Journal of Radiology and Oncology Open Access HTTPS://WWW.HEIGHPUBS.ORG 012 ISSN 2573-7724 ABSTRACT Determination of the detector efficiency using volumetric cylindrical sources is very important in various scientific and industrial fields, especially in the field of quantitative analysis. To calculate the absolute activity of any sample, the full-energy peak efficiency (FEPE) of the detector is needed. By applying the efficiency transfer method, the FEPE of the detector would be determined easily without using the standard sources. This approach depends on two main factors. The first one, is the reference efficiency of the reference source, which is determined experimentally, and the second one, is the calculation of the effective solid angle ratio between the sample and the reference source geometries. This work introduces an empirical formula for calculating the second factor for using two different sizes of NaI(Tl) detectors. The validity of this empirical formula was successfully demonstrated by comparing the calculating values with the experimental values. Research Article Empirical formulae for calculating γ-ray detectors effective solid angle ratio Ahmed M El Khatib 1 , Mohamed S Badawi 1,2 *, Mohamed A Elzaher 3 , Mona M Gouda 1 , Abouzeid A Thabet 4 , Mahmoud I Abbas 1 and Kholud S Almugren 5 1 Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt 2 Department of Physics, Faculty of Science, Beirut Arab University, Beirut, Lebanon 3 Department of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt 4 Department of Medical Equipment Technology, Faculty of Allied Medical Sciences, Pharos University in Alexandria, Alexandria, Egypt 5 Physics Department, Faculty of Science, Princess Nourah Bint Abdulrahaman University, 11544-55532 Riyadh, Saudi Arabia *Address for Correspondence: Mohamed S Badawi, Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt, Tel: +201005154976; Email: ms241178@hotmail.com Submitted: 19 December 2016 Approved: 25 January 2017 Published: 27 January 2017 Copyright: 2017 El Khatib AM, 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. Keywords: NaI (Tl) detector; Effective solid angle ratio; Full-Energy peak efficiency Acknowledgement: All of us would like to thank Prof. Dr. Nasser. M El Maghraby, Dean of Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt for his valuable assistance in the mathematical part. How to cite this article: El Khatib AM, Badawi MS, Elzaher MA, Gouda MM, Thabet AA, et al. Empirical Formulae for Calculating γ-ray Detectors Effective Solid Angle Ratio. J Radiol Oncol. 2017; 1: 012-021. https://doi.org/10.29328/journal.jro.1001002 INTRODUCTION The scintillation counters are used to measure the radiation in different applications such as, radiation survey meters, medical imaging, nuclear plant safety, measuring radon levels, oil well logging and monitoring for radioactive contamination. In the gamma-ray spectroscopy, one usually needs to know the full-energy peak efϐiciency for any speciϐic source-to-detector conϐiguration of concern. Traditionally, measurements are performed in gamma-ray spectrometry by the relative method, according to which the measured sample is ϐirst prepared, that should match the used standard source in all the important characteristics, such as its size, chemical composition and density [1]. This method is tedious and time consuming process. In order to overcome the problems of the experimental method, several non-experimental methods [2-6] have been proposed and applied, depending on the photon energy, source-to-detector geometry and volume. One of the most common approaches is called the efϐiciency transfer method. In this technique, the detector efϐiciency of using various source dimensions is derived from the known efϐiciency for the reference source-to-detector geometry. The efϐiciency transfer method is particularly useful due to, its insensitivity to the