QUANTIFICATION OF UNCERTAINTIES IN GAMMA RAY SPECTROMETRIC MEASUREMENTS: A CASE STUDY

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1 Journal of Nuclear and Radiation Physics, Vol. 6, No. 1&, pp QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA SPECTROMETRIC MEASUREMENTS: A CASE STUD W. F. Bakr 1 and.. Ebaid 1 Central Laboratory of Environmental Radioactivity Measurements, National Center for Nuclear Safety and Radiation Control, EAEA, Cairo, Egypt Faculty of Science, Fayoum University, Fayoum, Egypt Rec. 6/1/011 Accept. 13/9/011 The assessment of the radioactive content of any sample implies an evaluation of the uncertainty associated with its determination process. An evaluation of relative standard uncertainty of the gamma detector efficiency, its dependence on other factors in the measurements procedure as well as its contribution to the total relative standard uncertainty has been performed. The calculations are used for the evaluation of uncertainty of the activity concentration of 6 Ra in reference soil samples. Keywords: Gamma Spectrometry, Efficiency Calibration, Total Uncertainty INTRODUCTION A measurement result is complete only when accompanied by a quantitative statement of its uncertainty. The uncertainty is required in order to decide whether the result is adequate for its intended purpose and to ascertain if it is consistent with other similar results [1]. The combined uncertainty should be characterized by the numerical value obtained by applying the usual method for the combination of variances. The combined uncertainty and its components should be expressed in the form of standard deviations []. The estimation of result s uncertainty is the most important issue in analytical techniques especially in the determination of radioactivity in

2 56 W.F. Bakr etal environmental samples in which their activity concentration is mainly low (30Bq/kg in soil sample). The aim of gamma spectrometric analysis for environmental samples is to determine the activity of gamma ray emitting radionuclides along with the associated uncertainty of the results. The method of the determination of the activity of natural and anthropogenic gamma emitters in environmental samples by gamma ray spectrometry is illustrated in Fig. (1) Sampling Sample Preparation Energy Calibration Measurements Efficiency Calibration Data Evaluation Reporting of Results Figure 1. Analytical steps for the determination of radioactivity contents in environmental samples. The aim of this work is to analyze the relative standard uncertainty due to the efficiency calibration of hyper pure germanium detector and its related factors and to evaluate its contribution to the total uncertainty of the measured activity concentration in terms of variance. 1- Sources of Uncertainty Identifying the sources of uncertainty in nuclear analytical techniques is an important step for reporting high quality data. The most important sources of uncertainty and the magnitude of their contribution in the case of gamma spectrometry are given in table (1). Other sources of uncertainties including sample geometry,

3 QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA 57 background peak area and net count peak area determination must be taken into consideration. EXPERIMENTAL WORK 1- Relative Efficiency Calibration of Hyper Pure Germanium Detector As the gamma emission is a random process and due to the interaction of gamma rays with the material of the detector, the efficiency of gamma spectrometry is not absolute, so the aim of the efficiency calibration of the system is the determination of a factor corresponding to each gamma line that normalizes their activity concentration to its absolute value. Typically, a standard or reference mixed gamma source with multiple energy transitions, in a similar geometry to the measured samples, should be used to produce an absolute efficiency calibration curve along with the necessary attenuation corrections [3, 4]. These reference materials should be traceable to a well known international reference materials manufacturing organization e.g. NIST and IAEA. However, occasionally these kinds of sources might not be available for every laboratory. As a result, an alternative calibration procedure can be employed, namely relative efficiency calibration. In our case, a relative efficiency calibration for a hyper pure germanium detector (Coaxial, 40% efficiency) was done in two steps in the energy range from kev to kev. First, a relative efficiency curve of the detector was produced using a 6 Ra point source [5], with an activity of 0.1 Ci. The source was counted at two positions from the detector (coaxial and lateral) at 15 cm distance from the top surface of the detector (the same geometry of the measured samples). Most intensive gamma rays of 6 Ra in equilibrium with its daughters have been used. In order to achieve the relative efficiency curve, the relative intensities of the photopeaks corresponding to these gamma ray lines have been experimentally calculated (by dividing the net count of each gamma line by the net count of kev gamma transition). The photopeak relative efficiency was obtained by dividing the calculated relative intensity of the photopeak with energy (E) on the reference relative intensity of the same photopeak, i.e. I ( E) i M R ( E) ( E), (1)

