Journal of Radiology and Oncology

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Empirical formulae for calculating γ-ray detectors effective solid angle ratios

Ahmed. M. El Khatib1, Mohamed. S. Badawi1,2*, Mohamed. A. Elzaher3, Mona. M. Gouda1, Abouzeid. A. Thabet4, Mahmoud. I. Abbas1 and Kholud. S. Almugren5

1Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

2Department of Physics, Faculty of Science, Beirut Arab University, Beirut, Lebanon

3Department of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt

4Department of Medical Equipment Technology, Faculty of Allied Medical Sciences, Pharos University in Alexandria, Alexandria, Egypt

5Physics 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

Dates: Submitted: 19 December 2016; Approved: 25 January 2017; Published: 27 January 2017

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.

Copyright: 2017 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.

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.

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 efficiency for any specific source-to-detector configuration of concern. Traditionally, measurements are performed in gamma-ray spectrometry by the relative method, according to which the measured sample is first 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 efficiency transfer method. In this technique, the detector efficiency of using various source dimensions is derived from the known efficiency for the reference source-to-detector geometry. The efficiency transfer method is particularly useful due to, its insensitivity to the inaccuracy of the input data, such as the uncertainty of the detector characterization [7,8].

Badawi, et al. [9-11] were introduced an approach to calculate the full-energy peak efficiency for NaI(Tl) and HPGe detectors, with respect to different volumetric sources. This approach stated that, the detector efficiency using a certain cylindrical radioactive source, ε( E,Cyl ) MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaaiiaaqaaaaaaaaaWdbiab=v7aLnaabmaapaqaa8qacaqGfbGaaeilaiaaboeacaqG5bGaaeiBaaGaayjkaiaawMcaaaaa@4038@ , equal the reference efficiency of using reference radioactive point source, ε( E, P ο ) MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaaiiaaqaaaaaaaaaWdbiab=v7aLnaabmaapaqaa8qacaqGfbGaaiilaiaabcfapaWaaSbaaSqaa8qacaqG=oaapaqabaaak8qacaGLOaGaayzkaaaaaa@4014@ , with the same detector multiplied by the effective solid angle ratio, R, between the two geometries and expressed by the following equation

ε( E,Cyl )=ε( E, P ο ) . R          (1) MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaakeaaiiaaqaaaaaaaaaWdbiab=v7aLnaabmaapaqaa8qacaqGfbGaaeilaiaaboeacaqG5bGaaeiBaaGaayjkaiaawMcaaiabg2da9iab=v7aLnaabmaapaqaa8qacaqGfbGaaiilaiaabcfapaWaaSbaaSqaa8qacaqG=oaapaqabaaak8qacaGLOaGaayzkaaGaaeiiaiaac6cacaqGGaGaaeOuaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeymaiaabMcaaaa@53C2@

Calculations of the effective solid angle are based on the direct mathematical method which reported by Selim and Abbas [12-16] and used successfully before to calibrate different detectors with different sources. The present work will introduce empirical equations to calculate the effective solid angle ratios of two NaI(Tl) detectors with different geometries. The effective solid angle ratio can be used as a conversion factor from using the radioactive point source case to the case in which the cylindrical radioactive sources were used. Consequently, the corresponding full-energy peak efficiency can be calculated simply.

EXPERIMENTAL SETUP

The full-energy peak efficiency (FEPE) values were determined for two NaI (Tl) detectors with resolutions 8.5% and 7.5% at the 662 keV peaks of 137Cs labeled as D1 and D2 respectively. The manufacturer parameters and the setup values are shown in table 1. The experimental measurements were carried out by using point and cylindrical radioactive sources.

Table 1: The manufacturer parameters and the setup values.
Items Detector (D1) Detector (D2)
Manufacturer Canberra Canberra
Serial Number 09L 654 09L 652
Detector Model 802 802
Type Cylindrical Cylindrical
Mounting Vertical Vertical
Resolution (FWHM) at 661 keV 7.5% 8.5%
Cathode to Anode voltage +900 V dc +800V dc
Dynode to Dynode +80 V dc +80 V dc
Cathode to Dynode +150 V dc +150 V dc
Tube Base Model 2007 Model 2007
Shaping Mode Gaussian Gaussian
Detector Type NaI(Tl) NaI(Tl)
Crystal Diameter (mm) 50.8 76.2
Crystal Length (mm) 50.8 76.2
Top cover Thickness (mm) Al (0.5) Al (0.5)
Side cover Thickness (mm) Al (0.5) Al (0.5)
Reflector – Oxide (mm) 2.5 2.5
Weight (Kg) 0.77 1.8
Outer Diameter (mm) 57.2 80.9
Outer Length (mm) 53.9 79.4
Crystal Volume in (cm3) 103.004 347.639

