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 0.121–1.408 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 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(1)Ω=∫ϕ∫θsinθdθdϕThe 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 γ-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 [4–17] and the experimental measurements.
Well-type detector with an isotropic radiating axial point source in the detector well-cavity.
For the polar (θ) and azimuthal (φ) angles, the azimuthal angle, φ, earns the values from 0 to 2π, while the polar angle, (θ), earns four different values built on the source-to-detector configuration.(2)θ1=tan-1R1h,θ2=π-tan-1R1S-h,θ3=π-tan-1R2S-h,θ4=tan-1R2L-S+h,where R1 is the detector well-cavity inner radius, R2 is the outer radius, S is the well depth, and L is the detector side length, as exposed in Figure 1. There are two main cases to determine the detector efficiency depending on the source-to-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: (3)d1=L-Scosθ,d2=R2sinθ-hcosθ,d3=L-S+hcosθ-R1sinθ,d4=R2sinθ-R1sinθ,d5=S-hcosθ-R1sinθ.
In case of θ2>θ3>θ1>θ4 existing in Figure 2(a), the four possible path lengths have been initiated to be (d1, d2, d4, and d5) and the detection efficiency will be specified by(4)ε=14π∫02π∫0θ4fattf1sinθdθ+∫θ4θ1fattf2sinθdθ+∫θ1θ3fattf4sinθdθ+∫θ3θ2fattf5sinθdθdφ.
In case of θ2>θ3>θ4>θ1 existing in Figure 2(b), the four possible path lengths have been initiated to be d1, d3, d4, and d6 and the detection efficiency will be specified by(5)ε=14π∫02π∫0θ1fattf1sinθdθ+∫θ1θ4fattf3sinθdθ+∫θ4θ3fattf4sinθdθ+∫θ3θ2fattf5sinθdθdφ,
where(6)fatt=1-e-μ·di,i=1–5,where μ is the detector attenuation coefficient for a photon with energy, Eγ, and di are the possible path lengths covered by the photons in the detector. Meanwhile the factor fatt is the attenuation factor for the absorbing layers with attenuation coefficient μ1,μ2,…,μn and with the thickness t1,t2,…,tn in front of the detector face and it is described as (7)fatt=e-∑i=1nμiδi,where(8)δi=ticosθfor the horizontal absorber layers,δi=tisinθfor the vertical absorber layers.
The two possible cases of the photon path lengths.
Case 1. θ2>θ3>θ1>θ4
Case 2. θ2>θ3>θ4>θ1
2. 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 manufactory diagram of 7.62×7.62 cm^{2} well-type NaI(Tl) scintillation detector.
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 γ-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 (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).
PTB radioactive sources activities and their uncertainties.
PTBNuclide
ActivitykBq
UncertaintykBq
^{152}Eu
290.0
±4.0
^{137}Cs
385.0
±4.0
^{60}Co
212.1
±1.5
Specifications of the radionuclides.
PTBNuclide
EnergykeV
Emission probability%
Half LifeDays
^{152}Eu
121.78
28.4
4943.29
244.69
7.49
344.28
26.6
778.90
12.96
964.13
14.0
1408.01
20.87
^{137}Cs
661.66
85.21
11004.98
^{60}Co
1173.23
99.9
1925.31
1332.50
99.982
The photopeak efficiencies were obtained experimentally by using (9) as follows:(9)εE=NEt·AS·PE∏Ci,where N(E) is the counts number in the photopeak (obtained using Genie 2000 software), t is the time of measurement (in seconds), P(E) is the photon branching ratio at energy E, AS is the nuclide activity, and Ci are the correction factors because of coincidence summing corrections, radionuclide decay, and dead time. The decay correction (Cd) was given by(10)Cd=eλ·ΔT,where λ is the decay constant and Δt 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, σε, was given by (11)σε=ε·∂ε∂A2·σA2+∂ε∂P2·σP2+∂ε∂N2·σN2,where the uncertainties σA, σP, and, σN are linked with the quantities AS, P(E), and N(E), respectively. The percentage of deviation among the calculated and measured efficiencies is given by (12)Δ%=εTh-εExpεTh×100,where εTh and εExp 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) 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 (X) is a first-degree polynomial and can be given by (13)E=a+b·X,where E is the γ-ray energy in keV and X is the spectral channel number of the center of the peak corresponding to the energy E, while the parameters a=-41.47075 and b=2.94174 are constants to be calculated by the energy calibration process.
The calibration energy curves (measured and fit) using standard point sources (^{60}Co and ^{137}Cs) with NaI(Tl) well-type detector.
The calibration energy curves (measured and fit) using standard point sources (^{60}Co and ^{137}Cs) with NaI(Tl) well-type detector.
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(14)FWHM keV=a+b·E,while the parameters a=8.70616 and b=-0.00269 are constants to be calculated by the shape calibration process.
4. 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. 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: (15)logε=∑i=03ailogEi,where ai are the coefficients to be determined by the calculations and ε is the photopeak efficiency (FEPE) of the well-type sodium iodide detectors at energy E. 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%.
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.
Conflicts of Interest
The author declares that there are no conflicts of interest regarding the publication of this paper.
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