DIRECT ANALYTICAL EFFICIENCY ASSESSMENT OF THE NAI(TL) GAMMA-RAY DETECTOR (ROMASHKA)

Abouzeid A. THABET 1,2 , Mohamed S. BADAWI 3,4* , Ayman HAMZAWY 5, Ivan N. RUSKOV 6,7 , Mohamed I. BADAWI 1, Ivan A. SIRAKOV 7, Yuri N. KOPATCH 6, Dimitar N. GROZDANOV 6,7 , and Bohaysa A. SALEM 8

1 Department of Biomedical Equipment Technology, Faculty of Applied Health Sciences Technology, Pharos University, Alex andria, Egypt
2 Department of Educational Studies, University of Technology and Applied Sciences, Khasab, Oman
3 Physics Department, Faculty of Science, Alex andria University, Alex andria, Egypt
4 Faculty of Sciences, Alamein International University, Alamein City, Matrouh Governorate, Egypt
5 College of Pharmacy, Al-Farahidi University, Baghdad, Iraq
6 Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russia
7 Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
8 Basic Science Department, Faculty of Physical Therapy, Pharos University in Alex andria, Egypt

Scientific paper https://www.carmenthyssenmalaga.org present study focuses on the ana lyt ical and numerical calcula tions of the solid an gle, ef - fective solid angle, efficiency, and gamma-ray average path length within the detector ma teri - als as a function of the source position. This analysis is conducted for a Romashka module of the 4  NaI(Tl) gamma-ray detector array (NaGRaDA). NaGRaDA comprises 2  2 gamma-ray detector modules, with each module consist ing of six NaI(Tl) crystals arranged in a compact configura tion resembling a Daisy flower (known as Romashka in Russian). Each of the twelve scintilla tors has a unique design, distinguishing them in shape and size from con - ventional scintilla tion detectors. This type of 4  multi-detector system is applica ble for mea - suring gamma ra dia tion from samples exhibiting very low activity. It is employed in neu tron activa tion analysis and prompt-gamma neutron activa tion analysis. Furthermore, this system can be instrumental in the experimental investiga tion of the characteristics of neu tron-in - duced nuclear reactions. The results obtained throuh direct ana lyt ical and numerical methods will be compared with the upcoming comprehensive characteriza tion of the upgraded and modernized Romashka NaGRaDA. This comparison will utilize GEANT4 simula tions along - side standard point-type gamma-ray sources.
Key words: 4 multi-detectors array, geometrical solid angle, total efficiency, average path length
INTRODUCTION
The NaI(Tl) scintillation crystals are available in single and polycrystalline forms, ex hib iting a high light production. Furthermore, they demon strate negligible self-absorption of scin tillation light. The emission spec - trum aligns effectively with the sensitivity characteris - tics of bialkali photocathodes used in photomultiplier tubes (PMT) [1-3]. The NaI(Tl) detectors ex hibit ex - ceptionally high lu minescence efficiency and can be fabricated in different dimen sions and geometries. This versatility makes them the most commonly used scintil - lators in various ap plications. Thallium-doped NaI scintillator produces one of the high est sig nals in a photomultiplier tube for a given amount of absorbed ra - diation. Under optimal con ditions, approximately 10 4 photoelectrons are gen erated per 1 MeV gamma-ray en ergy [4-6]. The NaI(Tl) ex hibits multiple decay time constant mechanisms. The primary sin gle ex ponen tial decay con stant at room temperature is approximately 250 ns. As temperature rises, the longer time con stant components and the response curves converge, reduc - ing the decay time from 1 ms to 12 ms [7, 8].
The scintillation crystal should not be subjected to ultraviolet (UV) radiation from sunlight or luminous lamps, as such exposure can significantly impair and di - minish the scintillation performance [9, 10]. The NaI(Tl) scintillation crystals are routinely manufactured with po - tassium concentrations below 0.5 parts per million (ppm), which makes them particularly suitable for low back - ground applications. These NaI(Tl) crystals are exten - sively used in various radiation detection applications.
A. A. Thabet., et al ., Direct An alytical Efficiency Assessment of the Nai(Tl) ... 22 Nuclear Tech nology & Radiation Protection: Year 2025, Vol. 40, No. 1, pp. 22-36
* Corresponding author, e-mail: ms241178 @hotmail.com
They are particularly prevalent in well logging, environ - mental monitoring, nuclear medicine, aerial surveys, and nuclear physics, among several other applications [11-13]. In summary, protecting scintillation crystals from UV exposure and moisture is essential. Further - more, the development of low-potassium sodium iodide doped with thallium NaI(Tl) crystals enhances their ef - fectiveness in sensitive detection applications. Currently, polycrystalline NaI(Tl) scintillation detectors are increas - ingly recognized as viable alternatives to single-crystal scintillators in various applications where mechanical and thermal shocks are prevalent, such as in gas exploration and oil extraction. These detectors offer a combination of robustness and scintillation performance comparable to that of single-crystal NaI(Tl) detectors [5, 14].
The polycrystalline configuration of NaI(Tl) is produced through a well-defined pro cess in which sin - gle-crystal bricks are recrystallized under applied pres - sure and heat. The resulting material can be characterized as a polycrystalline substance comprising randomly ori - ented crystal particles within a mixed structural frame - work [5, 15]. The density of NaI remains unchanged dur - ing the development process. This characteristic en hances the mechan ical strength of the material without impacting the performance of the scin tillation process, as the optical prop erties of NaI(Tl) in polycrystalline form are comparable to those of single-crystal NaI(Tl) [5, 16]. Cracks that occur due to mechanical or thermal shock in NaI(Tl) polycrystals are typically confined to small local regions known as grains. Since the cleavage planes of the grains are randomly oriented, it is unlikely that a small crack would propagate across the grain boundaries. This characteristic makes NaI(Tl) polycrystalline material a preferred choice in applications where durability is criti - cal, such as aerospace and well-logging [5, 17-19].
