THE EFFICIENCY DEPENDENCE ON THE ANALYZED SAMPLE CHARACTERISTICS IN GAMMA-RAY SPECTROMETRIC ANALYSIS

THE EFFICIENCY DEPENDENCE ON THE ANALYZED SAMPLE CHARACTERISTICS IN GAMMA-RAY SPECTROMETRIC ANALYSIS LAURENTIU DONE, LIVIU CORNEL TUGULAN, FELICIA DRAGOLICI, CARMELA ALEXANDRU, MARIA SAHAGIA National Institute for Physics and Nuclear Engineering Horia Hulubei 30, Reactorului str., RO-077125, P.O. Box MG-6, Magurele (Ilfov) Romania, EU E-mail: donelaur@yahoo.com Received February 10, 2014 This paper proposes a comparative study of a HP-Ge detector efficiencies for various geometrical configurations of the calibration samples with properties close to the environmental ones. The detection efficiency for the studied analysis geometries was calculated using the LabSOCS software (Laboratory Sourceless Calibration Software). This program calculates the detector efficiency versus incident photons energy, for the operator s set analysis geometry, by the Monte Carlo simulation. The detection efficiency variation was studied as function of the analyzed sample shape, height and mass. Key words: gamma-ray spectrometry, environmental samples, detection efficiency. 1. INTRODUCTION In the last couple of decades the communities have become more and more aware of the importance of preserving the natural environment and the deployment of all the human activities with a decreased pollution degree. The monitoring and supervision of all kinds of parameters, which can give us an insight into the Earth health, has become increasingly a more important worldwide activity. As a result, the scientists are trying, on the one hand to discover and devise new methods to measure the environment pollution level, and on the other hand to increase the precision and accuracy of these measurements. The gamma-ray spectrometric analysis of environmental samples (soil, sediment, water, vegetation, air) gives us informations on both natural radionuclides concentration and the time evolution of these concentrations, but mostly we can warn of the occurrence in the environment of anthropogenic radionuclides, due to the human activities. Rom. Journ. Phys., Vol. 59, Nos. 9 10, P. 1012 1024, Bucharest, 2014

2 The efficiency of gamma-ray spectrometric analysis 1013 The activity calculation of a gamma-ray emitter radionuclide in a sample, by the gamma spectrometric quantitative analysis, is based on the recording of the net area expression A n (E) of the Full-Energy Peak (FEP) of the photon specific energy E, in a gamma-ray spectrometric installation, and its relation with the activity, expressed by equation (1): A ( E ) = Λ I t ε ε f (1) n γ where: Λ is the radionuclide activity from the sample, I γ (Yield) is the emission probability of the photons with energy E, t is the effective time of the spectrum acquisition (live time), ε int is the detector intrinsic efficiency at energy E, ε geo is the detection geometrical efficiency at energy E, f is the coincidence summing correction factor, especially important in the case of the cascade emission of the gamma ray radionuclides. For a sample with a Λ activity and a given detector intrinsic efficiency, a better statistical analysis is obtained if the peak net area of E energy is larger. From equation (1) is noticed that the net peak area is directly proportional to two parameters on which the operator can act: a) the spectrum acquisition time, t; b) the geometrical detection efficiency, ε geo. The gamma-ray spectrum aquisition time can be increased only in the reasonable limits, depending on the needed number of samples to be analyzed in a given period. The second solution to increase the peak net area is to perform the analysis in a larger efficiency geometry. Note: Further, for a given detector, the calculations refer to the total detection efficiency, ε T = ε int ε geo, where the variation is due to the geometrical efficiency, ε geo. This paper especially refers to the environmental samples analysis, having relatively low activity; therefore, in this study the approached geometries are those in which the sample is in contact with the detector (close measurement geometry). O. Sima in the paper [1] and G. Gilmore in the paper [2] mention the importance of the coincidence summing effects in the case of the closest detectorsource geometry and the necessity of applying corrections in activity calculation, with the specific factors of this phenomenon. int geo 2. METHODS AND EQUIPMENT The efficiency was calculated for a hyperpure germanium detector, REGe type (Reverse-Electrode Germanium), GR4020 model, with thin carbonate window (0.6 mm), manufactured by CANBERRA, with the following characteristics: 5 10 000 kev energy range; detector diameter: 76 mm, Ge cristal diameter: 61 mm; HPGe cristal length: 65 mm; resolution: 0.895 kev at 122 kev and