The radioactive standard point sources (241Am, 133Ba, 152Eu, 137Cs, and 60Co) are used for the calibration of gamma spectrometers. The radioactive substance is a very thin, compact grained layer applied to a circular area about 5 mm in diameter, in the middle of the source between two polyethylene foils and each having a mass per unit area of (21.3±1.8) mg.cm-2. By heating under pressure, the two foils are welded together over the whole area so that they are leak-proofed. To facilitate handling, the foil 26 mm in diameter is mounted in a circular aluminum ring (outer diameter: 30 mm, height: 3 mm) from which it can easily be removed if and when required. These point sources were purchased from the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig and Berlin, which is the national institute for science and technology and the highest technical authority of the Federal Republic of Germany in the field of metrology and certain sectors of safety engineering. The sources activities and their uncertainties, half-lives, photon energies, and photon emission probabilities per decay for all of PTB sources are listed in table 2.

Table 2: Point sources activities and their uncertainties, half lives, photon energies and photon emission probabilities per decay for the all radionuclides used in this work.
PTB
Nuclide
Energy
(keV)
Emission
Probability %
Half Life (Days) Activity (kBq)
At 1.June 2009 00:00 Hr
Uncertainty
(KBq)
241Am 59.52 35.9 157861.05 259.0 ±2.6
133Ba 80.99 34.1 3847.91 275.3 ±2.8
152Eu 121.78 28.4   4943.29 290.0 ±4.0
244.69 7.49
344.28 26.6
778.91 12.96
964.13 14.0
1408.01 20.87
137Cs 661.66 85.21 11004.98 385.0 ±4.0
60Co 1173.23 99.99 1925.31 212.1 ±1.5
1332.51 99.98

The homemade Plexiglas holder was used to measure these standard point sources, each at seven different axial distances starting from 20 cm up to 50 cm from the surface of the detector (with a 5 cm as a step). The measurements started from a source-to-detector distance equals 20 cm to minimize the effect of the coincidence summing effect. Spectra were recorded as, P4D1, where P refers to the source type (point) measured at the detector (D1) at position number (4), which equal 20 cm.

The cylindrical radioactive sources were in polypropylene plastic vials form with radius greater than the radius of the detectors, and volumes of 200 ml, 300 ml and 400 ml filled with an aqueous solution containing 152Eu radionuclide, which used for the calibration process. The 152Eu source emits γ-ray in the energy range from 121.78 keV up to 1408.01 keV. Table 3 shows the source dimensions. In order to minimize the dead time, the activity of the sources is prepared to be a few kilo Becquerel (5048±49.98 Bq).

Table 3: Parameters of the radioactive cylindrical volumetric sources.
Items Source Volume (ml)
V1=200 V2=300 V3=400
Inner diameter (mm) 111.50
Height (mm) 21.45 31.59 41.83
Wall and Bottom thickness (mm) 2.03
Activity (Bq)
At 1.Jan 2010 00:00 Hr
5048 ± 49.98

The radioactive volumetric cylindrical sources were measured on a 0.36 cm thickness Plexiglas cover and placed directly on the detector end-cap. These measurements were done using two cylindrical detectors with numbers (D1 & D2). Figure 1 shows a diagram of a cylindrical detector with cylindrical source. Spectra were recorded as V1D2, where V1 is the volume (V1) measured at the detector (D2). The angular correlation effects can be neglected for the low source-to-detector distance [17,18].

Figure 1: A diagram of a cylindrical detector with radioactive cylindrical source.

All the measurements are carried out to obtain statistically significant main peaks in the spectra that are recorded and processed by winTMCA32 software made by ICx Technologies. Measured spectrum, which saved as spectrum ORTEC files can be opened by the Genie 2000 data acquisition and analysis software made by Canberra. The acquisition time is high enough to get at least the number of counts 20,000, which make the statistical uncertainties less than 0.1%. The spectra are analyzed with the program using its automatic peak search and peak area calculations, along with changes in the peak fit using the interactive peak fit interface when necessary to reduce the residuals and error in the peak area values. The peak areas, the live time, the run time and the start time for each spectrum were entered in the spreadsheets that are used to perform the calculations necessary to generate the efficiency curves.

