近年來於核能材料安保(nuclear security)與硼中子捕獲治療(boron neutron capture therapy, BNCT)等研究皆考量採用加速器驅動與產生之快中子源為其技術發展之基礎，並對可準確量測快中子能譜之技術有相當高的需求。本論文即著重發展使用有機閃爍體偵檢器量測1-10 MeV快中子時所適用之能譜反解技術(spectrum unfolding)，將EJ-309偵檢器所量測之光輸出能譜(light output spectrum)透過演算法(algorithm)反解出快中子能譜。研究使用Python 3程式語言實現GRAVEL、MAXED、SDPSO三種能譜反解演算法。
研究的第一部對演算法進行性能測試，將文獻所列之252Cf與241AmBe標準射源之快中子能譜代入偵檢器響應函數，以模擬偵檢器光輸出能譜並進行能譜反解測試，進而分析結果以確定演算法的準確度。在測試中，研究所實現之GRAVEL與MAXED方法展現極佳的反解能力，在241AmBe的反解結果可達到小於0.02的平均相對誤差(mean relative error, MRE)，相較之下SDPSO的反解結果波動較大使平均相對誤差約為0.06，因此後續僅使用GRAVEL與MAXED演算法反解實驗所量測之中子訊號。研究的第二部分則是使用EJ-309量測137Cs、60Co、混合137Cs與60Co以及152Eu等四種光子射源，並模擬響應函數進行光子能譜反解，在分析反解結果後確定量測和響應函數的準確性。此部分之研究也探討演算法的重要輸入參數，即初始能譜、卡方檢定χ2參數、量測能譜用於反解的能量底限值EE0對反解後能譜分佈的影響。結果顯示在最佳反解參數設定下，MAXED可以得到比GRAVEL為佳的反解結果，較能成功反解如152Eu複雜的能譜。研究的最後一部分為將發展的演算法應用於反解偵檢器所量測到由252Cf與241AmBe射源所發出快中子之能譜，並再次探討輸入參數對演算結果的影響。在對252Cf射源的量測結果上，GRAVEL與MAXED反解能譜的趨勢一致，並將兩者結果與最常用於描述252Cf 的Watt能譜相比十分接近。而對241AmBe的中子量測結果顯示由GRAVEL與MAXED所反解的能譜特徵一致，但由分析推論可知因目前由蒙地卡羅模擬所得之響應函數存在誤差，致使所反解之能譜存在誤差而向高能量區平移。對演算法輸入參數的分析顯示初始能譜是影響反解結果的關鍵因素，並可能限制演算法之收斂結果。而底限值EE0的設定也會影響中子能譜反解之結果，須適當去除低頻道數之加馬射線訊號以提升中子能譜反解之正確性。

Recently, the invention of accelerator-based neutron sources applicable with novel technologies for implementing nuclear security of special nuclear material or boron neutron capture therapy (BNCT) are highly demanded and motivates the development of detection technique capable of accurately characterizing the fast neutron in a timely and reliable manner. This study focuses on researching neuron spectrum unfolding method when analyzing light output spectrum produced by the EJ-309 organic scintillator when measuring fast neutrons. Three unfolding algorithms, GRAVEL, MAXED, and SDPSO were implemented by using Python 3.
The first part of the thesis reports the performance test for the 3 selected algorithms. By using Monte Carlo simulation to generate the response functions of EJ-309 then applying them with the standard neutron spectra of the 252Cf and the 241AmBe source, ideal detector light output spectra then were acquired for testing the unfolding algorithms. The results indicated that, in such an ideal condition, the GRAVEL and MAXED developed in this study can retrieve the neutron spectrum with a high accuracy, allowing the mean relative error (MRE) to < 0.02; in contrast, the output of SDPSO exhibited a relatively high fluctuation with a deteriorated MRE of 0.06. By using the GRAVEL and MAXED, the 2nd part of the thesis reports the results of retrieving the gamma spectra from the measurements of 137Cs, 60Co, 137Cs and 60Co mixed, and 152Eu sources using the EJ-309 detector. With the simulated response functions for gamma rays to interact with the EJ-309 detector, the effects of initial guess of the spectrum, the choice of chi-squared parameter, and the set of lower limits of energy (EE0) for the light output spectrum are investigated to improve the retrieved gamma spectra with a high accuracy. Under the optimal parameters, the results indicate that the MAXED shows a higher potential to successfully retrieve a gamma spectrum with a complicated structure, such as the one of 152Eu, than the GRAVEL.