In contrast, single crystals can fracture along spe - cific planes un der stress. In a detector assembly com - posed of single crystal material, even a minor crack can propagate throughout the en tire crystal, ad versely affect - ing signal height reso lution and the light collection pro - cess [5, 20, 21]. In nuclear physics, the prompt gamma neutron activation analysis (PGNAA) technique is rec - og nized as a highly effective method for simultaneously determining the quantity and presence of multiple ele - ments in samples with masses ranging from micrograms to several grams. This non-destructive technique is mini - mally affected by the sample's physical shape and chemi - cal composition. Classic measurements were obtained over durations ranging from several minutes to a few hours for each sample under investigation [22-24]. The technique can be described as the sample is irradiated with a narrow beam of neu trons. The constituent ele - ments within the sample capture a portion of these neu - trons, resulting in the emission of prompt gamma rays, which are precisely measured using a gamma-ray NaI(Tl) or HPGe spectrometer.
The energies of the emitted gamma-rays identify the neu tron-cap turing elements, while the in tensities of the gamma-ray peaks at these en ergies in dicate their con - centrations. The quan tity of the elements under in vestigation is determined by the ratio of the count rate of the peak of interest in the sample to the count rate of a known mass of an appropriate elemental standard irradi - ated under identical conditions [25-27]. Typically, the sample will not acquire significant long-lived radioactiv - ity, allowing for its potential removal from the irradiated facility for additional applications. One of the primary uses of PGNAA is as a mass material analyzer in the coal, mineral, and cement industries [28-30]. At the Institute for Nuclear Research and Nuclear Energy of the Bulgar - ian Academy of Sciences, a NaI(Tl) scintillator crystal system, designed in the shape of a daisy flower (referred to as Romashka ), has been constructed and tested [31, 32]. This system can investigate radiative neutron cap - ture and fission reactions [33, 34] involving various mono-isotopes that are important to nuclear science and its applications. The incorporation of high-quality lead shielding renders the system suitable for operation as a low-background radiation detector, facilitating the mea - surement of natu ral radioactiv ity in environmen tal mate - rial samples [35]. Ad ditionally, it can be utilized for ele - mental analysis of samples in conjunction with the resonance neutron time-of-flight spectrometer IREN at the Frank Laboratory of Neutron Physics of the Joint In - stitute for Nuclear Research [36]. In both types of inves - tigations, the potential application of the gamma- -multi - plicity method warrants exploration [37].
In all the aforemen tioned applications, accurate values of gamma-ray detection efficiency for NaI(Tl) or HPGe spectrometers at specific gamma energies are essential. Mitigating interference from different gamma en ergies requires a thorough un derstand ing of the detector's reso lution corresponding to these en er - gies [18, 19]. Resolu tion and detection efficiency val - ues vary depending on the detector size and other pa - rameters. Therefore, it is imperative to ascertain these values for a specific detector before its application in quan titative in vestigations [20, 21]. This study fo - cuses on the calculation of the solid angle, effective solid an gle, and efficiency of a Romashka module us - ing an an alytical numerical technique. Ad dition ally, it in vestigates the av erage path length within the detec - tor materials as a function of the source position. The 12 NaI(Tl) scintillator gamma detectors form a spe - cialized 4  multi-detector array system (NaGRaDA) that differs from conventional and well-known multi-detector gamma-ray spectrometers in both shape and size. This 4  system enables the measure - ment of samples with extremely low gamma activity and is applicable in conven tional instru men tal neutron activation analysis (INAA) and prompt-gamma neu - tron activation analysis. The results may pro vide valu - able insights for applications in radiation detection and nuclear physics. Additionally, they can inform sci - en tists regard ing the op timization and design of detec - tion setups tailored to specific ex perimen tal condi - tions.
A. A. Thabet., et al ., Direct An alytical Efficiency Assessment of the Nai(Tl) ... Nuclear Tech nology & Radiation Protection: Year 2025, Vol. 40, No. 1, pp. 22-36
MATHEMATICAL VIEW POINT
The an alytical numerical technique has been em - ployed to estimate the solid an gle, effective solid an - gle, efficiency of the Romashka NaI(Tl) mod ule, and the av erage gamma-ray path length within the materi - als of the detector, contingent upon the po sition of the source. The general ex pression for the geometric solid an gle, denoted as WG, formed between a radioactive source and a Romashka NaI(Tl) gamma-ray detector mod ule, in a spherical coordinate system, is repre - sented by the following eq.
WG   sin q q j qj d d (1)
The geo metrical efficiency of a Romashka gamma-ray detector mod ule, eG, is defined as
e p GG  W 4 (2)
The to tal efficiency, denoted as of a Romashka NaI(Tl) gamma-ray detector mod ule in relation to ra - dioactive sources, is represented by the following eq.
e p T(axial) eff  W 4 (3)
where Weff a denotes the effective solid angle between the source and the detector, accounting for all materi - als between the source and the detector, as well as the detector material itself. To calcu late the efficiency of the Romashka NaI(Tl) gamma-ray detector model, one must con sider the position ing of the radioactive source concerning the detector. Furthermore, this analy sis will address all potential scenarios in volving the utilization of a radio active point source, which will be discussed in next sections.
Case I: ( h  L)
The radioactive point source is positioned above the detector surface at a height ( h  L), where L represents the side length of the detector, as illustrated in fig. 1.
The effective solid angle, denoted as Weff , will take one of the following ex pressions, ranging from (a) to (e), depending on the values of the po lar angle.
( ) a q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q