Home About us Editorial board Search Ahead of print Current issue Archives Submit article Instructions Subscribe Contacts Login 
Home Print this page Email this page Small font size Default font size Increase font size Users Online: 141

 Table of Contents 
Year : 2016  |  Volume : 39  |  Issue : 2  |  Page : 75-82  

Prompt gamma-based neutron dosimetry for Am-Be and other workplace neutron spectra

Manipal Centre for Natural Sciences, Manipal University, Manipal, Karnataka, India

Date of Web Publication13-Sep-2016

Correspondence Address:
P K Sarkar
Manipal Centre for Natural Sciences, Manipal University, Manipal - 576 104, Karnataka
Login to access the Email id

Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0972-0464.190393

Rights and Permissions

A new field-deployable technique for estimating the neutron ambient dose equivalent H*(10) by using the measured prompt gamma intensities emitted from borated high-density polyethylene (BHDPE) and the combination of normal HDPE and BHDPE with different configurations have been evaluated in this work. Monte Carlo simulations using the FLUKA code has been employed to calculate the responses from the prompt gammas emitted due to the monoenergetic neutrons interacting with boron, hydrogen, and carbon nuclei. A suitable linear combination of these prompt gamma responses (dose conversion coefficient [DCC]-estimated) is generated to approximate the International Commission on Radiological Protection provided DCC using the cross-entropy minimization technique. In addition, the shape and configurations of the HDPE and BHDPE combined system are optimized using the FLUKA code simulation results. The proposed method is validated experimentally, as well as theoretically, using different workplace neutron spectra with a satisfactory outcome.

Keywords: Borated high-density polyethylene, cross-entropy minimization technique, Monte Carlo simulations, neutron ambient dose equivalent

How to cite this article:
Udupi A, Panikkath P, Sarkar P K. Prompt gamma-based neutron dosimetry for Am-Be and other workplace neutron spectra. Radiat Prot Environ 2016;39:75-82

How to cite this URL:
Udupi A, Panikkath P, Sarkar P K. Prompt gamma-based neutron dosimetry for Am-Be and other workplace neutron spectra. Radiat Prot Environ [serial online] 2016 [cited 2022 Jan 19];39:75-82. Available from: https://www.rpe.org.in/text.asp?2016/39/2/75/190393

  Introduction Top

In the neutron generating facilities such as accelerators and nuclear reactors, a large abundance of neutrons in the surrounding environment is observed. Hence, it is important to ensure the radiological safety outside the shield surrounding these facilities. For this purpose, an important operational radiological quantity, known as the neutron ambient dose equivalent, H*(10) is used.[1]

Rem-counters have been used as workplace neutron monitors for many years. These counters consist of polyethylene neutron moderators and thermal neutron detectors and the neutron ambient dose equivalent H*(10) is estimated using simulated response matrices obtained for different monoenergetic neutrons. The acceptable response for these rem-counters lies in the neutron energy range of thermal to about 10 MeV. Most of the commercially available monitors of such type underestimate H*(10) in the energy range of thermal to 1 eV and overestimate between energy 1 eV to 100 keV. The response reduces significantly above 10 MeV leading to an underestimation of H*(10).[2] Another disadvantage of using such rem-counters is that their response changes with time and hence frequent calibrations are required.

When a neutron interacts with any nuclei in the target (sample) material, the instantaneous gamma rays produced are known as prompt gammas. Based on the fact that prompt gamma intensities from any material are related to the material composition, incident neutron energy, and neutron fluence, a new technique has been introduced to estimate neutron ambient dose equivalent H*(10). [3] This method uses the measured prompt gamma intensities emitted from high-density polyethylene (HDPE) to estimate the H*(10). Since H*(10) is estimated from the energy-dependent neutron fluence using neutron fluence to ambient dose equivalent conversion coefficients (DCC), prompt gamma intensities can be related to neutron ambient dose equivalent.

In our previous work,[3] only HDPE cylinders were used as target material from which prompt gammas are emitted due to the interaction of neutrons of different energies with hydrogen and carbon nuclei in the energy range from about 0.5 to about 14 MeV. For neutron energies above 0.5 MeV, the HDPE responses approximated well the International Commission on Radiological Protection provided-DCC [4] (ICRP-DCC) values and overestimated the dose below 0.5 MeV.

