

ORIGINAL ARTICLE 

Year : 2015  Volume
: 38
 Issue : 4  Page : 130134 


Validation of analytical functions to fit detection efficiencies of NaI(Tl) scintillation detector in the energy range of 122–1332 keV
L Thilagam, MR Priya, DK Mohapatra
Nuclear Safety Analysis Section, Safety Research Institute, Atomic Energy Regulatory Board, Kalpakkam, Tamilnadu, India
Date of Web Publication  11Feb2016 
Correspondence Address: L Thilagam Safety Research Institute, Atomic Energy Regulatory Board, Kalpakkam  603 102, Tamil Nadu India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09720464.176154
Various analytical functions proposed to express the full energy photopeak efficiency (FEPE) of gamma ray detectors have been investigated for their performance to fit the percentage FEPE of AmcrysH made 2” × 2” NaI(Tl) scintillation detector. Initially, the experimental measurements on FEPEs of various gamma sources were used to validate the theoretical Monte Carlo (MC) simulations. The maximum deviation observed between the experimental efficiencies and MC simulations is 12.51%, which is observed for 356 keV of 133Ba. The percentage FEPEs obtained through validated MC simulations are then fitted against gamma energy in the range 122–1332 keV using the recommended efficiency functions to obtain the percentage FEPE as a smooth function of gamma energy for the source to detector distance of 5 cm. The analytical function recommended by McNelles, Campbell and Singh is identified as the most suitable for the detector type considered and this, in turn, is used to obtain fitting coefficients for all other source to detector distances. The fitted equations are found to provide the percentage FEPEs, which are well within ±6% deviation with respect to the theoretical MC simulations for most of the energies and distances. For the source to detector distances of 15 and 25 cm, the gamma energy of 500 keV is found to have the maximum deviations up to 7.6%. Keywords: Fitting analytical functions, Monte Carlo simulations, NaI(Tl) detector, photopeak efficiency
How to cite this article: Thilagam L, Priya M R, Mohapatra D K. Validation of analytical functions to fit detection efficiencies of NaI(Tl) scintillation detector in the energy range of 122–1332 keV. Radiat Prot Environ 2015;38:1304 
How to cite this URL: Thilagam L, Priya M R, Mohapatra D K. Validation of analytical functions to fit detection efficiencies of NaI(Tl) scintillation detector in the energy range of 122–1332 keV. Radiat Prot Environ [serial online] 2015 [cited 2022 Aug 13];38:1304. Available from: https://www.rpe.org.in/text.asp?2015/38/4/130/176154 
Introduction   
Gamma spectrometry requires accurate determination of the full energy photopeak efficiency (FEPE) of detectors for the activity estimations of natural and manmade radionuclides in environmental samples. A better way of obtaining FEPE as a continuous function of energy is to fit the basic discrete data points to some appropriate function and take the required values at energies of interest from the fitted equation.^{[1]} The Monte Carlo (MC) simulations, which are wellvalidated against experimental measurements, are gaining importance to obtain such a fit because MC simulations can provide more reliable data points to express FEPE as a smooth function of energy in the wide range. On the other hand, the experimental measurements are limited due to the facts; (i) lack of sources emitting gamma energies in the wide energy range and (ii) the contribution of higher energy Compton scattering components in the lower energy in the case of sources emitting multiple gamma energies. In MC simulations, the latter effect can be avoided by simulating each of the multiple energies separately. Furthermore, the FEPE can be obtained for any required energy through MC simulations.
In this study, the analytical functions proposed by various authors ^{[2],[3],[4],[5],[6],[7],[8],[9]} have been tested to fit FEPE of AmcrysH made 2” × 2” NaI(Tl) scintillation detector that was setup for environmental activity calculations. Scintillation based NaI(Tl) detectors have higher efficiencies for detecting gamma radiations.^{[10],[11]} Though the analytical functions were originally proposed for germanium detectors, they were tested ^{[12]} to fit FEPE of 3” × 3” and 2” × 2” NaI detectors. The present study is one such attempt to test the same for NaI(Tl) detector of a different make.
Initially, the experimental measurements were carried using standard gamma point sources to validate MC modeling of the detector. The validated MC model of the detector can then be used to obtain FEPEs for as many discrete energy points as required by simulating each of the energy separately and for all sources to detector distances. Using more data points for fitting enables to get FEPE as a smooth function of energy for a wide range. This methodology makes this study unique, and it can be used to obtain FEPE as a continuous function of energy for any detector system.
The paper describes in detail about the analytical functions tested, experimental measurements to validate MC modeling of the detector, MC simulations, the performance of the fitted equations, and discussion of results.