RESULTS AND DISCUSSIONS

The efficiency transfer theoretical method (ETTM) has been used to convert the (FEPE) curve for using radioactive point source at positions start from P4 up to P10 to the (FEPE) for using radioactive cylindrical sources, which represented in V1, V2, and V3. These calculations extended for two cylindrical NaI(Tl) detectors (D1 & D2). By using equation (1) and the experimental efficiency values for using point and cylindrical radioactive sources, that published before in 2012 [19], the one can calculate the effective solid angle ratio, R, values for both detectors experimentally as tabulated in table 4.

Table 4: The values of the effective solid angle ratio, R, for both detectors, which were obtained experimentally.
Effective solid angle ratio between different volumes and different positions with respect to (D1 and D2).(From Experimental Data)
Detector (D1) Effective solid angle ratio   Detector (D2) Effective solid angle ratio
Energy Ω V1 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@41FF@ Ω V1 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4200@ Ω V1 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4201@ Ω V1 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4202@ Ω V1 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4203@ Ω V1 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4204@ Ω V1 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B6@ Ω V1 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@41FF@ Ω V1 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4200@ Ω V1 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4201@ Ω V1 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4202@ Ω V1 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4203@ Ω V1 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4204@ Ω V1 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B6@
Eu-152 121.78 15.722 23.735 32.957 44.330 58.034 72.859 89.042 11.984 17.753 25.185 33.687 44.037 54.425 66.609
Eu-152 244.69 15.795 23.603 33.259 44.087 57.531 72.710 87.406 12.380 18.381 25.950 34.453 45.196 55.989 68.073
Eu-152 344.28 15.850 23.578 33.370 44.110 57.503 73.168 87.516 12.572 18.519 26.253 34.492 45.250 56.562 68.579
Eu-152 778.9 16.165 24.068 34.135 45.149 58.498 74.488 89.140 12.935 19.337 26.901 35.421 45.992 57.317 70.413
Eu-152 964.13 16.298 24.132 34.285 45.482 58.722 74.473 89.618 13.070 19.444 27.349 35.753 46.408 57.349 70.154
Eu-152 1408.01 16.465 24.458 34.752 45.831 59.643 74.802 89.715 13.182 19.596 27.499 36.195 46.989 58.306 71.399
   
Nuclide Energy Ω V2 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4200@ Ω V2 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4201@ Ω V2 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4202@ Ω V2 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4203@ Ω V2 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4204@ Ω V2 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4205@ Ω V2 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B7@ Ω V2 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4200@ Ω V2 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4201@ Ω V2 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4202@ Ω V2 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4203@ Ω V2 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4204@ Ω V2 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4205@ Ω V2 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B7@
Eu-152 121.78 13.216 19.951 27.703 37.263 48.782 61.244 74.847 10.313 15.278 21.674 28.990 37.897 46.837 57.322
Eu-152 244.69 13.222 19.758 27.841 36.905 48.159 60.864 73.166 10.572 15.697 22.161 29.423 38.598 47.815 58.134
Eu-152 344.28 13.372 19.892 28.153 37.214 48.514 61.730 73.835 10.679 15.731 22.300 29.298 38.437 48.045 58.253
Eu-152 778.9 13.755 20.480 29.046 38.418 49.777 63.383 75.851 11.215 16.767 23.326 30.713 39.878 49.699 61.054
Eu-152 964.13 13.911 20.597 29.263 38.820 50.121 63.565 76.491 11.303 16.814 23.650 30.918 40.132 49.593 60.666
Eu-152 1408.01 14.095 20.938 29.749 39.234 51.058 64.035 76.802 11.435 16.999 23.855 31.398 40.761 50.579 61.937
   
Nuclide Energy Ω V3 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4201@ Ω V3 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4202@ Ω V3 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4203@ Ω V3 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4204@ Ω V3 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4205@ Ω V3 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4206@ Ω V3 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B8@ Ω V3 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4201@ Ω V3 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4202@ Ω V3 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4203@ Ω V3 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4204@ Ω V3 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4205@ Ω V3 Ω P9 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Eu-152 121.78 11.152 16.835 23.377 31.444 41.164 51.679 63.158 8.760 12.977 18.410 24.624 32.190 39.783 48.690
Eu-152 244.69 11.372 16.994 23.947 31.743 41.423 52.352 62.933 9.009 13.376 18.884 25.072 32.889 40.743 49.536
Eu-152 344.28 11.483 17.082 24.176 31.957 41.661 53.010 63.405 9.167 13.504 19.143 25.150 32.995 41.243 50.005
Eu-152 778.9 11.901 17.720 25.132 33.242 43.070 54.842 65.630 9.582 14.325 19.929 26.241 34.072 42.462 52.164
Eu-152 964.13 12.024 17.803 25.294 33.553 43.321 54.942 66.115 9.878 14.695 20.669 27.021 35.073 43.342 53.020
Eu-152 1408.01 12.287 18.251 25.933 34.201 44.508 55.820 66.949 9.997 14.861 20.855 27.450 35.635 44.219 54.148

