CHARACTERIZATION OF THE EPITHERMAL NEUTRON FIELD PRODUCED BY p+7Li REACTION IN A TANDEM ACCELERATOR USING A BONNER SPHERE SPECTROMETER

CHARACTERIZATION OF THE EPITHERMAL NEUTRON FIELD PRODUCED BY p+7Li REACTION IN A TANDEM... Abstract The proton beam produced in the Nuclear Physics line of the tandem accelerator of the Centro Nacional de Aceleradores was used to generate a neutron field. In particular, 1.912 MeV protons were used to produce well-known epithermal neutrons through the p+7Li → n+7Be reaction. The aim of the work was to characterize this field while testing the performance of a Bonner sphere spectrometer in the epithermal range. Measurements were performed in four locations at different angle (0°, 30°, 60° and 90°) from beam incidence direction in order to study the angular dependence of the field. Both a parametric and numerical unfolding methods were tested to process the counts of the central detectors and obtain the energy distribution of the neutron fluence. In addition, a Monte Carlo simulation was carried out to complete the study and provide a guess spectrum for numerical unfolding. It was found that the fluence rate and mean energy decrease as the angle from beam direction increases. Total fluence was 2.75, 1.36, 0.366 and 0.216 cm−2 per charge collected in the target at 0°, 30°, 60° and 90°, respectively. Mean energy of the field ranges from 46 to 17 keV at 0° and 60°, respectively. In all cases, given that the irradiation room is so large, the contribution of thermal neutrons to the field is small. Regarding the unfolding, the total fluences estimated by all methods were in agreement within the uncertainties. INTRODUCTION The Centro Nacional de Aceleradores (CNA) is a joint center depending on the University of Seville, the Junta de Andalucía and the Spanish High Council of Scientific Research (CSIC). It has the mission of carrying out research in particle accelerators and their multiple applications. During the last years, they have been implementing the production of different neutron fields via nuclear reactions using a linear accelerator. First studies of viability of the new facility were carried out using the p+7Li → n+7Be and d + d → n+3He reactions in the Nuclear Physics line. In the case of the lithium reaction the use of protons at energies close to the reaction threshold produces an epithermal neutron field(1–3). This type of field is of interest for studies of the Maxwellian-averaged cross-section of 197Au(n,γ) which is used as a reference for activation measurements relevant to the s-process in Nuclear Astrophysics(4). In order to characterize the neutron field produced by the nuclear reaction, an experimental campaign was performed by the Grup de Recerca en Radiacions Ionitzants (GRRI) of Universitat Autònoma de Barcelona (UAB). A Bonner sphere spectrometer (BSS) was used to measure the neutron fluence spectrum at several points around the lithium target to check the angular dependence of the field. The kinematics of the nuclear reaction predicts that neutrons are ejected with an energy ranging from 0.4 to 108 keV, and with a maximum angle of emission of 63°(5). However, the target used is thick enough to produce a continuous neutron spectrum which will be additionally affected by the scatter with the backing of the target itself, the walls and the rest of elements inside the irradiation room. In addition to measurements, a Monte Carlo (MC) simulation of the reaction and neutron transport was carried out. The work also explores the unfolding process of detector readings which follows the measurements with a BSS system. This unfolding requires some kind of a priori information of the unknown field. Although MC simulation is commonly used to obtain this information, the so-called guess spectrum, there are some unfolding codes that allow starting the process with less pre-information(6). For example, the Frascati unfolding interactive tool (FRUIT) code(7) has the option of a parametric approach, which is based on varying the parameters which describe a physically meaningful spectrum for the situation studied. This approach is advantageous when MC simulation is not available and for well-known environments, such as, for example, medical particle accelerators, has led to results in agreement with an unfolding based on a MC guess spectrum(8). Therefore, the additional purpose of this work was to test the parametric approach in comparison with the solution obtained using a MC guess spectrum for numerical unfolding. MATERIAL AND METHODS Protons of 1912 keV impinged on a thick natural lithium layer (100 μm), which was cooled by water circulating inside a copper backing (3 × 3 × 0.8 cm3) with a centered hole of 1 cm diameter and 0.75 cm height to place the Li. Water circulated around the Li to avoid the moderation of neutrons. The produced neutron field at these conditions is well known because it has been measured many times(1–3). The stability of the proton beam was checked measuring the current on the target as a function of time. The accelerator terminal and the analyzing magnet were calibrated by using 991.86 keV 27Al(p,γ) and 2409 keV 24Mg(p,p′γ) resonances and the 7Li(p,n) reaction threshold (1880.4 keV). The energy spread of the protons at these energies was lower than ±1 keV, and the precision of the calibration lower than 1 kV for the terminal. Four points around the target at a different angle from the proton beam direction (0°, 30°, 60° and 90°) were selected for characterization of the field (Figure 1) through a calculation method and measurements. Figure 1. View largeDownload slide Scheme of the accelerator hall and measurement points. Figure 1. View largeDownload slide Scheme of the accelerator hall and measurement points. The calculation method is based on Lee and Zhou(9) in which the experimental energy and angular distributions of the 7Li(p,n) reaction were parameterized from threshold to 2.5 MeV. We included those distributions in MCNPX 2.7.0 code(10) for simulating the transport of the neutrons throughout the setup. We denoted this method by LZMC and has been successfully checked with its comparison with data of similar experiments(1–3), see Refs.(11, 12) for details. The experimental determination of the spectra was carried out using the UAB BSS(13). The UAB spectrometer is based on a cylindrical (9 mm diameter, 10 mm high) 3He filled (partial pressure of 800 kPa) proportional counter (model 05NH1 from EURISYS) and includes nine high density polyethylene spheres with diameter ranging from 2.5″ to 12″. It also includes three polyethylene spheres (2.5″, 3″ and 4.2″) with a 1.5 mm thick Cd shell. The response matrix of the spectrometer was evaluated using MCNPX 2.7.0(10) and validated in reference beams providing a total uncertainty of ± 3%. More details can be found in Ref.(8). FRUIT(7) was used to process the sphere counts and to obtain the energy distribution of the neutron fluence. FRUIT allows unfolding through two different methods: one based on a parametric approach (FRUIT-PAR) and the other employing a special gradient method (FRUIT-SGM)(14). While the FRUIT-PAR option is based on varying the parameters which describe a physically meaningful spectrum for the situation studied and does not require a guess spectrum, the FRUIT-SGM option unfolds the data by iteratively altering a guess spectrum according to a special gradient method(6). Both methods were used for all measurements. For FRUIT-PAR, the code allows selecting some predetermined neutron environments to start the process. Given that an epithermal field is not available for selection in the code, a narrow source (0.3 MeV) and a moderated 252Cf source were selected. For FRUIT-SGM, a Gaussian function centered at the neutron energy expected by the kinematics of the reaction was used as a guess spectrum. These energies were 108, 79 and 15 keV, at 0°, 30° and 60°, respectively. For the point at 90°, where neutrons are not expected, the same energy of 60° was used. For all the cases previously commented, the initial energy distribution of neutrons may seem to be unphysical, especially if we assume that some neutrons have energies exceeding the reaction maximum. However, it has to be noticed that the aim was studying situations where there is no previous information and to test the performance of the unfolding code, even when an a priori unrealistic starting point is used. If necessary, a maximum energy cut-off was considered during unfolding. In order to evaluate the obtained results using the presented approaches, the calculated spectra using the LZMC method was also used as guess spectra for FRUIT-SGM. Results obtained from this unfolding will be considered the reference for comparisons. RESULTS AND DISCUSSION Figure 2 shows the neutron energy spectra obtained in point #1 by FRUIT-PAR (narrow source and moderated 252Cf source) and FRUIT-SGM (Gaussian function as a guess with and without energy cut-off and MC guess). Table 1 displays the global dosimetric quantities and the fraction of neutrons in the different energy ranges. Results are expressed in terms of the charge collected in the target. As it can be noticed in Figure 2, spectra obtained by FRUIT-PAR are very different from those obtained by FRUIT-SGM. First, FRUIT-PAR shifts the maximum energy down to around 30 and 40 keV, while