Research Article  Open Access
Dalal Al Oraini, "Calibration of the Absolute Efficiency of WellType NaI(Tl) Scintillation Detector in 0.121–1.408 MeV Energy Range", Science and Technology of Nuclear Installations, vol. 2018, Article ID 6432380, 6 pages, 2018. https://doi.org/10.1155/2018/6432380
Calibration of the Absolute Efficiency of WellType NaI(Tl) Scintillation Detector in 0.121–1.408 MeV Energy Range
Abstract
Welltype NaI(Tl) detectors are beneficial for lowlevel photon activity measurements because of the near 4π solid angle that can be gained with them. The detection efficiency can differ with the sourcetodetector system geometries, the absorption of the photon in the detector material, and attenuation layers in front of the detector face. For these purposes, the absolute efficiency and the coincidence corrections of the welltype sodium iodide detector have been measured at 0.121–1.408 MeV energy range (obtained from ^{152}Eu, ^{137}Cs, and ^{60}Co radioactive isotopes). The covenant between the experimental (present work) and the published theoretical values is good, with the high discrepancies being less than 1%.
1. Theoretical Viewpoint
In the case where an isotropic radiating axial point source is in the detector wellcavity at a distance, , from cavity bottom (see Figure 1), the path of the photon is well defined by the geometrical solid angle, , subtended by the sourcetodetector system at the point of entry. The solid angle is given asThe usage of welltype gamma spectrometry systems is useful for lowlevel gamma activity measurements. To measure the sample’s activity, the photopeak efficiency (FEPE) of the detector for each photon energy is needed. This is usually obtained by the efficiency calibration by the use of standard radioactive sources of identical geometrical shape and dimensions with the samples under study [1]. However, the MC simulations consider the detailed characteristics of the sourcetodetector system in calculating the photopeak efficiency. This approach (MC) is inadequate in its accuracy because of the inaccuracy in the parameters accompanying the detector’s geometrical dimensions and the structure of the sample [2]. The accuracy is also affected by the uncertainty in nuclear data and the calculation uncertainties of the MC code [3], but these are likely to be as important as the parameters linked with the detector’s geometrical dimensions and the material composition of the sample. The physical dimensions provided by suppliers are usually unsatisfactory for accurate efficiency calculations because any slight change in some of these geometrical parameters can cause significant deviations from experimental values. Several studies of the response of γray spectrometers using MC simulations have been published. Most of the authors report agreement with experimentally obtained efficiency values within 10%. One useful way to stun these complications is the use of the straightforward direct mathematical method [4–17] and the experimental measurements.
For the polar and azimuthal angles, the azimuthal angle, , earns the values from 0 to , while the polar angle, , earns four different values built on the sourcetodetector configuration.where is the detector wellcavity inner radius, is the outer radius, is the well depth, and is the detector side length, as exposed in Figure 1. There are two main cases to determine the detector efficiency depending on the sourcetodetector well bottom, ; these two main cases contain five subcases. The photons have different five possible path lengths affording to the photon entrance and emittance point from the detector body. These path lengths are represented in Figure 2 and are specified by equation (3) as follows: (a)In case of existing in Figure 2(a), the four possible path lengths have been initiated to be (, , , and ) and the detection efficiency will be specified by(b)In case of existing in Figure 2(b), the four possible path lengths have been initiated to be , , , and and the detection efficiency will be specified bywherewhere is the detector attenuation coefficient for a photon with energy, , and are the possible path lengths covered by the photons in the detector. Meanwhile the factor is the attenuation factor for the absorbing layers with attenuation coefficient and with the thickness in front of the detector face and it is described as where
(a) Case 1.
(b) Case 2.
2. Experimental Setup
The cm^{2} welltype sodium iodide detector, model number 802, made by CANBERRA Company was used (see Figure 3).
The detector was mounted vertically, the cathode to anode voltage was equal to +600 V dc, the dynode to dynode was +80 V dc, the cathode to dynode was +150 V dc, and the total weight was 1.8 kg. The detector dimensions were given as 0.5 mm Al end cap thickness, 2.5 mm Al2O3 face reflector layer, 1.85 mm Al2O3 side reflector layer, 8.33 mm cavity radius, and 49.87 cavity depth. The detector energy resolution (FWHM) was 9% at the 661 keV γray line of 137Cs source ground on the manufactory certificate and the shaping mode was Gaussian. The detector was coupled to a CANBERRA data acquisition system (Osprey™ Base) applying a Genie 2000 analysis software, with many functions including peak area determination. The type of the used sources is radioactive point sources ^{152}Eu, ^{137}Cs, and ^{60}Co (see Tables 1 and 2).