1014 Laurentiu Done et al. 3 1.96 kev at 1332 kev; peak/compton ratio: 58.9; relative efficiency (measured by the manufacturer): 47.5%. The detector is mounted in a CANBERRA manufactured lead shield, model 747, and was ISOXCALL characterized by the manufacturer. The multichannel analyzer is of DSA 1000 type. The acquisition and processing of gamma spectra software is GENIE 2000. Canberra company provided us the LabSOCS software, based on the ISOXCALL detector characterization and the MCNP code (Monte Carlo N-Particle), developed by Los Alamos National Laboratory. This software is customized for the mentioned detector and uses the Monte Carlo simulation to calculate the efficiency and the coincidence summing corrections, for various geometries set by the operator or supplied by the manufacturer. 3. RESULTS AND DISCUSSIONS 3.1. THE DETECTION EFFICIENCY DEPENDENCE ON THE SAMPLES GEOMETRICAL SHAPE (i) A hypotethical sample with the following characteristics was analyzed, using the LabSOCS software: density ρ = 1.4 g/cm 3, corresponding approximately to the density of the dry sediment, or the soil samples, with particles size less than 1 mm; sample mass m = 1042 g, which would be required to fill a Marinelli beaker, type 130G to the overall height of 111 mm, which means that the samples height on the flat detector surface would be 36 mm. The detector efficiency was calculated for the following sample s geometries: Marinelli beaker 130G type, D mean inside = 122 mm; plexiglas cylinder with D inside = 122 mm, the bottom thickness of 2.09 mm and the wall thickness of 1 mm, plexiglas density 1.2 g/cm 3 (characteristics for the Sarpagan type box); cube with the side l inside = 92 mm and wall thickness of 2.09 mm; sphere with R inside = 57 mm and wall thickness of 2.09 mm; cylinder with D = 70 mm (diameter of a Sarpagan beaker) and bottom thickness 2.09 mm. The detection efficiency variation versus photon s energy, for these analysed geometries, was graphically represented in Figure 1. For this study energy interest range (10 2000 kev), the following remarks are to be done: a) The detection efficiency for the sample analyzed in the Marinelli beaker is the highest; b) In the case of the sample analyzed in cylindrical geometry with the diameter D = 122 mm, the detection efficiency is greater than in the vessel with the diameter D = 70 mm; c) The detection efficiency is greater for cylinder with D = 122 mm than for a cube with the same volume (with side size l = 92 mm);

4 The efficiency of gamma-ray spectrometric analysis 1015 d) If one notes with h c the distance between the sample gravity center and the flat top surface of the cylindrical detector, it is observed that the detection efficiency increases as the distance h c is lower. The sample described in the Marinelli beaker, due to its shape (the beaker "envelops" a certain volume of the detector) has the gravity center inside the detector at 7.1 mm below its flat side. In this case, the virtual sample concentrated in the volumic sample s gravity center, are inside the detector, and consequently h c = 7.1 mm. Fig. 1 The detection efficiency dependence on the energy, for samples in different geometries. The detection efficiency calculated in Marinelli and in various diameters of cylindrical geometries, as well as the h c distance for each geometry, corresponding to four significant energies, in the range 10 2000 kev, as presented in Fig. 1, are given in Table 1. Table 1 Calculated efficienciy values for various geometries, for the analysed sample Geometry h c [mm] Eff. at 60 kev Eff. at 120 kev Eff. at 600keV Eff. at 1400 kev Marinelli -7.1 4.755E-02 6.196E-02 2.335E-02 1.297E-02 D=130 mm 29.1 2.155E-02 2.860E-02 1.145E-02 6.656E-03 D=122 mm 33.1 2.068E-02 2.750E-02 1.102E-02 6.426E-03 D=100 mm 49.2 1.789E-02 2.324E-02 9.282E-03 5.444E-03 D=70 mm 100.3 1.271E-02 1.553E-02 5.910E-03 3.467E-03

1016 Laurentiu Done et al. 5 If one considers the detection efficiency graphical representation of the volume sample above, depending on the h c distance between the detector and the sample s centroid from Figure 2, one may fit an efficiency dependence on the h c represented by the following semiempirical equation, deduced by supposing a relation of the type (2). a1 + a 2 hc ε ( h c ) = a + a h + a h 3 4 c 5 where a 1 a 5 are real coefficients, with h c variation between 10 mm and +200 mm. For example, the detection efficiency at 60 kev, depends on the distance h c by a semiempirical relation of the form: 0.0342 + 0.002 h c ε ( h c ) = (3) 2 1 + 0.0865 h + 0.0008 h c 2 c c (2) Fig. 2 The detection efficiency at four energy values as function of the distance h c. (ii) The second hypothetical sample. Let s suppose that, for practical reasons, we can not take a soil sample with a mass of 1042 g; for a soil sample, in the Marinelli 130G type beaker, we need a sample mass greater than 500 g, to reach the detector front. Note: especially for a beryllium or carbonate detector window (for the low energy photons detection), is important that a large part of the sample be located on the detector plane front. In this case we are forced to analyze the sample in a lower geometry efficiency, suppose in a cylindrical vessel. Naturally, the question of choice the optimum diameter of the beaker in which we prepare the sample arises, so that we have the maximum detection efficiency. Using the same software, we calculated that the detection efficiency of the detector above, considering a sample with mass m = 500 g and a density of 1.4 g/cm 3, for cylindrical geometry with the following