the expected maximum by LZMC guess is 79 keV. In addition, the parametric unfolding introduces a higher amount of thermal neutrons. On the other hand, the use of a Gaussian function as a guess allows reproducing the peak with a tail at lower energies. However, an energy cut-off was needed in order to avoid a solution with neutrons more energetic than those produced in the nuclear reaction. In fact, the solution with the energy cut-off reproduces the position of the maximum. Conversely, in the thermal range, the Gaussian guess does not predict any neutron. All the spectral differences are reflected in the fluence fractions and mean energy reported in Table 1. Despite the different energy distribution, total fluence is in agreement within the uncertainties in all cases. Given that ambient dose equivalent evaluation is strongly dependent on the spectrum used, the values obtained using FRUIT-PAR and FRUIT-SGM do not agree. Figure 2. View largeDownload slide Neutron spectra in point #1 obtained by FRUIT-PAR (narrow source and moderated 252Cf source) and FRUIT-SGM (Gaussian guess function with and without an energy cut-off and LZMC guess). No uncertainties are shown in order to allow the comparison. Figure 2. View largeDownload slide Neutron spectra in point #1 obtained by FRUIT-PAR (narrow source and moderated 252Cf source) and FRUIT-SGM (Gaussian guess function with and without an energy cut-off and LZMC guess). No uncertainties are shown in order to allow the comparison. Table 1. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in point #1 obtained by the different unfolding methods. FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. View Large Table 1. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in point #1 obtained by the different unfolding methods. FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. View Large For the remaining points, FRUIT-SGM with the Gaussian guess also led to the best agreement with LZMC result. Therefore, the former approach allows estimating the dosimetric quantities when a simulation is not available. Table 2 displays the dosimetric quantities and spectral information obtained by FRUIT-SGM with LZMC guess for all points. Table 2. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in all points obtained by FRUIT-SGM with LZMC guess. #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. Table 2. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in all points obtained by FRUIT-SGM with LZMC guess. #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. In Figure 3, the final (unfolded) spectra are depicted together with the spectra obtained directly by simulation. Spectra are normalized to unit area to allow comparison. The kinematics of the nuclear reaction in lithium predicts a reduction in the energy of the emitted neutron as its angle increases. Accordingly, as it can be noticed in Figure 3, the maximum of the peak decreases from points #1 (79 keV) to #3 (20 keV). Fluence and ambient dose equivalent also decreases (Table 2). In point #4, no neutrons were expected from the nuclear reaction. However, scatter inside the target and its backing allows neutrons arriving up to 90° from the beam direction. These scatter neutrons appear also in point #3 as a small shoulder at higher energies. Figure 3. View largeDownload slide Final neutron spectra in points #1, #2, #3 and #4. Figure 3. View largeDownload slide Final neutron spectra in points #1, #2, #3 and #4. In general, the unfolding process introduces small differences, except in the case of point #4, for which the unfolding reduces the thermal component from 27 to 4%. It has to be taken into account that simulation only includes the walls, but the room is plenty of elements that may interfere with the thermalization and absorption of neutrons and this effect is highlighted in a point with a low contribution of direct neutrons from target and its backing, such as point #4. On the other hand, unfolded results in the other points also show a low proportion of thermal neutrons as a consequence of the small difference in the counts in the smallest spheres (2.5″, 3″ and 4.2″) with and without the Cd shell (a thermal neutron absorbent). The mean value of this difference was only 6%. The geometry of the irradiation room can explain the result. Although the line is close to a wall, the high size of the room makes that multiple scatter cannot contribute. CONCLUSIONS A BSS has been used to characterize the neutron field produced through the 7Li(p,n)7Be reaction using a proton energy close to the reaction threshold. The energy distribution of neutrons has a peak centered at 79 keV in the position behind the target. This