Finally, the developed algorithms of GRAVEL and MAXED were applied to retrieve the spectra of 252Cf and 241AmBe from experimentally measured data from the EJ-309, in addition to testing the effect of input parameters set for the two algorithms. For the results of 252Cf, both the GRAVEL and MAXED can retrieve a neutron spectrum close to the Watt spectrum generally used to characterize the one from the 252Cf. However, compared to the default neutron spectrum of 241AmBe, the unfolded spectra from GRAVEL and MAXED both show a tendency to shift by 0.5 MeV for the majority of the components, which can be attributed to the incompleteness of the response function simulated by the current Monte Carlo model. Regarding the choice of input parameters for the algorithms, the set of initial spectrum was a crucial factor that may direct the unfolding algorithms to finally acquire a suboptimal result with obvious deviations still. Meanwhile, the assignment of EE0 was critical in unfolding neutron spectrum, in order to appropriately excluding the noises within channels of lower numbers caused by the low-energy gammas.

摘要 i
Abstact iii
致謝 v
目錄 vi
表目錄 ix
圖目錄 xi
第一章 緒論 1
1.1 研究目的 1
1.2 中子能譜量測技術 2
1.3 研究架構 3
第二章 快中子量測與能譜反解技術 5
2.1 自發分裂與Α誘發核反應射源 5
2.2 加速器中子源 6
2.3 能譜反解技術原理 8
2.4 響應函數 9
2.4.1 光子響應函數 9
2.4.2 中子響應函數 10
2.5 能譜反解演算法 11
2.5.1 較成熟的能譜反解演算法 11
2.5.2 GRAVEL 12
2.5.3 MAXED 13
2.5.3.1 熵 13
2.5.3.2 MAXED程式概念 14
2.5.4 SDPSO 20
2.6 反解方法性能測試 22
2.7 反解參數設定方法 23
2.7.1 初始能譜的選擇 23
2.7.2 χ2的選擇 24
2.7.3 底限值EE0的選擇 25
第三章 實驗架設 26
3.1 有機閃爍體偵檢器 26
3.2 光子射源量測 27
3.2.1 實驗架設 27
3.2.2 響應函數模擬方法 29
3.3 中子射源量測 30
3.3.1 實驗架設 30
3.3.1.1 252Cf 30
3.3.1.2 241AmBe 31
3.3.2 響應函數模擬方法 32
第四章 結果與討論 34
4.1 反解方法性能測試結果 34
4.1.1 GRAVEL 34
4.1.2 MAXED 36
4.1.3 SDPSO 37
4.2 光子射源量測實驗 39
4.2.1 響應函數結果 39
4.2.2 有機閃爍體偵檢器量測結果與討論 41
4.2.3 能譜反解與最佳參數設定結果 45
4.2.3.1 137Cs射源 45
4.2.3.2 60Co射源 50
4.2.3.3 137Cs與60Co混合射源 56
4.2.3.4 152Eu射源 61
4.2.4 反解結果比較與分析 65
4.3 中子射源量測實驗 69
4.3.1 響應函數結果 69
4.3.2 有機閃爍體偵檢器量測結果 71
4.3.3 252Cf中子射源反解設定與結果 72
4.3.4 241AmBe中子射源反解結果與改善 74
4.3.4.1 反解設定與結果 74
4.3.4.2 能量校正改善 76
4.3.4.3 人為修正響應函數 78
4.3.4.4 初始能譜的影響 81
第五章 結論與未來工作 83
5.1 結論 83
5.2 未來工作 84
參考文獻 86

[1] A. Pietropaolo, M. Angelone, R. Bedogni, N. Colonna, A. J. Hurd, A. Khaplanov, F. Murtas, M. Pillon, F. Piscitelli, E. M. Schooneveld, K. Zeitelhack, “Neutron detection techniques from µeV to GeV,” Phys. Rep., vol. 875, pp. 1-65 (2020).