6 The efficiency of gamma-ray spectrometric analysis 1017 diameters: 70, 80, 100, 120, 140, 160, 180 mm. Figure 3 represents the detection efficiency variation depending on the sample diameter, for a few gamma-ray energies. Fig. 3 The detection efficiency as function of the sample cylindrical geometry diameter. From this graphical representation it results that the detection efficiency is maximum for the cylindrical geometry with a diameter of 120-140 mm. 3.2. THE DEPENDENCE OF THE DETECTION EFFICIENCY ON THE SAMPLE HEIGHT We consider the gamma-ray spectrometric analysis of a sample with mass of 200 g, in Sarpagan type box with the following dimensions: plexiglass material, density ρ = 1.2 g/cm 3 ; diameter, D = 70 mm; the bottom beaker thickness, G = 2.09 mm. The initial height of the sample is h 1 = 50 mm and density ρ 1 = 1.04 g/cm 3. Suppose that we can compress the sample by 5 mm steps up to h 10 = 5 mm, density of sample taking the values in the Table 2. Table 2 Densitiy values of the sample compressed at various heights Sample height in Sarpagan vessel [mm] 50 45 40 35 30 25 20 15 10 5 Sample density [g/cm 3 ] 1.04 1.15 1.30 1.48 1.73 2.08 2.60 3.46 5.20 10.4 The calculated values of efficiency at 5 significant energies within the interval 45 kev 1400 kev as function of the sample height is presented in Figure 4.

1018 Laurentiu Done et al. 7 Fig. 4 The detection efficiency at 45, 60, 120, 600 and 1400 kev, depending on the sample height in a Sarpagan beaker. From the graphical representation of Figure 4 we can see that the detection efficiency is better with decreasing the sample height. In fact we have a competitive process, which partially compensates: as more we subtract the sample height, as more the radioactive matrix is closer to the detector (h c decreases), but at the same time, increasing the sample density, the photons attenuation in the radioactive matrix, selfattenuation, increases. The graphical representation demonstrates that, within the studied limits, carrying out the whole radioactive mass near the detector (the sample height loss) leads to higher efficiency growth than the attenuation by self-absorption, which would lead to the efficiency decrease. This means that we can analyze a soil or a sediment sample in Sarpagan beaker (cylindrical) with better efficiency, if by some method we compress the sample into a cylindrical mold. The same exercise for a sample in Marinelli-type vessel leads to similar results regarding the increase of the detection efficiency with the sample height decreasing. However, compressing a sample in the form of a Marinelli beaker is difficult to achieve in practice. 3.3. PEAK NET AREA VARIATION WITH THE ANALYZED SAMPLE MASS As a result of the environmental sample preparation according to the specific procedures, they are volumic ones, homogeneous in terms of the contained radionuclides activity distribution. The question is how much of the prepared sample is subjected to analysis so that the accuracy of the analysis to be as good as possible. This is translated into obtaining a gamma spectrum of the net areas peaks as large as possible. From equation (1) it results that a net peak area increases

8 The efficiency of gamma-ray spectrometric analysis 1019 proportionally to the sample activity. The activity of a homogeneous sample is an additional magnitude in relation to the mass. If the test sample is not subject to the radionuclides concentration by chemical methods, the net area of a peak is proportional to the mass of the sample. It results that, for the analysis accuracy increase, the sample mass must be as large as posible. On the other hand, with the sample mass increase, and implicit its volume, the detection efficiency is changed. Further on, we want to see how the detection efficiency is changed depending on the sample mass. 3.3.1. Sample in Sarpagan beaker Let us suppose that there are two series of ten samples analyzed, a series with density of 1.0 g/cm 3 and another with density of 1.4 g/cm 3, in Sarpagan type box with the following dimensions: the inner box diameter, 70 mm; sidewall thickness, 1 mm; bottom box thickness, 2.09 mm; plexiglass density, 1.2 g/cm 3 ; detector sample distance, 0 mm. Samples with densities of ρ 1 = 1.0 g/cm 3 and ρ 2 = 1.4 g/cm 3 with masses within the interval 25 g 250 g, varying in steps of 25 g. For each set of 10 samples, the detection efficiency for the 10 2000 kev incident photon energy range was calculated; Figures 5 present the detection efficiency, depending on the incident photons energy, for the samples with mass m = 25, 125 and 250 g. Fig. 5 The detection efficiency versus energy, for samples of m = 25 g, 125 g and 250 g, with density of 1.0 g/cm 3, in Sarpagan beaker. From the Figures 5 we find that the detection efficiency decreases with sample mass increase. The same efficiency evolution with the sample mass is also observed for the samples of 1.4 g/cm 3 density. It results that in the relation (1), with the mass increase, the net area on the one hand increases with the sample mass, and on the other hand it decreases due to the detection efficiency decrease. With these