To overcome this drawback, boron is used as the low energy neutron absorber in the present work. By considering borated HDPE (BHDPE) and the combination of HDPE and BHDPE in different configurations as prompt gamma generating sample materials, we have tried to study the possible improvements in the estimation of neutron dose. The neutron ambient dose can be estimated by measuring the peak intensities of the characteristic prompt gammas emitted from boron (0.477 MeV), hydrogen (2.2 MeV), and carbon (4.43 MeV) nuclei present in the target material. For theoretical considerations, simulations have been carried out for the above-mentioned configurations by Monte Carlo simulations using FLUKA code. [5],[6] A response matrix of prompt gamma generating responses of boron, hydrogen, and carbon is estimated for various monoenergetic neutrons. These responses are combined suitably to obtain a close match of the combined response (DCC-estimated) to the ICRP-DCC values.


In the present work HDPE with a cylindrical configuration, pure BHDPE with conical configuration and combination of HDPE and BHDPE with spherical configurations are considered as samples. The combined HDPE and BHDPE with spherical configurations is optimized for different dimensions to arrive at a configuration which is in better agreement with the ICRP-DCC. The DCC-estimated and ICRP-DCC are folded with neutron fluence to obtain H*(10)R and H*(10), respectively, for different workplace neutron spectra.

  Materials and Methods Top

Sample configuration and composition

BHDPE constitutes of hydrogen, carbon, and around 5% of boron which is a good low energy neutron absorber. In the current work, theoretical and experimental studies have been done for both cylindrical HDPE and conical BHDPE, and also the combination of both in spherical configuration is studied theoretically. The density of HDPE is 0.98 g/cm 3 with a weight fraction of hydrogen and carbon as 0.144 and 0.856, respectively, and the density of BHDPE is 1.08 g/cm 3 with a weight fraction of HDPE and boron as 0.95 and 0.05, respectively. In the case of combination configuration, a HDPE sphere surrounded by the BHDPE layer is selected with different sizes for optimization. The dimensions of the pure HDPE cylindrical configuration are 10.25 cm radius and 22.5 cm of length, whereas those of pure BHDPE conical configuration are base radius 10 cm, apex radius 5 cm, and length 40 cm. The combination configuration is having a 4 cm radius HDPE sphere surrounded by a 5.5 cm thick BHDPE layer. When the thermal and fast neutrons interact with the material, characteristic prompt gammas are emitted. The reactions responsible for the emission of prompt gamma are 10 B (n, α)7 Li (0.447 MeV of boron),1 H (n, γ)2 H (2.2 MeV of hydrogen), and 12 C (n, n')12 C (4.43 MeV of carbon).

Dose estimation method

BHDPE consists of boron, hydrogen, and carbon, whereas HDPE consists of only hydrogen and carbon. Even though HDPE is a good neutron moderator, it does not absorb the low energy neutrons as much as BHDPE, which is a better absorber of low energy neutrons. When prompt gammas are emitted from the sample, the significant constituents can be identified by the well-resolved peaks in gamma spectrum and the net area under any one of these peaks can be determined using a NaI (Tl) gamma-ray spectrometer.

The area under the photopeak Ai where i denotes the constituent elements (boron, hydrogen, or carbon) is related to incident neutron energy distributionφ j and the response matrix Rij as,

Where, Rij is the probability that a neutron emitted from the source in the energy bin j interacts with the nuclei of sample material, undergoes a possible change in energy, and produces a gamma photon which is detected in the NaI detector and contributes to the peak area count.

The constituents of the matrix Rij are combined and made to fit the ICRP-DCC [4] denoted by Fj using the parameters Ci that can be estimated by cross-entropy minimization technique.

Where, εj is the fitting error in the j-th energy bin. By minimizing the magnitude of εj, one can obtain the optimal values of the coefficients Ci(i = 1, 2, 3). Here, εj is an unknown factor which may have a positive or negative contribution.