The analytical expressions presented in [19] were used to calculate the effective solid angle ratio as presented in table 5, these values were tested before to obtain the detector FEPE and it was accepted by comparison with the experimental values. The percentage deviations between the effective solid angle ratio values obtained by the two methods are shown in figure 2. A remarkable agreement between them was achieved with discrepancies less than 10%.

Table 5: The values of the effective solid angle ratio, R, for both detectors, which are obtained analytically [19].
Effective solid angle ratio between different volumes and different positions with respect to (D1 and D2).
Detector (D1) Effective solid angle ratio   Detector (D2) Effective solid angle ratio
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Am-241 59.53 14.637 21.861 31.549 40.638 53.398 66.338 83.377 11.666 17.293 24.512 32.344 42.805 51.785 62.635
Ba-133 80.99 14.903 22.260 31.895 41.453 54.488 68.058 84.158 11.703 17.359 24.550 32.436 42.850 52.310 63.409
Eu-152 121.78 15.209 22.720 32.416 42.347 55.684 69.808 85.445 11.867 17.612 24.869 32.889 43.394 53.301 64.747
Eu-152 244.69 15.779 23.573 33.496 43.962 57.849 72.828 88.196 12.293 18.254 25.728 34.071 44.887 55.523 67.663
Eu-152 344.28 16.080 24.024 34.078 44.815 58.992 74.403 89.687 12.528 18.608 26.206 34.725 45.718 56.725 69.230
Cs-137 661.66 16.633 24.852 35.145 46.375 61.084 77.302 92.414 12.965 19.266 27.093 35.941 47.263 58.969 72.169
Eu-152 778.9 16.766 25.051 35.401 46.751 61.588 77.999 93.070 13.070 19.424 27.307 36.233 47.635 59.509 72.876
Eu-152 964.13 16.933 25.302 35.724 47.224 62.223 78.880 93.897 13.203 19.625 27.577 36.603 48.104 60.193 73.773
Co-60 1173.23 17.081 25.523 36.010 47.642 62.783 79.658 94.628 13.322 19.803 27.818 36.933 48.523 60.802 74.571
Co-60 1332.5 17.175 25.663 36.191 47.907 63.138 80.149 95.090 13.397 19.916 27.969 37.141 48.788 61.186 75.074
Eu-152 1408.01 17.216 25.724 36.270 48.022 63.292 80.363 95.293 13.429 19.964 28.034 37.230 48.900 61.350 75.290
Nuclide Energy Ω V2 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4200@ Ω V2 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4201@ Ω V2 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4202@ Ω V2 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4203@ Ω V2 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4204@ Ω V2 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4205@ Ω V2 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B7@   Ω V2 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4200@ Ω V2 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4201@ Ω V2 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4202@ Ω V2 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4203@ Ω V2 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4204@ Ω V2 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4205@ Ω V2 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B7@
Am-241 59.53 12.081 18.044 26.041 33.544 44.076 54.757 68.821 9.926 14.714 20.855 27.519 36.419 44.060 53.292
Ba-133 80.99 12.365 18.470 26.464 34.394 45.210 56.469 69.827 10.011 14.851 21.002 27.749 36.657 44.751 54.246
Eu-152 121.78 12.691 18.959 27.050 35.336 46.466 58.251 71.300 10.214 15.159 21.405 28.308 37.350 45.877 55.728
Eu-152 244.69 13.301 19.872 28.238 37.060 48.767 61.394 74.350 10.698 15.886 22.391 29.651 39.064 48.320 58.886
Eu-152 344.28 13.628 20.361 28.882 37.981 49.996 63.057 76.010 10.966 16.288 22.938 30.395 40.018 49.652 60.598
Cs-137 661.66 14.232 21.265 30.072 39.682 52.268 66.145 79.076 11.467 17.039 23.962 31.787 41.800 52.153 63.828
Eu-152 778.9 14.378 21.484 30.360 40.094 52.818 66.893 79.817 11.588 17.221 24.210 32.124 42.232 52.760 64.611
Eu-152 964.13 14.563 21.761 30.725 40.615 53.514 67.841 80.756 11.742 17.452 24.524 32.551 42.779 53.529 65.606
Co-60 1173.23 14.727 22.006 31.048 41.077 54.131 68.680 81.587 11.879 17.658 24.804 32.932 43.267 54.216 66.493
Co-60 1332.5 14.831 22.161 31.252 41.369 54.522 69.212 82.114 11.966 17.788 24.982 33.173 43.576 54.649 67.054
Eu-152 1408.01 14.877 22.229 31.342 41.497 54.693 69.445 82.346 12.003 17.844 25.058 33.277 43.709 54.837 67.297
   