maximum decreases to 20 keV at 60° from the beam direction. Total fluence ranges between 2.75 and 0.216 × 104 cm−2 mC−1 approximately; being smaller as the angle from the incident direction increases. The scatter in the target and its backing has as a consequence that neutrons can arrive up to 90°, not expected by the kinematics of the point-like reaction. In addition to characterizing the field, the measurement campaign allowed to test the performance of the spectrometer together with the unfolding code in an epithermal field. In contrast with the experience in other types of environments, such as neutron radioactive sources or medical particle accelerators, using a parametric method does not converge to the expected energy distribution. Using a Gaussian function as a guess spectrum for the numerical unfolding led to the closest results to the expected ones. In any case, it is worth to notice that all methods are valid for estimation of total fluence when simulation is not available. Nevertheless, for this type of field is advisable a LZMC simulation to provide the starting point for numerical unfolding. FUNDING The research presented in this article has been financed by the Spanish Ministry of Economy and Competivity under grant numbers (FIS 2012-39104-C02-01 and FPA2013-47327-C2-1-R). REFERENCES 1 Ratynski , W. and Käppeler , F. Neutron capture cross section of 197Au: a standard for stellar nucleosynthesis . Phys. Rev. C Nucl. Phys. 37 , 595 – 604 ( 1988 ). Google Scholar CrossRef Search ADS PubMed 2 Lederer , C. et al. . Definition of a standard neutron field with the7Li(p,n)7Be reaction . Phys. Rev. C 85 , 055809 ( 2012 ). Google Scholar CrossRef Search ADS 3 Feinberg , G. et al. . Quasi-stellar neutrons from the7Li(p,n)7Be reaction with an energy-broadened proton beam . Phys. Rev. C 85 , 055810 ( 2012 ). Google Scholar CrossRef Search ADS 4 Jiménez-Bonilla , P. and Praena , J. PoS (NIC XIII) 102 , https://pos.sissa.it/204/. 5 http://skisickness.com/2010/04/relativistic-kinematics-calculator/ 6 Matzke , M. Unfolding procedures . Radiat. Prot. Dosim. 107 , 155 – 174 ( 2003 ). Google Scholar CrossRef Search ADS 7 Bedogni , R. , Domingo , C. , Esposito , A. , Fernández , F. FRUIT: an operational tool for multisphere neutron spectrometry in workplaces . Nucl. Instrum. Methods Phys. Res. A 580 , 1301 – 1309 ( 2007 ). Google Scholar CrossRef Search ADS 8 Mares , V. et al. . A comprehensive spectrometry study of a stray neutron radiation field in scanning proton therapy . Phys. Med. Biol. 61 , 4127 – 4140 ( 2016 ). Google Scholar CrossRef Search ADS PubMed 9 Lee , C. L. and Zhou , X.-L. Thick target neutron yields for the 7Li(p,n)7Be reaction near threshold . Nucl. Instrum. Methods Phys. B 152 , 1 – 11 ( 1999 ). Google Scholar CrossRef Search ADS 10 Pelowitz , D. B. LA-UR-11-02295 Report, Los Alamos ( 2011 ). 11 Praena , J. , Mastinu , P.F. , Pignatari , M. , Quesada , J.M. , García-López , J. , Lozano , M. , Dzysiuk , N. , Capote , R. , Martín-Hernández , G. Measurement of the MACS of at kT=30keV as a test of a method for Maxwellian neutron spectra generation . Nucl. Instrum. Methods. Phys. Res. A 727 , 1 – 6 ( 2013 ). Google Scholar CrossRef Search ADS 12 Praena , J. , Mastinu , P.F. , Pignatari , M. , Quesada , J.M. , Capote , R. , Morilla , Y. Measurement of the MACS of 159Tb(n, γ) at kT=30keV by Activation . Nucl. Data Sheets 120 , 205 – 207 ( 2014 ). Google Scholar CrossRef Search ADS 13 Bouassoule , T. , Fernández , F. , Tomás , M. , Bakali , M. , Castelo , J. , Carmena , P. , Lara , L. Monte Carlo calculations and experimental calibrations of Bonner sphere systems with a new cylindrical helium-3 proportional counter . Radiat. Meas. 34 , 199 – 202 ( 2001 ). Google Scholar CrossRef Search ADS 14 Amgarou , K. , Bedogni , R. , Domingo , C. , Esposito , A. , Gentile , A. , Carinci , G. , Russo , S. Measurement of the neutron fields produced by a 62MeV proton beam on a PMMA phantom using extended range Bonner sphere spectrometers . Nucl. Instrum. Methods Phys. Res. A 654 , 399 – 405 ( 2011 ). Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Radiation Protection Dosimetry Oxford University Press

CHARACTERIZATION OF THE EPITHERMAL NEUTRON FIELD PRODUCED BY p+7Li REACTION IN A TANDEM ACCELERATOR USING A BONNER SPHERE SPECTROMETER

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Abstract