The relation between neutron ambient dose and neutron fluence is given as,

Using Equations 1 and 2, one can write Equation 3 as,

Equation 4 gives the estimated value of neutron ambient dose equivalent from measured area under the peak of the prompt gammas produced due to the neutron interaction with sample material and approximates the actual dose H*(10) closely.

In the present work, we have defined another estimate of the ambient dose equivalent by multiplying φ j's with the response matrix (Rij) and summed:

Cross-entropy minimization technique

The cross-entropy minimization technique used in the present work is also known as Kullback–Leibler (KL) divergence [7],[8] and is a quantitative estimate of the difference or the distance between two probability distributions. In other words, KL divergence gives the measure of information lost when one distribution is being approximated by another. In this method, the distributions Fj(ICRP-DCC) and (DCC-estimated) are converted to corresponding probability distribution Pj and , respectively. Where,

And the probability distributions are given by and

The KL divergence of from Pj is given by,

Here D (Pj, PjC)1 is minimized by varying the coefficients C1, C2, and C3.

Monte Carlo simulations

The elements of response matrix are estimated using the Monte Carlo simulations in the FLUKA code of version 2011.2c.[5],[6] In the simulation, a plane-parallel beam of monoenergetic neutrons or neutrons with a distribution of energies is incident on the curved surface of the sample. The simulation is started by selecting a monoenergetic neutron from j-th energy bin of the source neutrons where the energy of the neutron is a mid-point energy of the energy bin. The collision point of the neutron inside the sample is chosen randomly using the macroscopic neutron interaction cross-sections. Moreover, the interacting nucleus (boron, hydrogen, or carbon) and interaction type (elastic or inelastic) are randomized. The neutron is followed inside the sample material until either it is absorbed by the sample or escapes from the sample. The emitted prompt gamma photons are followed till it is detected by a NaI detector. The USRTRACK option (track length estimator) available in FLUKA is used to estimate the gamma fluence. The incident neutron energy ranges from 10−7 MeV to 14 MeV in 34 steps. The emitted prompt gammas are estimated in the energy range of 0.15–15 MeV with the energy bin width of 0.15 MeV. The simulation is carried out with 107 histories which is divided into five separate batches.

Experimental details

The schematic of the experimental setup used in the present study is shown in [Figure 1]. The measurements are done using a 592 GBq (16 Ci) Am-Be neutron source doubly encapsulated in stainless steel placed inside a solid concrete bunker with dimensions 140 cm × 140 cm × 175 cm. The Am-Be source, manufactured by Amersham, UK, has a cylindrical configuration with diameter 5 cm and height 22 cm, emitting 4 × 107 neutrons per se cond in 4π directions. One side of the concrete bunker has an opening of 40 cm × 40 cm which allows the emitted neutrons to come out when the source is aligned at the center of the opening.
Figure 1: Cross-sectional view of experimental setup as used in the FLUKA simulations

Click here to view

The samples are placed such that the center of the sample is at 85 cm distance from the source and the central axis of the samples is at a level coinciding with the center of the source and the neutron beam falls on the curved surface of the sample. The NaI (Tl) detector has a diameter of 5 cm and length 5 cm, placed at a distance of 10 cm from the sample where it measures the prompt gamma energy spectrum emitted from the sample. During the measurements, the detector is covered with an annular lead shield of 20 cm outer diameter and 10 cm inner diameter which extends 10 cm above the top surface of the detector and has an opening of 10 cm at the top. A USB-based 1024 channel analyzer coupled to a 5 cm × 5 cm NaI (Tl) scintillation detector has been used as gamma spectroscopy system.

  Results and Discussions Top

Experimental results[Figure 2] and [Figure 3] show the experimentally measured prompt gamma spectra of a cylindrical HDPE and a conical BHDPE, respectively, having dimensions similar to the one used in the simulations. In the prompt gamma spectrum from cylindrical HDPE sample, only one prompt gamma peak (2.2 MeV) is observed which is from hydrogen nuclei. Due to the concrete shield around the Am-Be source, higher energy neutrons are depleted in the experimental spectrum. Hence, the prompt gamma peak due to carbon is not present in the spectrum shown in [Figure 2]. Similarly, in the prompt gamma spectrum of conical BHDPE sample shown in [Figure 3], only prompt gamma peak from boron is observed. The absence of 2.2 MeV peak can be explained by the fact that the prompt gamma response of hydrogen is much smaller compared to that of boron and the neutrons get absorbed in BHDPE by boron which has a very high absorption cross-section leading to a vanishingly small prompt gamma peak from hydrogen.
Figure 2: Experimentally measured gamma spectra from a cylindrical high-density polyethylene sample

