1)^{2} \exp [ - 35.97s]} \hfill \\ \end{array} $$
(6)
where s is the asymmetry parameter and defined as s = (N - Z)/A.

Results and Discussions

In this study, the pre-equilibrium and equilibrium reactions have been made for 19F 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.
https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig1_HTML.gif
Fig. 1

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 10–18 MeV. Experimental values were taken from Ref. [14]

https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig2_HTML.gif
Fig. 2

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 12–18 MeV. Experimental values were taken from Ref. [14]

The (n,α) reaction cross sections for 19F have been calculated with the equilibrium, pre-equilibrium reaction models and Tel et al. formula in Figs. 12. The all model are higher than the experimental data for the 19F(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 19F(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 19F(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 19F(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 19F(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 19F(n,α) reaction in Fig. 7. When correction factor = 5.0 for the model calculation correspond to experimental data.
https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig3_HTML.gif
Fig. 3

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 4–10 MeV. Experimental values were taken from Ref. [14]

https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig4_HTML.gif
Fig. 4

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 3–7 MeV. Experimental values were taken from Ref. [14]

https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig5_HTML.gif
Fig. 5

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 3–10 MeV. Experimental values were taken from Ref. [14]

https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig6_HTML.gif
Fig. 6

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 3–10 MeV. Experimental values were taken from Ref. [14]

https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig7_HTML.gif
Fig. 7

The comparison of calculated excitation function of 19F(n,α) reaction with the values reported in literature between 4–12 MeV. Experimental values were taken from Ref. [14]

We can say that if the neutron with 14.1 MeV energy hits to 19F target nucleus, 19F 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 19F, the experimental and theoretical cross-sections appear to give maximum value about emission proton energy 3–5 MeV.
https://static-content.springer.com/image/art%3A10.1007%2Fs10894-012-9587-4/MediaObjects/10894_2012_9587_Fig8_HTML.gif
Fig. 8

The comparison of alpha emission spectra of 19F (n,xα) reaction with the values reported in literature at 14.1 MeV incident neutron energy. Experimental values were taken from Ref. [14]

Summary and Conclusions

In this study, reaction cross section of 19F nucleus has been investigated. The available experimental data in literature and the theoretical data obtained in this work are plotted in Figs. 18. The results can be summarized and concluded as follows:
  1. 1.

    The all model are higher than the experimental data for the 19F(n,α) reaction for incident neutron energy between 10 and 18 MeV.

     
  2. 2.

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

     
  3. 3.

    The all model calculations are very lower than the experimental data for the 19F(n,α) reaction for incident neutron energy 3–5 MeV.

     
  4. 4.

    The all model calculations are lower than the experimental data for the 19F(n,α) reaction in for incident neutron energy 2–10 MeV.

     
  5. 5.

    If the neutron with 14.1 MeV energy hits to 19F target nucleus, 19F target can emit alpha particle which has about 12–13 MeV kinetic energy

     
  6. 6.

    When the neutron with kinetic energy 14.1 MeV hits 19F, the experimental and theoretical cross-sections appear to give maximum value about emission alpha energy 3–5 MeV.

     

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© Springer Science+Business Media New York 2012