Nuclide Energy Ω V3 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4201@ Ω V3 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4202@ Ω V3 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4203@ Ω V3 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4204@ Ω V3 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4205@ Ω V3 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4206@ Ω V3 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B8@   Ω V3 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4201@ Ω V3 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4202@ Ω V3 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4203@ Ω V3 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4204@ Ω V3 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4205@ Ω V3 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4206@ Ω V3 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B8@
Am-241 59.53 10.175 15.197 21.932 28.251 37.121 46.117 57.962 8.322 12.336 17.486 23.073 30.536 36.942 44.682
Ba-133 80.99 10.459 15.622 22.384 29.092 38.240 47.763 59.062 8.425 12.498 17.675 23.353 30.850 37.661 45.652
Eu-152 121.78 10.785 16.112 22.987 30.029 39.488 49.503 60.592 8.632 12.811 18.089 23.923 31.564 38.770 47.095
Eu-152 244.69 11.400 17.032 24.202 31.763 41.798 52.620 63.724 9.110 13.527 19.066 25.249 33.264 41.145 50.142
Eu-152 344.28 11.733 17.529 24.865 32.699 43.043 54.288 65.440 9.375 13.925 19.611 25.986 34.212 42.449 51.807
Cs-137 661.66 12.354 18.458 26.103 34.444 45.369 57.414 68.638 9.874 14.673 20.635 27.373 35.996 44.911 54.964
Eu-152 778.9 12.505 18.684 26.404 34.870 45.936 58.177 69.417 9.996 14.855 20.884 27.711 36.430 45.512 55.734
Eu-152 964.13 12.697 18.972 26.787 35.410 46.656 59.146 70.406 10.151 15.087 21.201 28.140 36.982 46.276 56.716
Co-60 1173.23 12.868 19.227 27.127 35.890 47.296 60.008 71.285 10.289 15.294 21.484 28.524 37.475 46.958 57.592
Co-60 1332.5 12.976 19.389 27.343 36.195 47.702 60.554 71.842 10.376 15.425 21.663 28.767 37.788 47.390 58.147
Eu-152 1408.01 13.024 19.461 27.438 36.329 47.881 60.795 72.089 10.414 15.482 21.741 28.872 37.923 47.578 58.388

Figure 2a: The deviation between the calculated effective solid angle ratio, R, that obtained analytically and the experimental one for D1.

Figure 2b: The deviation between the calculated effective solid angle ratio, R, that obtained analytically and the experimental one for D1.

By plotting a three dimensional relation between the Log values of the point source position, P (cm), the effective solid angle ratio, R, and the photon energy, E (keV) for the two detectors (D1 & D2) was done as shown in figure 3. The plotted data for each source volume (ml) with the two detectors have shown semi plane shape and the empirical formulae that represent these shapes are described below to calculate the effective solid angle ratios, R, for both detectors.

Figure 3: The relation between Log values of radioactive point source positions, P, solid angle ratio, R, and the photon energy, E, for D1 and D2.

The empirical formula for the detector (D1) is given by:

Log( E )26.77 Log( R ) + 49.18 Log( P )0.0176 V30.62 = 0          (2) MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@6988@

while, the empirical formula for the detector (D2) is given by:

Log( E )26.77 Log( R ) + 49.18 Log( P )0.0166 V33.63 = 0          (3) MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@69CB@

By knowing the photon energy and the reference position, the effective solid angle ratio, R, for both detectors was calculated using equations (2) and (3). The obtained values were tabulated in table 6. Therefore, these equations provide a simple method to calculate the full-energy peak efficiency (FEPE) of two different cylindrical NaI(Tl) scintillation detectors. These two formulae are valid through a wide energy range and different radioactive volumetric source geometries. The percentage deviations between the calculated effective solid angle ratio, that obtained experimentally and that obtained from equations (2) and (3) were shown in figure 4. A remarkable agreement between them was achieved with discrepancies less than 7%.

