Neutron spectrum unfolding using various computer codes: A comparison

energy, a common unit 
as “ ”). The relationship can be expressed as shown in Eq.(1). 
 ∑ (1) 
 A series of values as well as the values of can be treated as inputs of an international 
commercial unfolding code in order to deduce the incident neutron spectrum, which is a basic 
quantity to calculate other dosimetric quantities, i.e., 
 (1) an integrated neutron fluence rate overall the spectrum, ∑ , unit in 
 “ ” (“ represents for different neutron regions: thermal, ; epi-thermal, ; and 
 fast, ); 
 (2) a fractional neutron fluence rate in a specific energy region, ∑ , unit in 
 “ ” ( represents for the number of energy bins in the region); 
 (3) a fractional neutron ambient dose equivalent rate in a specific energy region, ̇ ( ) 
 ∑ , the unit can be converted to “ ” ( presents for a conversion factor 
 converting a unit neutron fluence rate into a neutron ambient dose equivalent rate); and 
 (4) a neutron ambient dose equivalent rate overall the spectrum, 
 ̇ ̇ 
 ( ) ∑ ( ) unit can be converted to “ ”. 
 In this work, various computer codes (i.e., FRUIT [2], MAXED [3], and GRAVEL [4]) 
applying different algorithms were used to unfold the incident neutron spectrum, based on the 
BSS measurements. The values of , , ̇ ( ) and ̇ ( ) were also calculated and 
compared to each other in order to confirm the proper operations of the three unfolding codes 
128 N. N. Quynh, , L. N. Thiem, “Neutron spectrum unfolding  a comparison.” 
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and the codes’ profound utility of authors in neutron spectrometry, dosimetry for radiation 
protection purposes. 
 II. MATERIAL AND METHOD 
2.1. Neutron standard field 
 Various neutron standard fields have been established at the Institute for Nuclear Science and 
Technology [5-8] in a room with inner dimensions of 7.0 x 7.0 x 7.0 . In this work, a 
simulated workplace neutron standard field of a neutron source moderated using 30 
cm diameter polyethylene sphere was investigated at various distances from the source’s center 
[7]. The X14-type encapsulation source with a neutron emission rate of 1.299 x 107 
 (on Jan.23-2015, the expanded uncertainty of 2.9% with a confidence level of 95%) is 
tracable to the National Institute of Standards and Technology (NIST, USA). More details of the 
neutron standard field can be found in previous works [6-8]. 
2.2. Bonner sphere spectrometer system 
 The BSS system consists of six spherical polyethylene moderators of different diameters (2, 
3, 5, 8, 10, and 12 inches) and a thermal neutron scintillator detector, (considered as a 
“bare” BSS in Fig. 1). The response functions of the BSS sytem ( in Eq.(1)) were simulated 
using Monte Carlo N-Particle, version 6 (MCNP6). The newest neutron cross-section library 
(ENDF/B-VIII.0 [9]) and thermal neutron scattering cross-section data (h-poly.80t [10]) were 
used in MCNP6 simulations. More detailed information can be found in previous works [6-8]. 
 Each Bonner ball was used to measure the reading (in Eq. (1)) at various distances in the 
neutron standard field. A series of values of different Bonner balls at a specific distance were 
used in combination with the corresponding values as inputs of international commercial 
computer codes to unfold the incident neutron spectrum. 
 In this work, the MCNP6 code was also used for simulating the initial guesses of incident 
neutron spectrum solutions which are required in the MAXED and GRAVEL unfolding codes. 
2.3. Unfolding code 
 Three different neutron spectrum unfolding codes with different algorithms were used to 
unfold the incident neutron spectra. The shapes of neutron spectra at a specific distance obtained 
from these three unfolding codes were then compared to each other to confirm their consistency. 
 FRUIT code 
 The FRUIT unfolding code was developed by R. Bedogni [2] with a user-friendly graphical 
interface. Neutron spectrum unfolding method is based on a linear relationship model between 
four neutron spectra in different energy regions: thermal ( ), epi-thermal ( ), fast ( ), and 
high ( ) energetic neutrons, see Eq. (2) for more details. 
 ( ) ( ) ( ) ( ) ( ) (2) 
 Where, ( ) is the thermal component with Maxellian distribution; ( ), ( ), 
 ( ) are the epi-thermal, fast, and high energetic components, respectively. The coefficients 
 , , , and are the fractional contributions of corresponding components, which are 
found by the FRUIT code to deduce the final solution. In this work’s circumstance, = 0 thus 
Eq. (2) can be rewritten as Eq. (3), if in which represents for thermal, epi-thermal, and fast 
energetic neutrons. 