[2] I. Oksuz, M. Bisbee, N. Cherepy, A. Townsend, J. Hall, J. Nicolino, J. Tringe, L. Cao, “Fast neutron computed tomography of multi-material complex objects,” Proc. SPIE, vol. 11838 (2021).
[3] M. Tichy, Report PTB-7.2-93-1, Physikalisch-Technische Bundesanstalt, Braunschweig (1993).
[4] N. Kocherov, Neutron metrology file NMF-90, Report IAEA-NDS-171, International Nuclear Energy Agency, Vienna (1996).
[5] F.G. Perey, Report ORNL/TM-6062, Oak Ridge National Laboratory, Oak Ridge (1978.)
[6] W. McElroy, S. Berg, T. Crockett, R. Hawkins, Report AFWL-TR-67-41, United States Air Force (1967).
[7] M. Matzke, “Unfolding of Pulse Height Spectra: The HEPRO Program System,” Physikalisch-Technische Bundesanstalt (1994).
[8] L.W. Brackenbush, R.I. Scherpelz, “Spectrum Unfolding Using Information Theory,” (1984).
[9] M. Matzke, “The HEPROW Program System. Technical Report,” Physikalisch-Technische Bundesanstalt (2003).
[10] M. Reginatto, P. Goldhagen, “MAXED, A Computer Code for the Deconvolution of
Multisphere Neutron Spectrometer Data Using the Maximum Entropy Method,” Environmental Measurements Laboratory, New York (1998).
[11] J.T. Routti, J.V. Sandberg, “General purpose unfolding program LOUHI78 with linear and nonlinear regularizations,” Comput. Phys. Commun., vol. 21, pp. 119-144 (1980).
[12] V. Suman, P.K. Sarkar, “Neutron spectrum unfolding using genetic algorithm in a Monte Carlo simulation,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 737, pp. 76-86 (2014).
[13] H. Shahabinejad, S.A. Hosseini, M. Sohrabpour, “A new neutron energy spectrum unfolding code using a two steps genetic algorithm,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 811, pp. 82-93 (2016).
[14] H. Shahabinejad, M. Sohrabpour, “A novel neutron energy spectrum unfolding code using particle swarm optimization,” Radiat. Phys. Chem., vol. 136, pp. 9-16 (2017).
[15] A. Zimbal, “Measurement of the spectral fluence rate of reference neutron sources with a liquid scintillation detector,” Radiat Prot Dosimetry., vol. 126, pp.413-417 (2007).
[16] H. Zhu, Y. Altmann, A. Di Fulvio, S. McLaughlin, S. Pozzi, A. Hero, “A Hierarchical Bayesian Approach to Neutron Spectrum Unfolding with Organic Scintillators,” IEEE Trans Nucl Sci, vol. 66, pp.2265-2274 (2019).
[17] M. Reginattoa, P. Goldhagena, S. Neumannb, “Spectrum unfolding, sensitivity analysis and propagation of uncertainties with the maximum entropy deconvolution code MAXED,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 476, pp. 242-246 (2002).
[18] S. Neumann, R. Bottger, S. Guldbakke, M. Matzke, W. Sosaat, “Neutron and photon spectrometry in monoenergetic neutron fields,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 476, pp. 353-357 (2002).
[19] H. Klein, S. Neumann, “Neutron and photon spectrometry with liquid scintillation detectors in mixed fields,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 476, pp. 132-142 (2002).
[20] S. Zhang, C. Liu, X. Yang, C. Huang, Q. Xie, Z. Hu, Z. Hu, C. Han, X. Bai, D. Huo, K. Wu, J. Wang, Y. Zhang, Z. Wei, Z. Yao, “Study of unfolded gamma spectra by using EJ309 liquid scintillator detector,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 1006, pp. 165407 (2021).
[21] L. Giacomelli, M. Reginatto, JET EFDA Contributors, “Optimization of MAXED input parameters with applications to the unfolding of neutron diagnostics data from the Joint European Torus,” Rev. Sci. Instrum., vol. 90, pp. 093505 (2019).