1020 Laurentiu Done et al. 9 two competitional trends, the next obvious question arises: how appropriate is to increase the mass of an analyzed sample to obtain a higher net peak area, so a better statistical analysis. In equation (1), if we neglect the coincidence summation phenomena, the net area of the E peak energy, for the sample mass m 1 = 25 g is given by the relation: n ( ) ( ) ( ) A m =Λ m I t ε ε m (4) 1 1 γ int geo 1 where: Λ(m 1 ) is the sample activity of mass m 1 and ε geo (m 1 ) is the detection geometrical efficiency for the sample m 1. If all the samples of the same density were obtained from a homogeneous radioactive matrix, the ratio between the activity of any two samples is equal to the ratio of these samples masses and the equation (4) written for a some m mass, becomes: ( m) ( m ) m ε geo An ( m) = An ( m1 ) (5) m ε 1 geo 1 If in the relation (5) we consider that A n (m 1 ), m 1 and ε geo (m 1 ) are constant quantities characterizing the sample of mass m 1 = 25 g, then the net area A n (m) of an uncertain mass sample depends only on the following product: ( ) ( ) P m = m ε m (6) For the two samples series with density ρ = 1 g/cm 3 and ρ = 1.4 g/cm 3, the product variations P(m), for a few energy lines is graphically represented in Figures 6 and 7. geo Fig. 6 The P(m) function for energy peaks E = 45, 60, 120, 600 and 1400 kev, sample density ρ = 1 g/cm 3 - Sarpagan beaker.

10 The efficiency of gamma-ray spectrometric analysis 1021 Fig. 7 P(m) function for energy peaks E = 45, 60, 120, 600 and 1400 kev, sample density ρ = 1.4 g/cm 3 - Sarpagan beaker. 3.3.2. Sample in Marinelli beaker 130G type Let us suppose that the same two samples, with densities of 1.0 and 1.4 g/cm 3 are analyzed in Marinelli geometry, 130G type, in contact with the detector. The samples mass (Table 3) was established so that it meets the following conditions: a) the m 1 samples masses, 535 g and respectively 750 g, were chosen so as to fill the beaker to a reasonable analysis height (15 mm on the detector front, mean overall height of 90 mm in Marinelli beaker); b) from one sample to the next, the mass increased so that the sample height rised steadily with 5 mm; c) the beaker size does not allow a total sample height greater than 140 mm. Table 3 The sample masses calculated for various heights of the samples No. Sample height [mm] m (ρ = 1.0 g/cm 3 ) [g] m (ρ = 1.4 g/cm 3 ) [g] 1 90 535 750 2 95 591 829 3 100 648 908 4 105 704 988 5 110 761 1066 6 115 818 1146 7 120 875 1226 8 125 932 1307 9 130 990 1387 10 135 1048 1468 The detection efficiency was calculated for the 10-2000 kev energy range, for all samples. For example, in Figures 8, a) and b), the detection efficiency is graphically represented depending on the photon s energy, for samples no. 1, 5 and

1022 Laurentiu Done et al. 11 10 of each density group. It was observed a decrease of the detection efficiency when the sample mass increases, similar to the samples contained in Sarpagan beaker. a) b) Fig. 8 The detector efficiency depending on the energy for: a) m = 535, 761 and 1048 g, the sample density of 1.0 g/cm3; b) m = 750, 1066 and 1468 g, the sample density of 1.4 g/cm3, in the Marinelli beaker. In Figures 9 and 10, the product P(m) variation described by the equation (6), which characterizes the net peak area evolution depending on the sample mass, for the samples with a density of 1 g/cm3 and 1.4 g/cm3 respectively, analyzed in Marinelli geometry, is graphically presented. In both cases, the Sarpagan and Marinelli - 130G beakers, is observed that with increasing the sample mass, within the limits imposed by the container volume, the net peak area increases, too. It follows that for the samples with a density of 1.0 g/cm3 and 1.4 g/cm3 we get a bigger net peak area, so a better statistical analysis, as that the sample mass is higher. Fig. 9 The P(m) function for energy peaks E = 45, 60, 120, 600 and 1400 kev, sample density ρ = 1.0 g/cm3 Marinelli beaker.