Table 6: The values of the effective solid angle ratio, R, for both detectors, which are obtained from empirical equations.
Effective solid angle ratio between different volumes and different positions with respect to (D1 and D2).(from the empirical formula)
Detector (D1) Effective solid angle ratio   Detector (D2) Effective solid angle ratio
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MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4202@ Ω V1 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4203@ Ω V1 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4204@ Ω V1 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaigdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B6@
Am-241 59.53 15.148 22.820 31.896 42.334 54.099 67.163 81.501 11.893 17.916 25.042 33.236 42.473 52.730 63.987
Ba-133 80.99 15.323 23.084 32.265 42.823 54.725 67.940 82.444 12.030 18.123 25.331 33.621 42.965 53.340 64.727
Eu-152 121.78 15.558 23.438 32.760 43.480 55.564 68.982 83.709 12.215 18.402 25.720 34.137 43.624 54.159 65.721
Eu-152 244.69 15.969 24.057 33.625 44.628 57.031 70.804 85.919 12.537 18.887 26.399 35.038 44.776 55.588 67.456
Eu-152 344.28 16.174 24.366 34.056 45.201 57.763 71.712 87.022 12.698 19.130 26.738 35.488 45.350 56.302 68.321
Cs-137 661.66 16.573 24.968 34.898 46.317 59.190 73.483 89.171 13.012 19.602 27.398 36.364 46.470 57.692 70.008
Eu-152 778.9 16.674 25.120 35.111 46.600 59.551 73.932 89.716 13.091 19.722 27.566 36.586 46.754 58.045 70.436
Eu-152 964.13 16.808 25.321 35.392 46.973 60.028 74.524 90.433 13.196 19.880 27.786 36.879 47.128 58.509 71.000
Co-60 1173.23 16.931 25.507 35.652 47.319 60.469 75.072 91.098 13.293 20.026 27.991 37.150 47.475 58.939 71.522
Co-60 1332.5 17.012 25.629 35.822 47.544 60.757 75.430 91.533 13.356 20.121 28.124 37.327 47.701 59.220 71.863
Eu-152 1408.01 17.047 25.682 35.896 47.642 60.883 75.585 91.721 13.384 20.163 28.182 37.404 47.799 59.342 72.011
Nuclide Energy Ω V2 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4200@ Ω V2 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4201@ Ω V2 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4202@ Ω V2 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4203@ Ω V2 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4204@ Ω V2 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4205@ Ω V2 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B7@   Ω V2 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4200@ Ω V2 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4201@ Ω V2 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4202@ Ω V2 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4203@ Ω V2 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4204@ Ω V2 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4205@ Ω V2 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaikdaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B7@
Am-241 59.53 13.014 19.605 27.403 36.370 46.477 57.701 70.019 10.308 15.529 21.705 28.808 36.814 45.704 55.462
Ba-133 80.99 13.164 19.832 27.719 36.790 47.015 58.368 70.829 10.427 15.709 21.956 29.141 37.240 46.233 56.103
Eu-152 121.78 13.366 20.136 28.145 37.355 47.736 59.264 71.916 10.587 15.950 22.293 29.588 37.812 46.942 56.964
