Unfolding neutron spectrum using Doppler broadened γ peak shapes

https://doi.org/10.1016/j.radphyschem.2021.109647Get rights and content

Highlights

  • Developed a Monte Carlo method to simulate the Doppler broadening process.

  • Calculated the Doppler broadening gamma peaks for different neutron energies.

  • Unfolded the neutron spectrum basing on the Doppler broadened gamma spectra.

Abstract

The Doppler broadening of gamma rays occurs in the fast neutron analysis with photons emitted in inelastic scattering reactions on certain nuclei, such as 12C and 14N. In this paper, we developed an algorithm based on the Monte Carlo method to calculate the Doppler broadened gamma peak shape of the 4.438 MeV gamma ray emitted by 12C in graphite when exposed to fast neutrons of different energies. The SAND-II unfolding iterative method is applied to obtain the spectrum of the incident neutron beam by using the Doppler broadened gamma spectra. In the calculation example, the unfolded neutron spectrum shows reasonable agreements with the original incident neutron spectrum.

Introduction

In prompt gamma neutron activation analysis, the Doppler broadening of gamma rays may occur in the fast neutron analysis due to photons emitted in inelastic scattering reactions on light nuclei, such as 12C or 14N with excited states featuring lifetimes much shorter than the time of flight of a recoiling nucleus in the material (Barzilov and Womble, 2014). The Doppler broadening may affect the accurate measurements of the intensity of the prompt gamma-rays. On the other hand, using Doppler broadened gamma peak shapes, information such as neutron energy, lifetime of the excited recoiling nucleus or stopping power of the material for a given recoiling nucleus can be derived.

The current methods for measuring neutron energy spectrum mainly include time-of-flight (TOF) method (Kim et al., 2009), Bonner sphere spectrometer (Ogata et al., 2011) and liquid scintillation spectrometer (Bai et al., 2018). These methods all measure the neutrons of different energies directly. In this paper, the neutron energy is tried to be obtained by measuring the gamma spectra of Doppler effect generated by the neutrons. Because gamma energy spectrum measurement has higher accuracy and efficiency and is easier to implement, this method will be a good supplement to the traditional neutron measurement.

The line shape of Doppler broadened gamma-ray peaks is related to the energy of the emitted neutron, lifetime of the recoiling nucleus, stopping power of the material and geometrical condition. Therefore, the shapes of the gamma peaks can be calculated for the given nucleus when the physical condition is given. A method for calculating Doppler broadened peak shapes is presented together with a discussion on how to obtain information from the line-shape (Fynbo, 2003; Fynbo et al., 2004).

In an experimental condition where the target nucleus, material and geometrical layout are fixed, the Doppler broadened gamma peak shape is only determined by the neutron energy. In this paper, we developed an algorithm based on the Monte Carlo method to calculate the Doppler broadened gamma peak shape of the 4.438 MeV gamma ray emitted by 12C in graphite when exposed to fast neutrons of different energies. We also applied the SAND-II method to unfold the spectrum of the incident neutron beam by using the Doppler broadened gamma-ray spectra.

Section snippets

Calculation of Doppler broadened gamma peak shapes

The target nucleus emits a gamma-ray along its path inside the material after the excitation by the incident neutron and the theory of how to calculate the Doppler broadened gamma-ray peaks can be found in Ref. (Fynbo, 2003). In the section we develop a Monte Carlo program to simulate this process. As shown in Fig. 1, the target nucleus is 12C in graphite and the detector is a High Purity Germanium detector in this calculation.

First, we calculate the initial velocity β0 (β0 = v0/c, where v0 is

Peak shapes

The energy threshold Eth for the neutron inelastic reaction n+12C→n'+12C*+γ is 4.8 MeV. Therefore, the Doppler gamma peak shapes for incident neutrons with energies between 5 MeV and 10 MeV are calculated. We select two arrangements (θ = 0° and θ = 90°) to calculate the peak shapes and the results are shown in Fig. 3 and Fig. 4. Fig. 3 shows the parts of the calculated peak shapes of Doppler gamma of 12C induced by different incident neutron energy with the detector placed at position 1 and

Unfolding the neutron spectrum

The energy of a mono-energetic incident neutron beam can be easily derived from the peak shapes of Doppler broadened gamma rays because of the direct correspondence between them. Therefore, it can be inferred that the spectrum of a complicated incident neutron beam could be obtained by analyzing the Doppler broadened gamma peak shapes. Is this section, some attempts are made to derive the neutron spectrum from the gamma peak shapes. It is assumed that the energy spectrum of incident neutron Φ

Conclusion

In this paper, we developed an algorithm based on Monte Carlo method to calculate the Doppler gamma peak shapes of the 4.438 MeV gamma ray emitted by 12C in graphite when exposed to fast neutrons with different energies. The calculated peak shapes show direct relationship with the energy of the incident neutron. Based on this relationship, we apply a SAND-II iterative method to unfold the spectrum of the incident neutron beam by using the Doppler broadened gamma spectra. In the given example,

Credit author statement

Yi Lu: Writing the initial draft. Zhaohui Song: Ideas and suggestions, Zengqi Cui: Data Processing, Huaiyong Bai: Figure processing, Haoyu Jiang: Unfolding Method, Luyu Zhang: Revision, Guohui Zhang: Corresponding author, reviewing and editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The present work is financially supported by the National Natural Science Foundation of China (No. 11575146 and No.11535010).

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