12 The efficiency of gamma-ray spectrometric analysis 1023 Fig. 10 The P(m) function for energy peaks E = 45, 60, 120, 600 and 1400 kev, sample density ρ = 1.4 g/cm 3 Marinelli beaker. The graphical representations show that the net peak area increasing has the tendency of saturation, the trend being increasing with the sample density and the peaks energy decrease. This trend shows, that an increase in sample mass over a certain value to get a better statistics is becoming useless for the purpose. Example: for the sample with density of 1.4 g/cm 3 in Marinelli beaker, the increase of the sample mass over aprox. 990 g, leads to an insignificant increase of the net peak area of 45 kev. 3.4. THE EFFICIENCY UNCERTAINTY CALCULATED BY THE LABSOCS SOFTWARE The technical documentation for validation and verification of the software [3] contains the comparison data between the efficiency calculated with LabSOCS and the efficiency calculated with volumic standard sources (detector with 42% relative efficiency, sources with 1.15 g/cm 3 density, in Marinelli beaker of 1 liter and in cylindrical geometry about 125 ml, placed on the detector). The conclusion of the validation tests for the geometries used in the laboratory, according to [3] is: the standard deviation average is 7.1% for 50 100 kev, 5.5% for 100 400 kev and 4.3% for E>400 kev. It is noticed that at low energies, i.e. 59.5 kev, Am-241, the efficiency calculated by LabSOCS is closer to the efficiency value determined with standard sources in cylindrical geometry, the difference being of 9% against 20%, for Marinelli geometry. At high energies, over 800 kev, i.e. Co-60, Y-88, the tendency is reverse. The final conclusion is that the deviations between the two manners of calculating the efficiencies are larger than two standard deviations (k=2); it means that some other supplementary corrections, such as coincidence summation etc., sould be taken into account.

1024 Laurentiu Done et al. 13 The same type of tests were performed by J.P.Steward and D. Groff, in order to verify the LabSOCS calculated efficiency using volumic standard cylindrical sources, as described in paper [4]. The results are similar with those obtained in the technical validation documentation. 4. CONCLUSIONS From the efficiency calculations performed with the LabSOCS software, by Monte Carlo simulation, for the volumic samples analyzed in contact with the detector, the following conclusions can be drawn: i) the detection efficiency depends on the sample geometrical shape, observing that for the constant mass samples analyzed in Marinelli, cylindrical, cubical and spherical geometries, the detection efficiency is maximum in the case of the Marinelli geometry; ii) the detection efficiency increases with the decreasing of the distance between the sample gravity center and the detector plane surface; iii) the detection efficiency for the samples analyzed in the cylindrical geometry depends on the sample diameter, an optimum sample diameter interval is characteristic for each type of the detector; iv) for the Sarpagan and the Marinelli analysis geometries type, the analysis statistics improves (the peak net area increases) with the sample mass increasing, in the beaker dimensions limits. REFERENCES 1. O. Sima, Efficiency Calculation of Gamma Detectors by Monte Carlo Methods, Enciclopedia of Analytical Chemistry, JohnWilley & Sons, Ltd. (2012). 2. G. Gilmore, Practical Gamma-ray Spectrometry, 2 nd Edition, John Wiley & Sons, Ltd (2008). 3. CANBERRA Industries, Inc.: ISOCS/LabSOCS, Validation & Verification Manual (2002). 4. John P. Stewart (Sequoyah Nuclear Power Plant, Tennessee Valley Authority), David Groff (Canberra Industries, Meriden, CT., USA): LabSOCS vs. SOURCE-BASED GAMMA-RAY DETECTOR EFFICIENCY, COMPARISONS FOR NUCLEAR POWER PLANT GEOMETRIES, 48th Annual Radiobioassay & Radiochemical Measurements Conference, Knoxville, Tennessee (November 2002). 5. A. Luca, B. Neacsu, A. Antohe, M. Sahagia, Calibration of high and low resolution gamma-ray spectrometers, Romanian Reports in Physics, 64, 968 976 (2012). 6. R. Suvaila, O. Sima, Complex Gamma Ray spectra analysis, Romanian Reports in Physics, 63, 975 987 (2011). 7. E. Robu, C. Giovani, Gamma-ray self-attenuation corrections in environmental samples, Romanian Reports in Physics, 61, 295 300 (2009).