Calibration of the Absolute Efficiency of Well-Type NaI ( Tl ) Scintillation Detector in 0 . 121 – 1 . 408 MeV Energy Range

Well-type NaI(Tl) detectors are beneficial for low-level photon activity measurements because of the near 4π solid angle that can be gained with them. The detection efficiency can differ with the source-to-detector 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 well-type sodium iodide detector have been measured at 0.121–1.408MeV energy range (obtained from Eu, Cs, and 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%.


Theoretical Viewpoint
In the case where an isotropic radiating axial point source is in the detector well-cavity at a distance, ℎ, from cavity bottom (see Figure 1), the path of the photon is well defined by the geometrical solid angle, Ω, subtended by the source-to-detector system at the point of entry.The solid angle is given as The usage of well-type gamma spectrometry systems is useful for low-level 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 source-to-detector 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 -ray 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][5][6][7][8][9][10][11][12][13][14][15][16][17] and the experimental measurements.
For the polar () and azimuthal () angles, the azimuthal angle, , earns the values from 0 to 2, while the polar angle, (), earns four different values built on the source-to-detector configuration.where  1 is the detector well-cavity inner radius,  2 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 sourceto-detector well bottom, ℎ; 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  2 >  3 >  1 >  4 existing in Figure 2(a), the four possible path lengths have been initiated to be ( 1 ,  2 ,  4 , and  5 ) and the detection efficiency will be specified by , the four possible path lengths have been initiated to be  1 ,  3 ,  4 , and  6 and the detection efficiency will be specified by where where  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  att is the attenuation factor for the absorbing layers with attenuation coefficient  1 ,  2 , . . .,   and with the thickness  1 ,  2 , . . .,   in front of the detector face and it is described as where ) for the horizontal absorber layers, ) for the vertical absorber layers. (8)

Experimental Setup
The 7.62 × 7.62 cm 2 well-type 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 -ray 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 (Osprey6 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   where  is the decay constant and Δ 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  Th and  Exp are the theoretically and experimentally measured efficiencies, respectively.

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) well-type 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) well-type 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 first-degree polynomial and can be given by where  is the -ray energy in keV and  is the spectral channel number of the center of the peak corresponding to the energy , while the parameters  = −41.47075and  = 2.94174 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 first-degree polynomial and can be given by while the parameters  = 8.70616 and  = −0.00269are constants to be calculated by the shape calibration process.

Results and Conclusions
The well-type 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.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 well-type sodium iodide detectors at energy .As given in Figure 6, the variation of the experimentally measured and calculated photopeak efficiencies of the well-type 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 well-known activity and measured inside the well-type 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%.

Figure 1 :
Figure 1: Well-type detector with an isotropic radiating axial point source in the detector well-cavity.

Figure 2 :Figure 3 :
Figure 2: The two possible cases of the photon path lengths.

Figure 6 :
Figure 6: The variation of the calculated photopeak efficiency of 7.62 × 7.62 cm 2 NaI(Tl) well-type sodium iodide detector as a function of photon energy.Square symbols are the experimental present work; red solid line and its circles represent the values calculated using Abbas formulae [4] and dashed line is the fitting.

Table 1 :
PTB radioactive sources activities and their uncertainties.
is the nuclide activity, and   are the correction factors because of coincidence summing corrections, radionuclide decay, and dead time.The decay correction (  ) was given by

Table 2 :
Specifications of the radionuclides.
The overall efficiency curves are obtained by fitting a polynomial logarithmic function of third order Figure 5: The calibration energy curves (measured and fit) using standard point sources ( 60 Co and 137 Cs) with NaI(Tl) well-type detector.