4 58 W. F. Bakr etal where (E) is the relative efficiency at energy (E), I M is the relative intensity measured by the detector for the photopeak with energy (E) and, I R is the reference relative intensity of the same photopeak. Six order polynomial fitting efficiency curve was established between the gamma transitions (gamma energy) versus the calculated relative efficiency of each gamma line. The second step for relative efficiency calibration is the normalization of, the relative efficiency curve of the detector to an absolute efficiency value using the same geometry of the measured sample. This step was done using standard solutions of potassium chloride [6]. KCl has been used as low activity standard source for efficiency calibration of gamma ray spectrometer in measuring large volumes of low specific activity materials [7]. In this study, the normalization was performed using known concentration of KCl for the geometrical configuration as the real sample. Using this concentration and the corresponding counting rate, a normalizing factor for any radionuclide can be calculated relatively to the potassium chloride solution through the following equations: A N, () M AAvog, ln A, (3) M. W t 1/ where A: is the specific activity of 40 K (Bq/kg) M: is the mass of 40 K (kg) A avog. : is the Avogadro no. (6.05 x 10 3 mol -1 ) M.W: is the molecular weight of KCl T 1/ : is the half life of 40 K in seconds % 40 K: is the relative abundance of 40 K in KCl From equation (3), the normalizing factor of 40 K can be calculated as: 40 M *16.38 N. F.( K) * t, (4) N K where, N K the net count under the peak area at kev gamma line of 40 K in the standard solution and, t: the real counting time The normalizing factor for each gamma line can be calculated as: R. E. (1460 kev ) B. R 40 ( K ) N. F N. F, (5) 40 ( K ) R. E B. R

5 QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA 59 where, N.F is the normalizing factor of gamma line corresponding to the peak energy of () radiounclide, R.E. (1460) is the relative efficiency of the gamma line 40 K, R.E. () is the relative efficiency of gamma line corresponding to the peak energy of () radiounclide, B.R ( 40 K) is the emission probability of the gamma line corresponding to the peak energy of 40 K, B.R.() is the emission probability of the gamma line corresponding to the peak energy of () radionuclide,and N.F. ( 40 K) is the normalizing factor of 40 K. - Activity Calculations According to our procedure for efficiency calibration of hyper pure germanium detector, the activity concentration for any radionuclide (i) is determined through the equation [8] 1 A i *( N s ) B. R. * t * M, (6) where, A : is the activity concentration of radionuclide (i) (Bq/kg) B.R. : the emission probability of the gamma line corresponding to the peak energy () of the radionuclide (i) η : the spectrometer's efficiency corresponding to the peak energy () at the specific geometry, N s : the net count under the peak area of the selected gamma line for the measured sample t: the real counting time M: the mass of the sample (kg) Equation (6), can be written as: N. F. N s Ai, (7) M * t where, N.F. is the calculated normalizing factor for () gamma line; determined experimentally from the efficiency calibration procedure of the system. 3- Uncertainty calculation The combined standard uncertainty, u c (y), of the quantity of interest (the measured, y) could be derived by applying the propagation of error law of Gauss []. The combined standard uncertainty of the measurement result y is the square root of the estimated combined variances u c (y).

6 60 W. F. Bakr etal n u y) ( u( ), (8) c x i i1 For multiplicative function of x 1, x, x n, the following equation is used to determine the relative combined standard uncertainty n u n ( y) u( x i ), (9) y i1 xi The error associated with any particular counting result is determined by the use of the following equation [9]. N N r, (10) t t t where r : is the net count rate In this case we are interested in subtracting one count from another (gross counts minus background counts) and determining the resulting % error of the (net count per second) ncps based on the standard deviation value. Counting instruments typically have a confidence interval of 95%. Thus equation (10) is written as:- r r 0 s n, (11) t0 ts where, r 0, r s : are the net count rate at the gamma line () for the background and the sample respectively, t o,t s : are the real counting time of the background and the sample respectively. Following [10] of the measurement, standard uncertainty of the activity concentration is calculated by propagation of the relative standard uncertainties in the magnitudes, which appears in the equation used for its determination. From equation (7&11) the relative standard uncertainty of the activity concentration of the radionuclides in the sample can be determined as: u rel rel rel N u ( M ) ( A) u ( N. F ) u, (1) 1 ro rs urel ( A) urelu ( N. F. ) * u ( M ) rel ( rs ro ) to t, (13) s In the above equation,, the terms on the right-hand side are the relative standard uncertainty of the determined normalizing factor for each gamma line (), the relative s rel