Click here to view
Figure 3: Experimentally measured gamma spectra from a conical borated high-density polyethylene sample

Click here to view

The gamma peaks observed without the HDPE or the BHDPE samples (background) are contributed mainly by the elements present in the concrete bunker surrounding the source and the walls of the room. Even though, the detector is shielded with lead the high energy gammas like 4.4 MeV from C, 2.6 MeV from Pb (shield material), etc., can reach to the detector. Since carbon and hydrogen are present in both concrete and sample, we observe the 4.4 and 2.2 MeV peak in both spectra. Thus, the peaks observed without sample are from the concrete and lead shield. The peaks observed with the sample are the increased contribution due to the C, H, and B from the sample which coincides with the background peaks.

Measurements of prompt gamma peaks from BHDPE and HDPE are fraught with two major practical difficulties. First, in the case of BHDPE, the prompt gammas of 0.477 MeV from boron have significant interference from 0.511 MeV annihilation gammas originating in the lead shield or surrounding materials due to pair production from 2.2 MeV prompt gammas from hydrogen. The NaI (Tl) detector used in the present case cannot resolve these two closely spaced gamma energies what a high-resolution HpGe detector could have done. It is found from the simulated results that this interference increases with increasing incident neutron energy. To reduce the effect of this interference, in the present case, the experimental determination of the neutron dose is done using the coefficient Ci obtained by fitting the response up to a neutron energy of 0.3 MeV. This is somewhat justified because in the present case, about 75% of the neutrons emerging from the concrete bunker have energies below 0.3 MeV. Second, in the case of HDPE, the 5 cm × 5 cm NaI detector has very low detection efficiency for 2.2 MeV gammas from hydrogen thereby underestimating the peak intensity. The effect due to reduced efficiency has been corrected using Monte Carlo simulations.

[Table 1] gives the dose rates (µSv/s) obtained from the experimental measurement of cylindrical HDPE and conical BHDPE and compared with the actual dose rate H*(10) [Equation 3], as well as H*(10)R[Equation 5]. The coefficients for dose estimation are obtained using the FLUKA simulations described in the next section.
Table 1: Comparison of neutron dose rate measured in experiment with actual and computed dose rates (μSv/s) for neutrons emerging out of the concrete bunker containing a 592 GBq Am.Be neutron source

Click here to view

Simulation results

The individual responses of boron, hydrogen, and carbon are shown in [Figure 4] where the responses are normalized at 1 MeV for boron and hydrogen, while the carbon response is normalized at 10 MeV. A linear combination of the prompt gamma responses of boron (0.477 MeV), hydrogen (2.2 MeV), and carbon (4.43 MeV) is taken by multiplying with the coefficients CB(boron), CH(hydrogen), and CC(carbon) to get DCC-estimated. A minimization technique based on cross-entropy minimization is used to estimate the coefficients (in units of pSv/count). These responses are approximated to ICRP-DCC using cross-entropy minimization technique and plotted along with ICRP-DCC in [Figure 5]. From [Figure 5], it can be observed that cylindrical HDPE gives a poor fit in the lower energy region when compared with the conical BHDPE.
Figure 4: Individual responses of the boron, hydrogen, and carbon for different neutron energies plotted along with the International Commission on Radiological Protection-dose conversion coefficient

Click here to view
Figure 5: Dose conversion coefficient estimated for cylindrical high-density polyethylene and conical borated high-density polyethylene plotted along with International Commission on Radiological Protection-dose conversion coefficient

Click here to view

The above results indicate that only HDPE or only BHDPE alone cannot be used efficiently to measure the neutron ambient dose equivalent. Hence, a combination of both HDPE and BHDPE in spherical configuration is considered for the further study. To optimize the thickness of HDPE and BHDPE in a spherical configuration, simulations have been carried out to arrive at the DCC-estimated which matches well with ICRP-DCC.