 ( ) ∑ (3) 
Tạp chí Nghiên cứu KH&CN quân sự, Số 71, 02 - 2021 129 
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 MAXED code 
 The MAXED unfolding code was developed by M. Reginatto [3] based on the 
principle of maximum entropy. The final neutron spectrum, in Eq. (1), is found so that the 
entropy, in Eq. (4), reaches its maximum value. Where, is an initial guess neutron 
spectrum at ith energy bin, which is required as an input in the MAXED unfolding code. In this 
work, various values were obtained using MCNP6 simulations. 
 ∑ { ( ) } (4) 
 GRAVEL code 
 The GRAVEL unfolding code applied the iterative algorithm to find out the final neutron 
spectrum [4]. The spectral neutron fluence at the energy bin of the ( ) iteration 
was determined by the value of the iteration following Eq. (5). Where, is reading of 
 th 
detector ; is the response of detector at the i energy bin; is a coefficient calculated at 
the Jth iteration of the detector at the ith energy bin. The GRAVEL unfolding code also requires 
an initial guess neutron spectrum with non-negative values. These iterative procedures always 
lead to a non-negative solution spectrum which tends to have a better agreement between the 
unfolding solution and experimental data. 
 ∑ ( )
 ∑ 
 (5) 
 ∑ 
 ( )
 3. RESULT AND DISCUSSION 
3.1. Neutron spectrum 
 As results of the unfolding process using three unfolding codes (FRUIT, MAXED, and 
GRAVEL), the total neutron spectra of the 30 cm diameter polyethylene sphere moderated 
neutron standard field of the source (at 100 cm, 150 cm, and 200 cm) were 
obtained, the spectra at 100 cm and 200 cm from the source are shown in Fig. (1). 
 Figure 1. Neutron spectra of the 30 cm diameter polyethylene sphere moderated neutron 
 standard field at 100 cm (left) and 200 cm (right) from the 241Am-Be source, obtained by 
 different unfolding codes. 
130 N. N. Quynh, , L. N. Thiem, “Neutron spectrum unfolding  a comparison.” 
Nghiên cứu khoa học công nghệ 
 There are three main regions of spectrum components (i.e., thermal, epi-thermal, and fast 
energetic neutrons). The thermal neutrons consider the energy region lower than MeV 
caused by moderation process, the epi-thermal neutrons consider the energy region in the range 
from to MeV caused by the scattering process of neutrons with objects in the room, 
and fast neutrons consider the energy region from to MeV (in this work) representing 
the original spectrum of source reduced by a further distance. From Fig. (1), ones 
can also figure out that there is a good agreement in unfolding spectra between the MAXED and 
GRAVEL while there is a slight difference between the results obtained from these two codes 
and that obtained from the FRUIT code. 
3.2. Neutron fluence rate 
 Since the neutron spectra at three different distances (100, 150, and 200 cm) are available, the 
integrated and the fractional neutron fluence rates (unit in ) are deduced (see the 
introduction section for more details). Those values from different unfolding codes are tabulated 
in Tab. 1. Ones can figure out that neutron fluence rates of different components are consistent to 
each other within 3%. That means three different unfolding codes are reliable for neutron safety 
assessment. 
 Table 1. Neutron fluence rate ( ) of the overall spectrum ( ) and of the fractional 
 regions: thermal ( ), epi-thermal ( ), and fast ( ) at various distances in the 
 neutron standard field of a 30 cm diameter spherical polyethylene moderator, 
 obtained by different unfolding codes. 
 100 cm 150 cm 200 cm 
Quantity 
 FRUIT MAXED GRAVEL FRUIT MAXED GRAVEL FRUIT MAXED GRAVEL 
 21.43 19.86 20.14 13.64 13.93 13.61 11.35 11.60 11.29 
 18.90 18.32 18.00 11.74 11.70 11.48 9.37 9.24 9.26 
 37.29 38.66 38.88 18.65 18.89 19.36 12.28 12.35 12.56 
 77.61 76.84 77.03 44.02 44.52 44.45 33.00 33.19 33.11 
3.3. Neutron ambient dose equivalent rate 
 Since the neutron spectra at three different distances (100, 150, and 200 cm) are available, the 
integrated and the fractional neutron ambient dose equivalent rates (unit in ) are 
deduced based on ICRP 74 conversion coefficients converting from a unit neutron fluence rate to 
a neutron ambient dose equivalent rate [11]. Those values from different unfolding codes are 
tabulated in Tab. 2. Ones can figure out that neutron ambient dose equivalent rates of different 
components are consistent with each other within 3%. That means three different unfolding 
codes are reliable for neutron safety assessment. 