Abstract The proton beam produced in the Nuclear Physics line of the tandem accelerator of the Centro Nacional de Aceleradores was used to generate a neutron field. In particular, 1.912 MeV protons were used to produce well-known epithermal neutrons through the p+7Li → n+7Be reaction. The aim of the work was to characterize this field while testing the performance of a Bonner sphere spectrometer in the epithermal range. Measurements were performed in four locations at different angle (0°, 30°, 60° and 90°) from beam incidence direction in order to study the angular dependence of the field. Both a parametric and numerical unfolding methods were tested to process the counts of the central detectors and obtain the energy distribution of the neutron fluence. In addition, a Monte Carlo simulation was carried out to complete the study and provide a guess spectrum for numerical unfolding. It was found that the fluence rate and mean energy decrease as the angle from beam direction increases. Total fluence was 2.75, 1.36, 0.366 and 0.216 cm−2 per charge collected in the target at 0°, 30°, 60° and 90°, respectively. Mean energy of the field ranges from 46 to 17 keV at 0° and 60°, respectively. In all cases, given that the irradiation room is so large, the contribution of thermal neutrons to the field is small. Regarding the unfolding, the total fluences estimated by all methods were in agreement within the uncertainties. INTRODUCTION The Centro Nacional de Aceleradores (CNA) is a joint center depending on the University of Seville, the Junta de Andalucía and the Spanish High Council of Scientific Research (CSIC). It has the mission of carrying out research in particle accelerators and their multiple applications. During the last years, they have been implementing the production of different neutron fields via nuclear reactions using a linear accelerator. First studies of viability of the new facility were carried out using the p+7Li → n+7Be and d + d → n+3He reactions in the Nuclear Physics line. In the case of the lithium reaction the use of protons at energies close to the reaction threshold produces an epithermal neutron field(1–3). This type of field is of interest for studies of the Maxwellian-averaged cross-section of 197Au(n,γ) which is used as a reference for activation measurements relevant to the s-process in Nuclear Astrophysics(4). In order to characterize the neutron field produced by the nuclear reaction, an experimental campaign was performed by the Grup de Recerca en Radiacions Ionitzants (GRRI) of Universitat Autònoma de Barcelona (UAB). A Bonner sphere spectrometer (BSS) was used to measure the neutron fluence spectrum at several points around the lithium target to check the angular dependence of the field. The kinematics of the nuclear reaction predicts that neutrons are ejected with an energy ranging from 0.4 to 108 keV, and with a maximum angle of emission of 63°(5). However, the target used is thick enough to produce a continuous neutron spectrum which will be additionally affected by the scatter with the backing of the target itself, the walls and the rest of elements inside the irradiation room. In addition to measurements, a Monte Carlo (MC) simulation of the reaction and neutron transport was carried out. The work also explores the unfolding process of detector readings which follows the measurements with a BSS system. This unfolding requires some kind of a priori information of the unknown field. Although MC simulation is commonly used to obtain this information, the so-called guess spectrum, there are some unfolding codes that allow starting the process with less pre-information(6). For example, the Frascati unfolding interactive tool (FRUIT) code(7) has the option of a parametric approach, which is based on varying the parameters which describe a physically meaningful spectrum for the situation studied. This approach is advantageous when MC simulation is not available and for well-known environments, such as, for example, medical particle accelerators, has led to results in agreement with an unfolding based on a MC guess spectrum(8). Therefore, the additional purpose of this work was to test the parametric approach in comparison with the solution obtained using a MC guess spectrum for numerical unfolding. MATERIAL AND METHODS Protons of 1912 keV impinged on a thick natural lithium layer (100 μm), which was cooled by water circulating inside a copper backing (3 × 3 × 0.8 cm3) with a centered hole of 1 cm diameter and 0.75 cm height to place the Li. Water circulated around the Li to avoid the moderation of neutrons. The produced neutron field at these conditions is well known because it has been measured many times(1–3). The stability of the proton beam was checked measuring the current on the target as a function of time. The accelerator terminal and the analyzing magnet were calibrated by using 991.86 keV 27Al(p,γ) and 2409 keV 24Mg(p,p′γ) resonances and the 7Li(p,n) reaction threshold (1880.4 keV). The energy spread of the protons at these energies was lower than ±1 keV, and the precision of the calibration lower than 1 kV for the terminal. Four points around the target at a different angle from the proton beam direction (0°, 30°, 60° and 90°) were selected for characterization of the field (Figure 1) through a calculation method and measurements. Figure 1. View largeDownload slide Scheme of the accelerator hall and measurement points. Figure 1. View largeDownload slide Scheme of the accelerator hall and measurement points. The calculation method is based on Lee and Zhou(9) in which the experimental energy and angular distributions of the 7Li(p,n) reaction were parameterized from threshold to 2.5 MeV. We included those distributions in MCNPX 2.7.0 code(10) for simulating the transport of the neutrons throughout the setup. We denoted this method by LZMC and has been successfully checked with its comparison with data of similar experiments(1–3), see Refs.(11, 12) for details. The experimental determination of the spectra was carried out using the UAB BSS(13). The UAB spectrometer is based on a cylindrical (9 mm diameter, 10 mm high) 3He filled (partial pressure of 800 kPa) proportional counter (model 05NH1 from EURISYS) and includes nine high density polyethylene spheres with diameter ranging from 2.5″ to 12″. It also includes three polyethylene spheres (2.5″, 3″ and 4.2″) with a 1.5 mm thick Cd shell. The response matrix of the spectrometer was evaluated using MCNPX 2.7.0(10) and validated in reference beams providing a total uncertainty of ± 3%. More details can be found in Ref.(8). FRUIT(7) was used to process the sphere counts and to obtain the energy distribution of the neutron fluence. FRUIT allows unfolding through two different methods: one based on a parametric approach (FRUIT-PAR) and the other employing a special gradient method (FRUIT-SGM)(14). While the FRUIT-PAR option is based on varying the parameters which describe a physically meaningful spectrum for the situation studied and does not require a guess spectrum, the FRUIT-SGM option unfolds the data by iteratively altering a guess spectrum according to a special gradient method(6). Both methods were used for all measurements. For FRUIT-PAR, the code allows selecting some predetermined neutron environments to start the process. Given that an epithermal field is not available for selection in the code, a narrow source (0.3 MeV) and a moderated 252Cf source were selected. For FRUIT-SGM, a Gaussian function centered at the neutron energy expected by the kinematics of the reaction was used as a guess spectrum. These energies were 108, 79 and 15 keV, at 0°, 30° and 60°, respectively. For the point at 90°, where neutrons are not expected, the same energy of 60° was used. For all the cases previously commented, the initial energy distribution of neutrons may seem to be unphysical, especially if we assume that some neutrons have energies exceeding the reaction maximum. However, it has to be noticed that the aim was studying situations where there is no previous information and to test the performance of the unfolding code, even when an a priori unrealistic starting point is used. If necessary, a maximum energy cut-off was considered during unfolding. In order to evaluate the obtained results using the presented approaches, the calculated spectra using the LZMC method was also used as guess spectra for FRUIT-SGM. Results obtained from this unfolding will be considered the reference for comparisons. RESULTS AND DISCUSSION Figure 2 shows the neutron energy spectra obtained in point #1 by FRUIT-PAR (narrow source and moderated 252Cf source) and FRUIT-SGM (Gaussian function as a guess with and without energy cut-off and MC guess). Table 1 displays the global dosimetric quantities and the fraction of neutrons in the different energy ranges. Results are expressed in terms of the charge collected in the target. As it can be noticed in Figure 2, spectra obtained by FRUIT-PAR are very different from those obtained by FRUIT-SGM. First, FRUIT-PAR shifts the maximum energy down to around 30 and 40 keV, while the expected maximum by LZMC guess is 79 keV. In addition, the parametric unfolding introduces a higher amount of thermal neutrons. On the other hand, the use of a Gaussian function as a guess allows reproducing the peak with a tail at lower energies. However, an energy cut-off was needed in order to avoid a solution with neutrons more energetic than those produced in the nuclear reaction. In fact, the solution with the energy cut-off reproduces the position of the maximum. Conversely, in the thermal range, the Gaussian guess does