Optimization of sample configurations

In [Figure 6] where the DCC-estimated values for different spherical configurations of combined HDPE and BHDPE are plotted, the dimensions of inner and outer spheres are given as sph-(x, y), x being the radius of inner HDPE sphere in centimeter, and y being the outer BHDPE thickness in centimeter. Observations from [Figure 6] indicate that spherical configuration sph-(4, 5.5) is a better approximation to ICRP-DCC than other dimensions.
Figure 6: Dose conversion coefficient estimated at different neutron energies for six various dimensions for combined high-density polyethylene (in) borated high-density polyethylene (out) in spherical configurations plotted along with the International Commission on Radiological Protection-dose conversion coefficient

Click here to view

One way of quantifying this observation is to calculate the goodness of fit by calculating the reduced Chi-square using the equation,

Where O is the observed quantity, i.e., DCC-estimated, E is the expected quantity, i.e., ICRP-DCC, and θ is the measure of the degree of freedom (i.e., total number of points – [number of constraints + 1], where the constraints are the number of estimated parameters). The lower value of the reduced Chi-square indicates better fit wherein for a statistically good fit, the reduced Chi-square value should be equal to 1. In the present work, we have considered the lowest reduced Chi-square value as the best fit. The reduced Chi-square is estimated for the entire neutron energy range, as well as for lower (E ≤0.05 MeV) and higher (E >0.05 MeV) energy regions separately. [Table 2] gives the estimated reduced Chi-square values for various sample geometries such as combined spherical HDPE and BHDPE, cylindrical HDPE and conical BHDPE configurations. From [Table 2], it is clear that sph-(4, 5.5) has the lowest reduced Chi-squarevalue (7.96) in the full energy range, which is in accordance with [Figure 6]. Therefore, sph-(4, 5.5) is considered as the optimized configuration for estimating the dose equivalent.
Table 2: Reduced Chi-square values related to dose conversion coefficients estimated from different sample configurations used in the simulation for the entire energy region, as well as for E ≤0.05 MeV and E >0.05 MeV

Click here to view

The coefficients estimated using cross-entropy minimization technique of sph-(4, 5.5) are CB= −1.68 × 107, CH= 1.86 × 108, and CC= 3.37 × 107.

Testing with workplace neutron spectra

The present technique has been tested with several workplace neutron spectra. They are (i) neutron distribution of a concrete shielded Am-Be source facility placed at a distance of 80 cm from the source,[3] (ii) measured spectrum in BWR,[9] (iii) experimentally measured neutron energy distribution at an extreme forward angle from 144 MeV C ions incident on a thick Ti target in an accelerator environment,[10] (iv) spectrum in a Czech PWR corridor,[9] (v) neutron distribution in a fusion environment (TEXTOR),[9] (vi) neutron spectra from a 252 Cf source,[9] (vii) ISO provided spectrum of moderated 252 Cf,[9] (viii) neutrons from bare Pu metal,[9] and (ix) neutron spectrum from PuO2.[9] The neutron energy distributions of these workplace spectra are shown in [Figure 7].
Figure 7: Neutron energy distribution of various workplace spectra used to estimate the neutron ambient dose equivalent

Click here to view

The neutron dose equivalent values estimated from above-mentioned methods using the optimized sample sph-(4, 5.5) are given in [Table 3] in units of pSv. Here, neutron equivalent dose H*(10) is considered as standard since we are directly multiplying neutron energy distribution with ICRP-DCC. The percentage deviations of the estimated H*(10)R from H*(10) are given in parenthesis along with the dose values. The fraction flux is given in the curly parenthesis in the second column in accordance with the energy range, for example, the fraction is 1 when the entire energy range is considered.
Table 3: Comparison of estimated neutron dose (pSv) using the calculated response matrix and neutron energy distribution folded with the dose conversion coefficients for various source spectra considering the optimized configuration sph-(4, 5.5)