 Table 2. Neutron ambient dose equivalent rates ( ) of the overall spectrum, ̇ ( ) 
 and of the fractional regions: thermal, ̇ ( ) epi-thermal, ̇ ( ) and fast, ̇ ( ) at 
 various distances in the neutron standard field of 30 cm diameter spherical 
 polyethylene moderator, obtained by different unfolding codes. 
 100 cm 150 cm 200 cm 
 Quantity 
 FRUIT MAXED GRAVEL FRUIT MAXED GRAVEL FRUIT MAXED GRAVEL 
 ̇ 
 ( ) 0.82 0.78 0.79 0.53 0.54 0.53 0.44 0.45 0.44 
 ̇ 
 ( ) 1.03 1.03 1.02 0.60 0.65 0.64 0.50 0.51 0.52 
 ̇ 
 ( ) 52.05 53.25 53.54 26.17 25.60 26.27 16.79 16.47 16.75 
 ̇ ( ) 53.90 55.06 55.34 27.29 26.79 27.44 17.73 17.43 17.70 
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 4. CONCLUSION 
 Three different neutron spectrum unfolding codes (FRUIT, MAXED, and GRAVEL) were 
applied to investigate dosimetric quantities (i.e., the shape of neutron spectrum, neutron fluence 
rate, and neutron ambient dose equivalent rate) of a moderated neutron standard field. The 
shapes of neutron spectra obtained from these three unfolding codes have a slight difference 
between those obtained from MAXED and GRAVEL and that obtained from FRUIT. However, 
the values of neutron fluence rates and neutron ambient dose equivalent rates are in good 
agreement within 3% between the results obtained from these three different unfolding codes. 
That means these three unfolding codes are reliable for neutron safety assessment for radiation 
protection purposes. 
 Acknowledgment: The authors would like to sincerely thank Dr. Roberto Bedogni (National 
Laboratory of Frascati, Italy) who has approved the use of the FRUIT code. Dr. M. Reginatto (National 
Metrology Institute of Germany) is also highly appreciated for distributing to us the UMG package 
(containing MAXED and GRAVEL codes). This work was funded by Vietnam Ministry of Science and 
Technology through the supervision of the Vietnam Atomic Energy Institute via a research grant coded 
08/HĐ/ĐTCB. 
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[4]. M. Matzke, “Unfolding of pulse height spectra: The HEPRO program system”, Physikalisch-
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[6]. Ngoc-Thiem Le et al.; “Characterization of a neutron calibration field with source 
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[8]. Ngoc-Thiem Le; “Establishment of Neutron Reference Fields in Vietnam: A Review”; 
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132 N. N. Quynh, , L. N. Thiem, “Neutron spectrum unfolding  a comparison.” 
Nghiên cứu khoa học công nghệ 
 TÓM TẮT 
 TÁCH PHỔ THÔNG LƯỢNG NEUTRON SỬ DỤNG 
 CÁC PHẦN MỀM MÁY TÍNH KHÁC NHAU: SO SÁNH 
 Các đại lượng đo liều tại các khoảng cách khác nhau trong trường chuẩn liều neutron 
 của nguồn 241Am-Be được làm chậm bởi quả cầu polyethylene đường kính 30 cm đã được 
 nghiên cứu bởi hệ phổ kế cầu Bonner. Thêm vào đó, các phần mềm thương mại quốc tế 
 dùng trong tách phổ thông lượng neutron được sử dụng để thu được phổ thông lượng 
 neutron trong trường chuẩn, dạng phổ thông lượng neutron trong trường chuẩn được so 
 sánh với nhau giữa các kết quả nhận được bởi các phần mềm tách phổ khác nhau. Thông 
 lượng neutron toàn phổ và thông lượng neutron từng phần cũng được tính toán và so sánh 
 với nhau giữa các kết quả nhận được bởi các phần mềm tách phổ khác nhau. Đại lượng 
 quan trọng trong đánh giá an toàn bức xạ đối với neutron là tương đương liều neutron 
 môi trường cũng được tính toán và so sánh giữa các kết quả nhận được bởi các phần mềm 
 tách phổ khác nhau để khẳng định khả năng hoạt động chính xác của các phần mềm tách 
 phổ này. 
Từ khóa: Tách; Thông lượng neutron; Tương đương liều; Phổ. 
 Received 12th November 2020 
 Revised 10th December 2020 
 Accepted 5th January 2021 
Author affiliations: 
 1Institute for Nuclear Science and Technology; 179 Hoang Quoc Viet, Cau Giay, Hanoi; 
 2Hanoi Oncology Hospital; 42A Thanh Nhan, Hai Ba Trung, Hanoi; 
 3Vietnam Agency for Radiation and Nuclear Safety; 113 Tran Duy Hung, Hanoi. 
 *Corresponding author: LNThiem@vinatom.gov.vn. 
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