Proposed Analytical Functions   
Analytical functions proposed by various authors ^{[2],[3],[4],[5],[6],[7],[8],[9]} are listed in [Table 1] with the number of fitting parameters and the recommend energy range. As mentioned earlier, they were originally proposed for germanium detectors. For the 1^{st} time Sudharshan et al.^{[12]} investigated them for representing the FEPEs of Teledyne Isotopes, USA made 7.6 cm × 7.6 cm NaI(Tl) detector and Harshaw, USA made 5 cm × 5 cm NaI(Tl) detector. In their study, they found that the functions proposed by East and McNelles and Campbell ^{[3],[4],[5]} were found to be the best representations of their data.
Experimental Measurements   
The specifications of AmcrysH made 2” × 2” NaI(Tl) scintillation detector considered in the present study are given in [Table 2]. In order to validate MC modeling of the detector, experimental measurements of gamma radiation intensities were carried out using point gamma sources such as ^{133} Ba,^{57} Co,^{137} Cs, and ^{60} Co. The spectrum of each of these sources and the background spectrum are acquired separately for 2700 seconds for all source to detector distances 5, 10, 15, 20, 25, and 30 cm. To evaluate FEPE, the integral counts under the peak energy corresponding to each source are taken into account after subtracting the background from the spectrum of the individual radionuclide.
FEPE is calculated using the formula ^{[10]} given below.
“A_{0}” is the initial activity in disintegration per se cond.
“t” is the time period from the date of procurement of source to the time of measurement of activity (day).
“λ” is the decay constant of the radionuclide (day ^{−1}).
“I_{γ}” is the gamma ray intensity per decay, i.e., photons per disintegration.
In the case of gamma sources emitting multiples energies, FEPEs from the experimental measurements are considered only for the highest peak energy because their lower energy peaks contain Compton scattering components of the higher energies. The present study compares experimentally measured FEPEs of 122 keV of ^{57} Co, 356 keV of ^{133} Ba, 661keV of ^{137} Cs, and 1332 keV of ^{60} Co with MC simulations.
The main sources of experimental uncertainties are uncertainties in source activity “A” (nearly ± 10% in Board of Radiation and Isotope Technology (BRIT) point gamma sources as per their specification), errors in the counting measurement (inversely proportional to square root of N(E), the number of counts in the fullenergy peak) and uncertainties associated with the photon emission probabilities I_{γ}(E) of gamma energies. According to the propagation of error law, the relative uncertainty in the experimental FEPE is given by
As the relative uncertainties in the peak area are always kept to be minimum, and those associated with the emission probabilities are also less, the relative uncertainty in measurements are dominated by the relative uncertainty in the radionuclide activity. In this study, the uncertainty in the experimental FEPE is found to be nearly equal to ±10% for all energies. Experimental uncertainties of various gamma energies of interest are given in [Table 3].
Monte Carlo Simulations   
Theoretical MC calculations were carried out using MC NParticle code, MCNP ^{[13]} by simulating the exact geometry of the detector with the surrounding lead shield as per the specifications.
To calculate FEPE, integral counts in the photopeak regions are scored separately for individual energies of the gamma sources ^{133} Ba,^{57} Co,^{137} Cs, and ^{60} Co. Additional energies such as 100 keV, 200 keV, 500 keV, and 1000 keV are also considered to get more data points for fitting smooth functions. Pulse height tally type F8 was used with the Gaussian energy broadening (GEB) option to obtain realistic spectra that are similar to those obtained experimentally. The experimentally measured fullwidth half maximum values corresponding to different energies are employed to obtain the necessary GEB parameters. Each simulation has been carried out for 100 million histories to reduce the statistical uncertainties to <10% in each energy bin of F8 tallies.