Click here to view

It is observed from [Table 3] that overall estimated dose H*(10)R agrees well (with maximum error of about 18%) with the ICRP-DCC provided H*(10) in the case of optimized combination configuration sph-(4, 5.5) (2–18%) compared to cylindrical HDPE (23–59%) and conical BHDPE (17–86%). The dose estimated by the optimized sample agrees well with H*(10) in the case of Am-Be, 144C+Ti,252 Cf, and PuO2 sources where low energy neutron fluence is negligible. This result is in well accordance with the reduced Chi-square value given in [Table 2]. It is also observed that the deviation of estimated dose from H*(10) is more if there is more contribution in low energy (<0.05 MeV) region. These results indicate that by incorporating this optimized combination of spherical configuration with HDPE (4 cm) inside and BHDPE (5.5 cm) outside, one can improve the estimation of neutron ambient dose equivalent compared to only HDPE or only BHDPE.

  Conclusions Top

  • Combination of HDPE (in, 4 cm) and BHDPE (out, 5.5 cm) in spherical configuration gives better approximation with ICRP-DCC than cylindrical HDPE and conical BHDPE samples
  • Estimation of neutron dose equivalent can be done better with the combined sample of HDPE and BHDPE compared to only HDPE or only BHDPE
  • For workplace neutron spectra with high energy neutron (>0.05 MeV) contribution, the estimated dose from cylindrical HDPE is better than conical BHDPE
  • For the neutron spectrum, which has both lower and higher energy neutron contributions, the estimated dose in lower energy region (<0.05 MeV) for conical BHDPE is better, whereas in higher energy (>0.05 MeV), cylindrical HDPE is more accurate
  • A combination of HDPE and BHDPE is a better sample configuration to estimate dose equivalent in both lower and higher energy neutrons.


This work is done under a project (AERB/CSRP/Proj. No.60/12/2015) sponsored by the Atomic Energy Regulatory Board, India.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

  References Top

Sarkar PK. Neutron dosimetry in the particle accelerator environment. Radiat Meas 2010;45:1476.  Back to cited text no. 1
Sunil C, Shanbhag AA, Nandy M, Bandyopadhyay T, Tripathy SP, Lahiri C, et al. Directional distribution of the ambient neutron dose equivalent from 145-MeV 19 F projectiles incident on thick Al target. Radiat Prot Dosimetry 2011;143:4-11.  Back to cited text no. 2
Priyada P, Sarkar PK. Use of prompt gamma emissions from polyethylene to estimate neutron ambient dose equivalent. Nucl Instrum Methods Phys Res A 2015;785:135.  Back to cited text no. 3
ICRP. Conversion coefficients for use in radiological protection against external radiation. ICRP publication 74, International Commission on Radiological Protection. Ann ICRP 1996;26.  Back to cited text no. 4
Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: A Multiparticle transport code. CERN-2005-10, INFN/TC_05/11, SLAC-R-773. 2005.  Back to cited text no. 5
Battistoni G, Muraro S, Sala PR, Cerutti F, Ferrari A, Roesler S, et al. The FLUKA Code: Description and Benchmarking. In: Proceedings of the Hadronic Shower Simulation, Workshop 2006 Fermilab, 6-8 September, 2006, AIP Conference Proceedings 896; 2007. p. 31.  Back to cited text no. 6
Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat 1951;22:79-86.  Back to cited text no. 7
Kullback S. Letter to the editor. The Kullback-Leibler distance. Am Stat 1987;41:340-1.  Back to cited text no. 8
IAEA. Compendium of Neutron Spectra and Detector Responses for Radiation Protection Purposes, Technical Report Series No. 403. Vienna: International Atomic Energy Agency; 2001.  Back to cited text no. 9
Nandy M, Sarkar PK, Sanami T, Shibata T, Takada M. Neutron dose distribution from 12-C induced reactions on Ti and Ag using proton recoil scintillator. Radiat Meas 2010;45:1276.  Back to cited text no. 10


  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]

  [Table 1], [Table 2], [Table 3]


Similar in PUBMED
   Search Pubmed for
   Search in Google Scholar for
 Related articles
Access Statistics
Email Alert *
Add to My List *
* Registration required (free)

  In this article
Materials and Me...
Results and Disc...
Article Figures
Article Tables

 Article Access Statistics
    PDF Downloaded191    
    Comments [Add]    

Recommend this journal