Eu-152 244.69 13.719 20.668 28.888 38.341 48.997 60.829 73.815 10.867 16.371 22.882 30.370 38.810 48.182 58.468
Eu-152 344.28 13.895 20.933 29.259 38.833 49.625 61.609 74.762 11.006 16.581 23.175 30.759 39.308 48.800 59.218
Cs-137 661.66 14.238 21.450 29.981 39.792 50.851 63.131 76.608 11.278 16.990 23.748 31.519 40.278 50.005 60.681
Eu-152 778.9 14.325 21.581 30.164 40.035 51.162 63.516 77.076 11.347 17.094 23.893 31.711 40.525 50.311 61.051
Eu-152 964.13 14.440 21.754 30.406 40.355 51.571 64.025 77.693 11.438 17.231 24.084 31.965 40.849 50.713 61.540
Co-60 1173.23 14.546 21.914 30.629 40.652 51.950 64.496 78.264 11.522 17.358 24.261 32.200 41.149 51.086 61.992
Co-60 1332.5 14.615 22.018 30.775 40.846 52.198 64.803 78.637 11.577 17.440 24.377 32.354 41.345 51.330 62.288
Eu-152 1408.01 14.645 22.064 30.839 40.930 52.305 64.936 78.799 11.600 17.476 24.427 32.420 41.431 51.435 62.416
Nuclide Energy Ω V3 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4201@ Ω V3 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4202@ Ω V3 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4203@ Ω V3 Ω P7 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaG4naaWdaeqaaaaaaaa@4204@ Ω V3 Ω P8 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGioaaWdaeqaaaaaaaa@4205@ Ω V3 Ω P9 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGyoaaWdaeqaaaaaaaa@4206@ Ω V3 Ω P10 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGymaiaaicdaa8aabeaaaaaaaa@42B8@   Ω V3 Ω P4 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGinaaWdaeqaaaaaaaa@4201@ Ω V3 Ω P5 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGynaaWdaeqaaaaaaaa@4202@ Ω V3 Ω P6 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbs9MyVr3BaeXatLxBI9gBaerbd9wDYLwzYbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbeqaaeGaciGaaiaabeqaamaaeaqbaaGcbaaeaaaaaaaaa8qadaWcaaWdaeaapeGaeuyQdC1damaaBaaaleaapeGaaCOvaiaaiodaa8aabeaaaOqaa8qacqqHPoWvpaWaaSbaaSqaa8qacaWHqbGaaGOnaaWdaeqaaaaaaaa@4203@ Ω V3 Ω P7 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Am-241 59.53 11.180 16.843 23.542 31.246 39.930 49.572 60.155 8.935 13.460 18.813 24.970 31.909 39.615 48.072
Ba-133 80.99 11.310 17.038 23.814 31.607 40.391 50.145 60.850 9.038 13.616 19.031 25.258 32.278 40.073 48.628
Eu-152 121.78 11.483 17.300 24.180 32.092 41.011 50.915 61.784 9.177 13.825 19.323 25.646 32.774 40.688 49.374
Eu-152 244.69 11.786 17.756 24.818 32.939 42.094 52.259 63.415 9.419 14.190 19.833 26.323 33.639 41.762 50.678
Eu-152 344.28 11.937 17.984 25.137 33.362 42.634 52.930 64.229 9.540 14.372 20.088 26.661 34.070 42.298 51.328
Cs-137 661.66 12.232 18.428 25.757 34.186 43.687 54.237 65.815 9.775 14.727 20.584 27.319 34.912 43.343 52.595
Eu-152 778.9 12.307 18.541 25.915 34.395 43.954 54.568 66.218 9.835 14.817 20.709 27.486 35.125 43.607 52.917
Eu-152 964.13 12.405 18.689 26.122 34.670 44.305 55.005 66.747 9.914 14.935 20.875 27.706 35.406 43.956 53.340
Co-60 1173.23 12.497 18.827 26.314 34.925 44.631 55.409 67.238 9.987 15.045 21.029 27.910 35.667 44.280 53.733
Co-60 1332.5 12.556 18.916 26.440 35.092 44.844 55.673 67.559 10.034 15.117 21.129 28.043 35.837 44.491 53.989
Eu-152 1408.01 12.582 18.955 26.494 35.164 44.936 55.788 67.698 10.055 15.148 21.172 28.101 35.910 44.582 54.100