The photopeak efficiencies were obtained experimentally by using (9) as follows:where is the counts number in the photopeak (obtained using Genie 2000 software), is the time of measurement (in seconds), is the photon branching ratio at energy , is the nuclide activity, and are the correction factors because of coincidence summing corrections, radionuclide decay, and dead time. The decay correction was given bywhere is the decay constant and is the time interval between the source decay time and the run time. The main source of uncertainty in the efficiency calculations was the uncertainties of the activities of the standard source solutions. The uncertainty in the photopeak efficiency, , was given by where the uncertainties , , and, are linked with the quantities , , and , respectively. The percentage of deviation among the calculated and measured efficiencies is given by where and are the theoretically and experimentally measured efficiencies, respectively.
3. Energy Calibrations and Resolution
The detection system must be calibrated before the use in radiation detection to hide channel number to energy scale. The energy, shape, and efficiency calibration of the NaI(Tl) welltype detector was a procedure occasionally made to establish the linking between the energy of the photon, the channel number, and the detector efficiency. This process was done by using Osprey Universal Digital Multichannel Analyzer Base for scintillation spectrometry, where after the identification of the energy using standard sources, the efficiency values were calculated considering the probability of disintegration for each energy. The typical energy and shape calibration of the amplitudes from standard (^{60}Co and ^{137}Cs) radioactive sources used for calibration at position 25 cm are shown in Figures 4 and 5. The NaI(Tl) welltype detector energy resolution was found to be ~6.9% for 662 keV gammas from ^{137}Cs. The relation between the energy and the channel number is a firstdegree polynomial and can be given by where is the γray energy in keV and is the spectral channel number of the center of the peak corresponding to the energy , while the parameters and are constants to be calculated by the energy calibration process.
The resolution (FWHM) calibration curve was established as a role to pronounce the peak width against the spectral energy. It is considered as significant limit illustrating the system act in separating different photon emissions in an energy range, The relation between the FWHM and the energy is a firstdegree polynomial and can be given bywhile the parameters and are constants to be calculated by the shape calibration process.
4. Results and Conclusions
The welltype sodium iodide detector photopeak efficiency (FEPE) was measured and compared with the calculated values. The disparity of efficiency with the photon energy was also investigated. The overall efficiency curves are obtained by fitting a polynomial logarithmic function of third order for the photopeak efficiencies points, using a nonlinear least square fit built on the following equation: where are the coefficients to be determined by the calculations and is the photopeak efficiency (FEPE) of the welltype sodium iodide detectors at energy . As given in Figure 6, the variation of the experimentally measured and calculated photopeak efficiencies of the welltype scintillation detector as a function of the energy of photon can come into sight. The behavior of these curves was based on using a vile filled with small amount of ^{152}Eu aqueous solution of a wellknown activity and measured inside the welltype detectors cavity. Results based on ^{152}Eu sources indicate a good covenant between the measured photopeak efficiency values and the theoretical ones [4], with the high discrepancies being less than 1%.
Conflicts of Interest
The author declares that there are no conflicts of interest regarding the publication of this paper.