not predict any neutron. All the spectral differences are reflected in the fluence fractions and mean energy reported in Table 1. Despite the different energy distribution, total fluence is in agreement within the uncertainties in all cases. Given that ambient dose equivalent evaluation is strongly dependent on the spectrum used, the values obtained using FRUIT-PAR and FRUIT-SGM do not agree. Figure 2. View largeDownload slide Neutron spectra in point #1 obtained by FRUIT-PAR (narrow source and moderated 252Cf source) and FRUIT-SGM (Gaussian guess function with and without an energy cut-off and LZMC guess). No uncertainties are shown in order to allow the comparison. Figure 2. View largeDownload slide Neutron spectra in point #1 obtained by FRUIT-PAR (narrow source and moderated 252Cf source) and FRUIT-SGM (Gaussian guess function with and without an energy cut-off and LZMC guess). No uncertainties are shown in order to allow the comparison. Table 1. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in point #1 obtained by the different unfolding methods. FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. View Large Table 1. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in point #1 obtained by the different unfolding methods. FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — FRUIT-PAR FRUIT-SGM Narrow source Moderated 252Cf Gaussian without energy cut-off Gaussian with energy cut-off LZMC Fluence (×104 cm−2 mC−1) 2.90 ± 0.65 2.87 ± 0.64 2.63 ± 0.59 2.69 ± 0.60 2.75 ± 0.62 Ambient dose equivalent (μSv mC−1) 0.70 ± 0.16 0.73 ± 0.18 1.39 ± 0.31 0.97 ± 0.23 1.10 ± 0.25 Mean energy (keV) 29.1 29.4 60.2 41.2 46.4 Thermal fractiona 8% 7% — — 3% Epithermal fractionb 92% 92% 86% 100% 97% Fast fractionc — — 14% — — aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. View Large For the remaining points, FRUIT-SGM with the Gaussian guess also led to the best agreement with LZMC result. Therefore, the former approach allows estimating the dosimetric quantities when a simulation is not available. Table 2 displays the dosimetric quantities and spectral information obtained by FRUIT-SGM with LZMC guess for all points. Table 2. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in all points obtained by FRUIT-SGM with LZMC guess. #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. Table 2. Total fluence and ambient dose equivalent per collected charge in the target and spectral information in all points obtained by FRUIT-SGM with LZMC guess. #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% #1 #2 #3 #4 Fluence (×104 cm−2 mC−1) 2.75 ± 0.62 1.36 ± 0.30 0.366 ± 0.082 0.216 ± 0.048 Ambient dose equivalent rate (μSv·mC−1) 1.10 ± 0.25 0.50 ± 0.11 0.062 ± 0.015 0.050 ± 0.011 Mean energy (keV) 46 44 17 25 Thermal fractiona 3% 0% 6% 4% Epithermal fractionb 97% 100% 94% 96% Fast fractionc — 0% 0% 0% aE < 0.4 eV. b0.4 eV < E < 100 keV. c100 keV < E < 20 MeV. In Figure 3, the final (unfolded) spectra are depicted together with the spectra obtained directly by simulation. Spectra are normalized to unit area to allow comparison. The kinematics of the nuclear reaction in lithium predicts a reduction in the energy of the emitted neutron as its angle increases. Accordingly, as it can be noticed in Figure 3, the maximum of the peak decreases from points #1 (79 keV) to #3 (20 keV). Fluence and ambient dose equivalent also decreases (Table 2). In point #4, no neutrons were expected from the nuclear reaction. However, scatter inside the target and its backing allows neutrons arriving up to 90° from the beam direction. These scatter neutrons appear also in point #3 as a small shoulder at higher energies. Figure 3. View largeDownload slide Final neutron spectra in points #1, #2, #3 and #4. Figure 3. View largeDownload slide Final neutron spectra in points #1, #2, #3 and #4. In general, the unfolding process introduces small differences, except in the case of point #4, for which the unfolding reduces the thermal component from 27 to 4%. It has to be taken into account that simulation only includes the walls, but the room is plenty of elements that may interfere with the thermalization and absorption of neutrons and this effect is highlighted in a point with a low contribution of direct neutrons from target and its backing, such as point #4. On the other hand, unfolded results in the other points also show a low proportion of thermal neutrons as a consequence of the small difference in the counts in the smallest spheres (2.5″, 3″ and 4.2″) with and without the Cd shell (a thermal neutron absorbent). The mean value of this difference was only 6%. The geometry of the irradiation room can explain the