Science and Technology of Nuclear Installations

Volume 2015 (2015), Article ID 451932, 9 pages

http://dx.doi.org/10.1155/2015/451932

## NaI(Tl) Detector Efficiency Computation Using Radioactive Parallelepiped Sources Based on Efficiency Transfer Principle

^{1}Physics Department, Faculty of Science, Alexandria University, Alexandria 21511, Egypt^{2}Department of Medical Equipment Technology, Faculty of Allied Medical Sciences, Pharos University in Alexandria, Alexandria 21648, Egypt

Received 26 July 2015; Accepted 22 October 2015

Academic Editor: George Bakos

Copyright © 2015 Mohamed S. Badawi et al. 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.

#### Abstract

The efficiency transfer (ET) principle is considered as a simple numerical simulation method, which can be used to calculate the full-energy peak efficiency (FEPE) of NaI(Tl) scintillation detector over a wide energy range. In this work, the calculations of FEPE are based on computing the effective solid angle ratio between a radioactive point and parallelepiped sources located at various distances from the detector surface. Besides, the attenuation of the photon by the source-to-detector system (detector material, detector end cap, and holder material) was considered and determined. This method is straightforwardly useful in setting up the efficiency calibration curve for NaI(Tl) scintillation detector, when no calibration sources exist in volume shape. The values of the efficiency calculations using theoretical method are compared with the measured ones and the results show that the discrepancies in general for all the measurements are found to be less than 6%.

#### 1. Introduction

Determination of the absolute efficiency of NaI and Ge detectors has been a long standing problem in gamma-ray spectrometry and numerous reports have been published during the last decades as [1]. The calibration of gamma-ray detectors and sources is still laborious and time consuming and requires extensive operator experience [2]. Accurate calibrated photon emitting sources are difficult to prepare for all the geometrical arrangements used in gamma-ray spectroscopy and sometimes nonfeasible as, for example, in the case of metallic extended samples in neutron activation analysis [3]. In order to overcome the above problem, several nonexperimental methods have been proposed and applied, depending on the photon energy and source-detector geometry and volume [4]. An alternative possibility of being able to compute the efficiencies is thus highly desirable. One of the most common approaches, which only requires point source measurements, is called the efficiency transfer method and was pioneered by Moens et al. [5].

The efficiency transfer principle (ET) means the change in efficiency values under conditions of measurement different from those of calibration setup. It can be determined on the basis of variation of the geometrical parameters of the source-detector arrangement (effective solid angle ratio) [6]. In the previous group work, the efficiency transfer (ET) principle was used to determine the efficiency of the detector corresponding to different sample shapes at different distances from the detector surface [7]. The calculations of the effective solid angle ratio including the attenuation of any material between the source and the detector are based on the direct mathematical method, such as that reported in [8], which was successfully used to calibrate different detectors using different shapes radioactive sources.

In the present work, the efficiency transfer (ET) principle is used to calculate the full-energy peak efficiency (FEPE) of NaI(Tl) detector for axial radioactive parallelepiped sources based on the FEPE calibration for point source as a reference [9]. The calculations of the effective solid angle are based on new mathematical method reported by Hamzawy [10], where an expression to calculate the total efficiency was derivative of the cylindrical NaI(Tl) detector for using axis-off point and coaxial circular disc sources. These expressions are shorter than those in previous studies and easier to calculate, where they are in a form of an elliptical integrations type, which saves the program length and the running time and increases the accuracy of calculations [11].

#### 2. Mathematical Viewpoint

The efficiency transfer principle as presented in [12] was applied to obtain the efficiency calibration curves of the gamma-ray detectors based on the following equation:where and are the detector (FEPE) for a reference source at another position and the effective solid angle subtended by the detector surface and the reference source at that position, respectively. In order to use the efficiency transfer principle, the experimental reference efficiency, , was essentially measured [13].

However, and are the detector (FEPE) for the target source and the effective solid angle subtended by the detector surface and the target source at that position, respectively.

Consider a cylindrical detector with radius, , length, , and a point source positioned at height, , from the detector surface and placed at a lateral distance from the detector axis, , smaller than the detector radius, as shown in Figure 1.