References
 M. J. Vargas, N. C. Diaz, and D. P. Sánchez, “Efficiency transfer in the calibration of a coaxial ptype HpGe detector using the Monte Carlo method,” Applied Radiation and Isotopes, vol. 58, no. 6, pp. 707–712, 2003. View at: Publisher Site  Google Scholar
 M. GarcíaTalavera, H. Neder, M. J. Daza, and B. Quintana, “Towards a proper modeling of detector and source characteristics in Monte Carlo simulations,” Applied Radiation and Isotopes, vol. 52, no. 3, pp. 777–783, 2000. View at: Publisher Site  Google Scholar
 J.M. Laborie, G. Le Petit, D. Abt, and M. Girard, “Monte Carlo calculation of the efficiency calibration curve and coincidencesumming corrections in lowlevel gammaray spectrometry using welltype HPGe detectors,” Applied Radiation and Isotopes, vol. 53, no. 12, pp. 57–62, 2000. View at: Publisher Site  Google Scholar
 M. I. Abbas, “Analytical formulae for welltype NaI (Tl) and HPGe detectors efficiency computation,” Applied Radiation and Isotopes, vol. 55, no. 2, pp. 245–252, 2001. View at: Publisher Site  Google Scholar
 M. I. Abbas, “Direct mathematical method for calculating fullenergy peak efficiency and coincidence corrections of HPGe detectors for extended sources,” Nuclear Instruments and Methods in Physics Research Section B, vol. 256, no. 1, pp. 554–557, 2007. View at: Publisher Site  Google Scholar
 S. S. Nafee and M. I. Abbas, “A theoretical approach to calibrate radiation portal monitor (RPM) systems,” Applied Radiation and Isotopes, vol. 66, no. 10, pp. 1474–1477, 2008. View at: Publisher Site  Google Scholar
 S. S. Nafee and M. I. Abbas, “Calibration of closedend HPGe detectors using bar (Parallelepiped) sources,” Nuclear Instruments and Methods in Physics Research Section A, vol. 592, no. 12, pp. 80–87, 2008. View at: Publisher Site  Google Scholar
 M. I. Abbas, “Analytical approach to calculate the efficiency of 4π NaI(Tl) gammaray detectors for extended sources,” Nuclear Instruments and Methods in Physics Research Section A, vol. 615, no. 1, pp. 48–52, 2010. View at: Publisher Site  Google Scholar
 M. I. Abbas, “A new analytical method to calibrate cylindrical phoswich and LaBr_{3}(Ce) scintillation detectors,” Nuclear Instruments and Methods in Physics Research Section A, vol. 621, no. 13, pp. 413–418, 2010. View at: Publisher Site  Google Scholar
 M. I. Abbas, “Analytical formulae for borehole scintillation detectors efficiency calibration,” Nuclear Instruments and Methods in Physics Research Section A, vol. 622, no. 1, pp. 171–175, 2010. View at: Publisher Site  Google Scholar
 M. I. Abbas and S. Noureddeen, “Analytical expression to calculate total and fullenergy peak efficiencies for cylindrical phoswich and lanthanum bromide scintillation detectors,” Radiation Measurements, vol. 46, no. 4, pp. 440–445, 2011. View at: Publisher Site  Google Scholar
 M. S. Badawi, I. Ruskov, M. M. Gouda et al., “A numerical approach to calculate the fullenergy peak efficiency of HPGe welltype detectors using the effective solid angle ratio,” Journal of Instrumentation, vol. 9, no. 7, p. P07030, 2014. View at: Publisher Site  Google Scholar
 M. I. Abbas, M. S. Badawi, I. N. Ruskov et al., “Calibration of а single hexagonal NaI(Tl) detector using a new numerical method based on the efficiency transfer method,” Nuclear Instruments and Methods in Physics Research Section A, vol. 771, pp. 110–114, 2015. View at: Publisher Site  Google Scholar
 M. I. Abbas, S. Hammoud, T. Ibrahim, and M. Sakr, “Analytical formulae to calculate the solid angle subtended at an arbitrarily positioned point source by an elliptical radiation detector,” Nuclear Instruments and Methods in Physics Research Section A, vol. 771, pp. 121–125, 2015. View at: Publisher Site  Google Scholar
 A. Hamzawy, D. N. Grozdanov, M. S. Badawi et al., “New numerical simulation method to calibrate the regular hexagonal NaI(Tl) detector with radioactive point sources situated nonaxial,” Review of Scientific Instruments, vol. 87, no. 11, Article ID 115105, 2016. View at: Publisher Site  Google Scholar
 M. I. Abbas, M. M. Gouda, M. S. Badawi, and A. M. ElKhatib, “Direct mathematical solutions for the gammaray detectors geometrical andtotal efficiencies integrable formulae,” Journal of Engineering Science & Technology, vol. 12, no. 3, pp. 701–715, 2017. View at: Google Scholar
 S. F. Noureldine, M. S. Badawi, and M. I. Abbas, “A hybrid analyticalnumerical method for efficiency calculations of spherical scintillation NaI(Tl) detectors and arbitrarily located point sources,” Nuclear Technology and Radiation Protection, vol. 32, no. 2, pp. 140–147, 2017. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2018 Dalal Al Oraini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.