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The computation of the FEP efficiency is widely used because the relative method of measurement has severe restrictions. The MC simulation of photon transport is the reference method of computing the FEP efficiency but it is rather complicate, time consuming and requires skilled people for determining optimal detector parameters.Hence, it is not convenient its use for many different source configurations and therefore simpler and faster methods must be developed.
In this work a novel deterministic method for fast computing of the FEP efficiency for cylindrical sources emitting photons in the range of 60-2000 keVusing coaxial HPGe detectors is described in detail. It has a sound theoretical basis being based on thefollowing integral equation(Stanga and Gurau, 2021)
ε_ps (μ_s,E)=1/V ∫_V▒〖F_ap (μ_s,E,r ⃗ ) ε_pp^o (E,r ⃗ )dV (1) 〗
where ε_ps (μ_s,E) is the FEP efficiency for a given sample.F_ap (μ_s,E,r ⃗ )is the attenuation factor for a point source embedded in the volume sample at the position r ⃗and ε_pp^o (E,r ⃗ ) is the FEP efficiency response of the detector. To apply Eq. (1), a gridding technique was used for computing ε_pp^o (E) (Venkataraman et al., 2005). Grids were created inside of a right circular cylinder placed on the detector end cap and having radius r (cm)[0, 20] and height h (cm)[0, 30]. This space can accommodate almost all samples measured by gamma spectrometry (GS) laboratories.A grid-based interpolation was employed to compute ε_pp^o (E) at any values of r, h and E using its computed values in grid points.It was shown that F_ap can be approximated with sufficient accuracyby the mean value of the transmission factor of photons through the sample (Stanga and Gurau, 2021) for values of the linear attenuation coefficient in the range 0.0-1.0 cm-1. Moreover,ε_ps (μ_s,E)values can be accurately computed because the computed values of F_ap have large errors (e.g. 10 %) only for small ε_pp^o (E,r ⃗ ) values.The attenuation factor was computed using MC integration and ε_ps (μ_s,E) was computed by numerical integration of the integral from Eq. (1) using mid-point rule.The method described above was implemented as a Matlabcode.
The methodwas applied in practice usinga GS system equipped with a p-type coaxial HPGe detector model B20214, and LabSOCS code. For this detector, the values of ε_pp^o (E) in grid points were computed by means of Gespecor code.Theε_ps (μ_s,E)values were computed for ten cylindrical samples (five water samples and five aluminum samples) and different photon energies using this novel method, Gespecor and LabSOCS codes. The discrepancies were smaller than 3 % and 5 % for water and aluminum samples, respectively. The activity of a cylindrical water sample containing 137Cs was measured using the value of ε_ps provided by this novel method. The measured and certified values of the activity agreed within the uncertainty.
Stanga D. and Gurau D., (2021). Applied Radiation and Isotopes, 172.
Venkataraman, R., et al., (2005). J. Radioanal. Nucl. Chem., 264.
