A revision of the virtual point detector model for calculating Nai(Tl) detector efficiency

Highlights

• The virtual point detector model is studied and confirmed for both NaI(Tl) detectors.

• The coincidence summing correction factors are calculated by the MCNP-CP code.

• The position of the virtual point detector is depended on the incident photon energy.

• A semi-empirical equation is proposed to calculate the full energy peak efficiency.

• The results are a good agreement with the experiment in the range of 344–1408 keV.

Abstract

In present work, the validity of the virtual point detector (VPD) model for the NaI(Tl) detectors is studied and confirmed in the photon energy range of 60–1408 keV. The full energy peak efficiency (FEPE) of two NaI(Tl) detectors, which have scintillation crystal dimensions of 5.08 × 5.08 cm and 7.62 × 7.62 cm respectively, is measured for “point-like” radioactive sources on the symmetry axis with source-to-detector distances in the range of 2–40 cm. It is found that the VPD model is valid to fit too well to the experimental FEPE for the two surveyed NaI(Tl) detectors. The dependence of the VPD position on the incident photon energy for the NaI(Tl) detectors with different scintillation crystal dimensions is shown based on experimental data. A semi-empirical equation involving incident photon energy and source-to-detector distance is proposed to calculate the FEPE for the NaI(Tl) detectors. The calculated results for the two surveyed NaI(Tl) detectors by this equation are in a good agreement with experimental results for photon energies in the range of 344–1408 keV. However, the difference between experimental and calculated results is quite significant for source-to-detector close geometries for photon energies lower than 344 keV.

Introduction

An accurate knowledge of the FEPE is required for the operation of gamma-ray spectrometry applications in numerous fields, such as measurements of the absolute activity of gamma emitting radionuclides and calculation of the absorbed doses. The FEPE varies strongly with the source-to-detector distance and incident photon energy, due to the geometry and absorption factors. Thus, the calibration of FEPE for each measuring configuration is necessary. It is useful to study a mathematical model for quick and simple calculation of the FEPE at any source-to-detector distance with satisfactory accuracy. However, the dependence of FEPE on source-to-detector distance is generally a complex function of the shape, dimensions of detector and measurement geometry. This causes difficulty in calculating the effect of the varying distances. The VPD model was introduced by Notea (1971) for Ge(Li) detector to deal with this problem. It is suggested that the detector volume may be replaced for the FEPE calculations by a virtual equivalent point detector on the symmetry axis of the detector. Based on this model, the FEPE of the detector is represented by a simple quadratic inverse function of the source-to-VPD distance. Therefore, the VPD model can be used for facilitating FEPE calculations. Later, the VPD model was widely investigated for the HPGe detectors (Hoover, 2007; Mahling et al., 2006; Mohammadi et al., 2011; Presler et al., 2006).

The NaI(Tl) detectors are one of the most commonly used instruments for gamma-ray spectrometry applications in experimental nuclear physics. It is necessary to evaluate the accuracy and reliability of the FEPE calculations for NaI(Tl) detectors by the VPD model. In the past, the interpolation and extrapolation of counting efficiency of NaI(Tl) and BGO scintillation detectors for measurements of “point-like” radioactive sources (Presler et al., 2006) based on VPD model were investigated. However, in this report, the authors concluded that the VPD model does not seem to fit too well to the experimental data for the whole range (from 1 to 18 cm) of source-to-detector distances; VPD positions are constant and independent of incident photon energy. The calculated efficiencies show a quite high discrepancy from the measured efficiencies for photon energies in the range of 238–2614 keV, with the relative deviations up to several tens in percents. So, the question is whether the VPD model is really not suitable for the NaI(Tl) scintillation detectors. Besides, there is still a lack of experimental data to show the dependence of the VPD position on the incident photon energy and the NaI(Tl) crystal dimensions, although simulation study have been reported by Rubin et al. (2019).

This paper provides a revision of the validity of the VPD model for calculating the FEPE of NaI(Tl) detectors. Measurements of “point-like” radioactive sources on the symmetry axis at several source-to-detector distances for two NaI(Tl) detectors, with scintillation crystal dimensions of 5.08 × 5.08 cm and 7.62 × 7.62 cm, are performed to obtain the FEPE in the photon energy range of 60–1408 keV. The validity of the VPD model for NaI(Tl) detectors is confirmed based on experimental FEPE at several source-to-detector distances in the range of 2–40 cm. The dependence of the VPD position on the incident photon energy for the NaI(Tl) detectors with different scintillation crystal dimensions is shown based on experimental data. Then, a semi-empirical equation involving incident photon energy and source-to-detector distance is proposed to calculate the FEPE for the two surveyed NaI(Tl) detectors. The reliability of this semi-empirical equation is evaluated by comparing the calculated and experimental results.