result. Although the line is close to a wall, the high size of the room makes that multiple scatter cannot contribute. CONCLUSIONS A BSS has been used to characterize the neutron field produced through the 7Li(p,n)7Be reaction using a proton energy close to the reaction threshold. The energy distribution of neutrons has a peak centered at 79 keV in the position behind the target. This maximum decreases to 20 keV at 60° from the beam direction. Total fluence ranges between 2.75 and 0.216 × 104 cm−2 mC−1 approximately; being smaller as the angle from the incident direction increases. The scatter in the target and its backing has as a consequence that neutrons can arrive up to 90°, not expected by the kinematics of the point-like reaction. In addition to characterizing the field, the measurement campaign allowed to test the performance of the spectrometer together with the unfolding code in an epithermal field. In contrast with the experience in other types of environments, such as neutron radioactive sources or medical particle accelerators, using a parametric method does not converge to the expected energy distribution. Using a Gaussian function as a guess spectrum for the numerical unfolding led to the closest results to the expected ones. In any case, it is worth to notice that all methods are valid for estimation of total fluence when simulation is not available. Nevertheless, for this type of field is advisable a LZMC simulation to provide the starting point for numerical unfolding. FUNDING The research presented in this article has been financed by the Spanish Ministry of Economy and Competivity under grant numbers (FIS 2012-39104-C02-01 and FPA2013-47327-C2-1-R). REFERENCES 1 Ratynski , W. and Käppeler , F. Neutron capture cross section of 197Au: a standard for stellar nucleosynthesis . Phys. Rev. C Nucl. Phys. 37 , 595 – 604 ( 1988 ). Google Scholar CrossRef Search ADS PubMed 2 Lederer , C. et al. . Definition of a standard neutron field with the7Li(p,n)7Be reaction . Phys. Rev. C 85 , 055809 ( 2012 ). Google Scholar CrossRef Search ADS 3 Feinberg , G. et al. . Quasi-stellar neutrons from the7Li(p,n)7Be reaction with an energy-broadened proton beam . Phys. Rev. C 85 , 055810 ( 2012 ). Google Scholar CrossRef Search ADS 4 Jiménez-Bonilla , P. and Praena , J. PoS (NIC XIII) 102 , https://pos.sissa.it/204/. 5 http://skisickness.com/2010/04/relativistic-kinematics-calculator/ 6 Matzke , M. Unfolding procedures . Radiat. Prot. Dosim. 107 , 155 – 174 ( 2003 ). Google Scholar CrossRef Search ADS 7 Bedogni , R. , Domingo , C. , Esposito , A. , Fernández , F. FRUIT: an operational tool for multisphere neutron spectrometry in workplaces . Nucl. Instrum. Methods Phys. Res. A 580 , 1301 – 1309 ( 2007 ). Google Scholar CrossRef Search ADS 8 Mares , V. et al. . A comprehensive spectrometry study of a stray neutron radiation field in scanning proton therapy . Phys. Med. Biol. 61 , 4127 – 4140 ( 2016 ). Google Scholar CrossRef Search ADS PubMed 9 Lee , C. L. and Zhou , X.-L. Thick target neutron yields for the 7Li(p,n)7Be reaction near threshold . Nucl. Instrum. Methods Phys. B 152 , 1 – 11 ( 1999 ). Google Scholar CrossRef Search ADS 10 Pelowitz , D. B. LA-UR-11-02295 Report, Los Alamos ( 2011 ). 11 Praena , J. , Mastinu , P.F. , Pignatari , M. , Quesada , J.M. , García-López , J. , Lozano , M. , Dzysiuk , N. , Capote , R. , Martín-Hernández , G. Measurement of the MACS of at kT=30keV as a test of a method for Maxwellian neutron spectra generation . Nucl. Instrum. Methods. Phys. Res. A 727 , 1 – 6 ( 2013 ). Google Scholar CrossRef Search ADS 12 Praena , J. , Mastinu , P.F. , Pignatari , M. , Quesada , J.M. , Capote , R. , Morilla , Y. Measurement of the MACS of 159Tb(n, γ) at kT=30keV by Activation . Nucl. Data Sheets 120 , 205 – 207 ( 2014 ). Google Scholar CrossRef Search ADS 13 Bouassoule , T. , Fernández , F. , Tomás , M. , Bakali , M. , Castelo , J. , Carmena , P. , Lara , L. Monte Carlo calculations and experimental calibrations of Bonner sphere systems with a new cylindrical helium-3 proportional counter . Radiat. Meas. 34 , 199 – 202 ( 2001 ). Google Scholar CrossRef Search ADS 14 Amgarou , K. , Bedogni , R. , Domingo , C. , Esposito , A. , Gentile , A. , Carinci , G. , Russo , S. Measurement of the neutron fields produced by a 62MeV proton beam on a PMMA phantom using extended range Bonner sphere spectrometers . Nucl. Instrum. Methods Phys. Res. A 654 , 399 – 405 ( 2011 ). Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

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Radiation Protection DosimetryOxford University Press

Published: Aug 1, 2018

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