[22] J. Scherzinger, J.R.M. Annand, G. Davatz, K.G. Fissum, U. Gendotti, R. Hall-Wilton, E. Håkansson, R. Jebali, K. Kanaki, M. Lundin, B. Nilsson, A. Rosborge, H. Svensson, “Tagging fast neutrons from an 241Am/9Be source,” Appl. Radiat. Isot., vol. 98, pp. 74-79 (2015).
[23] A. J. Grievson, “Time-of-flight spectrometry of the spontaneous fission neutron emission from 244Cm and 252Cf using EJ-309 liquid scintillators,” PhD thesis, Lancaster University (2020).
[24] International Organization for Standardization, part 1: characteristics and methods of production. ISO 8529-1 (2001).
[25] Y. Iwamoto et al., “Characterization of high-energy quasi-monoenergetic neutron energy spectra and ambient dose equivalents of 80–389 MeV 7 Li(p,n) reactions using a time-of-flight method,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 804, pp. 50-58 (2015).
[26] J. W. Shin, S. I. Bak, C. Ham, E. J. In, D. Y. Kim, K. J. Min, Y. Zhou, T. S. Park, S. W. Hong, V. N. Bhoraskar, “Neutron spectra produced by 30, 35 and 40 MeV proton beams at KIRAMS MC-50 cyclotron with a thick beryllium target,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 797, pp. 304-310 (2015).
[27] G. F. Knoll, “Radiation Detection and Measurement,” 4th Edition, Wiley (2010).
[28] R. Li, J. B. Yang, X.G. Tuo, J. Xu, R. Shi, “Unfolding neutron spectra from water-pumping-injection multilayered concentric sphere neutron spectrometer using selfadaptive differential evolution algorithm,” Nucl. Sci. Tech., vol. 32 (2021).
[29] J. Skilling, “Maximum Entropy and Bayesian Methods,” Kluwer Academic Publishers, Dordrecht, pp. 45 (1989).
[30] R. Byrd, P. Lu, J. Nocedal, C. Zhu, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Comput., vol. 16, pp. 1190-1208 (1995).
[31] R. Eberhart, J. Kennedy, “A new optimizer using particle swarm theory,” In: Proceedings of the Sixth International Symposium on Micro Machine and Human, pp. 39-43 (1995).
[32] R. Worrall, B. Colling, M.R. Gilbert, E. Litherland-Smith, C.R. Nobs, L.W. Packer, C. Wilson, A. Zohar, “The development, testing and comparison of unfolding methods in SPECTRA-UF for neutron spectrometry,” Fusion Eng. Des., vol. 161, pp. 112038 (2020).
[33] S. T. Park, “Neutron energy spectra of 252Cf, Am–Be source and of the D(d,n)3He reaction,” J. Radioanal. Nucl. Chem., vol. 256, pp. 163-166 (2003).
[34] S. D. Clarke, M. C. Hamel, A. Di Fulvio, S. A. Pozzi, “Neutron and gamma-ray energy reconstruction for characterization of special nuclear material,” Nucl. Eng. Technol., vol. 49, pp. 1354-1357 (2017).
[35] M. Reginatto, A. Zimbal, “Bayesian and maximum entropy methods for fusion diagnostic measurements with compact neutron spectrometers,” Rev. Sci. Instrum., vol. 79, pp. 023505 (2008).
[36] D.J. Thomas, “Neutron spectrometry,” Radiat. Meas., vol. 45, pp. 1178-1185 (2010).
[37] S. Agostinelliae et al., “Geant4—a simulation toolkit,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 506, pp. 250-303 (2003).
[38] M. A. Norsworthy, A. Poitrasson-Rivière, M. L. Ruch, S. D. Clarke, S. A. Pozzi, “Evaluation of Neutron Light Output Response Functions in EJ-309 Organic Scintillators,” Nucl. Instrum. Methods Phys. Res. Sect. A, vol. 842, pp. 20-27 (2017).
[39] T. A. Laplace et al., “Comparative scintillation performance of EJ-309, EJ-276, and a novel organic glass,” J. Instrum., vol. 15, pp. 11020 (2020).