Results and Discussions   
Experimental measurements are carried out to determine the percentage FEPEs of 122 keV of ^{57} Co, 356 keV of ^{133} Ba, 661 keV of ^{137} Cs, and 1332 keV of ^{60} Co and are compared with those obtained using MC simulations to validate its methodology. The comparisons are given in [Figure 1], which clearly demonstrates that the comparisons are generally good for all the energies and for all sources to detector distances. The percentage deviations observed between the measurements and MC simulations are shown in [Figure 2]. They range from −12.51% to 6.8%. The maximum deviation of − 12.51% is observed for 356 keV of ^{133} Ba. Considering the experimental uncertainty of ± 10% on FEPEs, these deviations are found to acceptable.  Figure 1: Comparison of experimental and Monte Carlo simulated percentage full energy photopeak efficiency versus energy
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 Figure 2: Percentage deviations between experimental and Monte Carlo simulated percentage full energy photopeak efficiencies
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The plots investigating the performance of seven different analytical functions to fit FEPE of NaI(Tl) scintillation detector as a function of gamma energy are given in [Figure 3] for a source to detector distance of 5 cm. The percentage deviations of the fitted percentage FEPEs from those of MC simulations are given in [Figure 4] for all analytical functions. This figure clearly shows that the percentage FEPEs fitted through the functions 2, 3, and 5 show better performances than other functions. The percentage deviations of the percentage FEPEs fitted through these functions 2, 3, and 5 from MC values are within 5.5%. Although the percentage deviation is nearly same for all the three functions, the function 3 is found to show closer agreement for all energies compared to the other two functions 2 and 5. Therefore, the function 3 recommended by McNelles, Campbell, and Singh ^{[4],[5]} is identified as the most suitable for our detector type. The percentage deviations observed for the function 1 are up to 10% and those of functions 4 and 6 are more up to 12.5%. The maximum deviations up to −15% are observed for the function 7 recommended by Lepy et al.^{[9]}  Figure 3: Percentage full energy photopeak efficiency fitted through analytical functions versus energy for source to detector distance of 5 cm
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 Figure 4: Percentage deviations of fitted percentage full energy photopeak efficiency from Monte Carlo simulations for source to detector distance of 5 cm
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The study has been extended to use the most suitable function 3 to fit the percentage FEPE as a function of energy for all other source to detector distances (10, 15, 20, 25, and 30 cm). The plots showing the performance of the function 3 to fit the percentage FEPE versus energy are given in [Figure 5]a collectively for all sources to detector distances. The percentage deviations of these fitted percentage FEPEs from MC simulations are given in [Figure 5]b for all distances. It is clear from these [Figure 5]a and [Figure 5]b that the function 3 is found to be suitable for all sources to detectors distances.  Figure 5: Percentage full energy photopeak efficiency fitted through function 3 versus energy for various source to detector distances and percentage deviations from Monte Carlo simulations. (a) Percentage FEPE vs. Energy. (b) Percenatge deviation of fitted FEPE from MC Simulations
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[Figure 5]b demonstrates that the fitted equations are found to provide the percentage FEPEs, which are well within ± 6% deviation with respect to the theoretical MC simulations for most of the energies and for most of the distances. For the source to detector distances of 15 cm and 25 cm, the gamma energy of 500 keV is found to have the maximum deviations up to 7.6%.
Conclusions   
The study to express the percentage FEPE of AmcrysH made 2” × 2” NaI(Tl) scintillation detector as a smooth function of gamma energy has been carried out. Seven different analytical functions proposed by various authors are tested for their performance to fit the percentage FEPE in the wide gamma energy range of 122 keV to 1332 keV. The percentage FEPEs obtained through the theoretical MC simulations, which were initially validated against experimental measurements, are fitted against gamma energy using the recommended efficiency functions for a source to detector distance of 5 cm. The most suitable function is identified for our detector type and this, in turn, is used to obtain fitting coefficients for all other source to detector distances. The broad observations made from the present study are:
 Comparison of MC simulated percentage FEPEs with those of experimental measurements on 122 keV of ^{57} Co, 356 keV of ^{133} Ba, 661 keV of ^{137} Cs, and 1332 keV of ^{60} Co shows that the comparisons are generally good for all the energies and for all source to detector distances. The percentage deviations observed between the measurements and MC simulations range from −12.51% to 6.8%. The maximum deviation of −12.51% is observed for 356 keV of ^{133} Ba. MC modeling of the detector is found to be suitable to generate more reliable data points on the percentage FEPEs
 Investigations of fitting performances of seven different analytical functions to fit MC simulated percentage FEPEs as a function energy for a source to detector distance of 5 cm led to the identification of the analytical function recommended by McNelles, Campbell and Singh ^{[4],[5]} as the most suitable for our detector type
 The identified most suitable function is used to obtain fitting coefficients for all other source to detector distances. The fitted equations obtained for these distances are found to provide the percentage FEPEs, which are well within ± 6% deviation with respect to the theoretical MC simulations for most of the energies and distances. For the source to detector distances of 15 cm and 25 cm, the gamma energy of 500 keV is found to have the maximum deviations up to 7.6%.
In summary, the methodology employed in the present study can be used to obtain the percentage FEPE as a continuous function of energy for any detector system.
Financial support and sponsorship
SRI/AERB.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2], [Table 3]