Figure 4a: The deviation between the calculated effective solid angle ratio, R, that obtained empirically and the experimental one for D1.

Figure 4b: The deviation between the calculated effective solid angle ratio, R, that obtained empirically and the experimental one for D2.

The main advantage of this process is the simplicity of obtaining the effective solid angle ratios, R, especially in between any two measured positions, without using analytical or experimental calculations. These ratios are considered to be the efficiency conversion factor between any two different geometrical conditions, and used to save the time in absent the standard calibration sources.

CONCLUSIONS

The present work leads to a simplified method to calculate the effective solid angle ratio empirical, which can be used to calculate the conversion factors of the detector efficiency, in the case of using point and cylindrical radioactive sources. The efficiencies can be determined at any calibration position or any energy situated in the domain of the study based on these conversion factors. These formulas are valid through a wide energy range and different source-to-detector geometries. Therefore the corresponding full-energy peak efficiency can be calculated simply, and the activity of unknown samples measured in the same conditions can be determined easily.

REFERENCES

  1. Debertin K, Helmer RG. Gamma- and X-ray spectrometry with semiconductor detectors. North-Holland. 1988; New York. Ref.: https://goo.gl/fHfUb8
  2. Lippert J. Detector-efficiency calculation based on point-source measurement. Int J Appl Radiat Isot. 1983; 34: 1097-1103. Ref.: https://goo.gl/wOQveD
  3. Moens L, Hoste J. Calculation of the peak efficiency of high-purity germanium detectors. Int J Appl Radiat Isot. 1983; 34: 1085-1095. Ref.: https://goo.gl/j3IxZv
  4. Haase G, Tait D, Wiechon A. Application of new monte carl method for determination of summation and self-attenuation corrections in gamma spectrometry. Nucl Instrum Methods. 1993; A336: 206-214. Ref.: https://goo.gl/x4tnng
  5. Wang TK, Mar WY, Ying TH, Liao CH, Tseng CL, et al. HPGe detector absolute-peak-efficiency calibration by using the ESOLAN program. Appl Radiat Isot. 1995; 46: 933-944. Ref.: https://goo.gl/Lgl3lc
  6. Wang TK, Mar WY, Ying TH, Tseng CH, Liao CH, et al. HPGe Detector efficiency calibration for extended cylinder and Marinelli- beaker sources using the ESOLAN program. Appl Radiat Isot. 1997; 48: 83-95. Ref.: https://goo.gl/dQNx77
  7. Lépy MC, Altzitzoglou T, Arnold D, Bronson F, Capote Noye R, et al. Intercomparison of efficiency transfer software for gamma-ray spectrometry. Appl Radiat Isot. 2001; 55: 493-503. Ref.: https://goo.gl/WfSS3v
  8. Vidmar T, Aubineau Laniece I, Anagnostakis MJ, et al. An intercomparison of monte carlo codes used in gamma-ray spectrometry. Appl Radiat Isot. 2008; 66: 764-768. Ref.: https://goo.gl/e35Sd8
  9. Badawi MS, El-Khatib AM, Krar ME. New numerical simulation approach to calibrate the NaI(Tl) detectors array using non-axial extended spherical sources. Journal of Instrumentation. 2013; 8: 11. Ref.: https://goo.gl/ut1p4i
  10. Badawi MS, Krar ME, El-Khatib AM, Jovanovic SI, Dlabac AD, et al. A new mathematical model for determining the full energy peak efficiency (FEPE) for an array of two γ-detectors counting rectangular parallelepiped source. Nuclear Technology & Radiation Protection Journal. 2013; 28: 370-380. Ref.: https://goo.gl/LYmnac
  11. Badawi MS, Elzaher MA, Thabet AA, El-khatib AM. An empirical formula to calculate the full energy peak efficiency of scintillation detectors. Appl Radiat Isot. 2013; 74: 46-49. Ref.: https://goo.gl/V5PDsr
  12. Abbas MI. A direct mathematical method to calculate the efficiencies of a parallelepiped detector for an arbitrarily positioned point source. Radiat Phys Chem. 2001a; 60: 3-9. Ref.: https://goo.gl/JypVh5
  13. Abbas MI. Analytical formulae for well-type NaI(Tl) and HPGe detectors efficiency computation. Appl Radiat Isot. 2001b; 55: 245-252. Ref.: https://goo.gl/hLQSKd
  14. Abbas MI, SelimYS. Calculation of relative full-energy peak efficiencies of well-type detectors. Nucl Instrum Methods A. 2002; 480: 651-657. Ref.: https://goo.gl/9AMrXx
  15. Abbas MI. HPGe detector absolute full-energy peak efficiency calibration including coincidence correction for circular disc sources. J Phys D Appl Phys. 2006; 39: 3952-3958. Ref.: https://goo.gl/89DOYb
  16. Abbas MI, Nafee SS, Selim YS. Calibration of cylindrical detectors using a simplified theoretical approach. Appl Radiat Isot. 2006; 64: 1057-1064. Ref.: https://goo.gl/M4DM6l
  17. Debertin K, Schotzig U. Coincidence summing corrections in Ge(Li)-spectrometry at low source-to-detector distances. Nucl Instrum Meth A. 1979; 158: 471-477. Ref.: https://goo.gl/CJ5NGn
  18. El-Khatib AM, Thabet AA, Elzaher MA, Badawi MS, Salem BA. Study on the effect of the, self-attenuation coefficient on γ-ray detector efficiency calculated at low and high energy regions. Journal of Nuclear Engineering and Technology. 2014; 46: 217-224. Ref.: https://goo.gl/wpoBxI
  19. El-Khatib AM, Badawi MS, Elzaher MA, Thabet AA. Calculation of the peak efficiency for NaI(Tl) gamma ray detector using the effective solid angle method. Journal of Advanced Research in Physics. 2012; 3: 021204. Ref.: https://goo.gl/bqKYOW