7 QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA 61 standard uncertainty of the sample net count rate at the same gamma line, and the relative standard uncertainty of the sample density respectively. Applying equations (4&5), the relative standard uncertainty due to the calculated normalizing factor can be determined as: 1 rok rk u rel rel ( N. F. ) urel ( BR. 40K ) urel ( BR.. ) u ( Mkcl) *, (14) ( rk rok ) t0 ts where the terms on the right-hand side of the equation are the relative standard uncertainty of the photon emission probability of kev gamma line of 40 K [11], the relative standard uncertainty of photon emission probability of the selected gamma line, the relative standard uncertainty of the weight of KCl, and the relative standard uncertainty of the net count rate at kev gamma line of 40 K, respectively In this work, the calculation of the relative standard uncertainties due to detector efficiency and other sources of uncertainties were applied to the determination of 6 Ra activity concentration in contaminated reference NORM sample prepared by the Syrian Atomic Energy [1] (with higher activity contents). The evaluation of the percent contribution of each uncertainty components to the total combined uncertainty was carried out. The gamma-ray spectrometric measurements were carried out using a hyper pure germanium detector of planner configuration CANBERA model GC5019, with relative efficiency 40% and resolution 1.95 kev (FWHM) at 1.33 MeV Co-60 gamma line. The gamma energy transitions of 95. kev (19.4%) and kev (37.1%) of 14 Pb and kev (46.1%) and kev (15.0%) of 14 Bi was used for 6 Ra determination. RESULTS AND DISCUSSIONS The certified activity concentration of 6 Ra daughters in the selected NORM sample (M=0.7 kg) are represented as 979 ± 333 Bq/kg for 14 Pb, 955 ± 417 Bq/kg for 14 Bi and 955 ± 558 Bq/kg for 6 Ra. The calculated activity concentration and its related standard uncertainty with 95% confidence level of the selected sample were 9430 ± 95 Bq/kg for 14 Pb and 97 ± 304 Bq/kg for 14 Bi. The results of the calculated relative standard uncertainties due to counting of KCl standard solution are given in table (). While table (3) and figure () present the percent contribution of relative standard uncertainty of each elements on the total uncertainty of the calculated normalizing factor.

8 6 W. F. Bakr etal Table (4) and figure (3) present the percent contribution of relative standard uncertainty of each element to the total uncertainty of the activity calculation. To evaluate the effect of counting statistics on the total uncertainty, different IAEA reference samples with different activity concentration contents of 6 Ra were counted and the percent contribution of the net counts to the activity standard uncertainty was represented. The activity concentration of 6 Ra in the selected samples is illustrated in table (5). Figure (4) illustrates the percent contribution of relative uncertainty of net count to the activity uncertainty of each sample. Table 1. Sources of uncertainty in gamma ray measurements. Uncertainty source Symbol Typical uncertainty value % Sample weight M <0.5 Detector efficiency.0 Counting statistics N 5.0 Half- life Emission probability Coincidences correction Attenuation correction T 1/ B.R. <.0 K c K a <0. <3.0 <1.0 Table. The calculated relative standard uncertainties due to KCl standard solution (Normalizing Factor of keV for 40 K). Term uncertainty Relative standard uncertainty value, u rel Mass 6.E-04 Net count rate Volume Total uncertainty combined 1.58E E %

9 QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA 63 Table 3. The percent contribution of relative standard uncertainty (U rel) of different elements on the calculated normalizing factors uncertainty Energy (kev) Percent contribution of different elements on the calculated normalizing factors % B.R.( 40 K) B.R. () Wt (KCl) Net Count of 40 K Table 4. The percent contribution of different elements on the calculated activity. Energy (kev) Percent contribution of different elements on the calculated activities N.F. Wt of Sample Net Count of Sample E E E E Table 5. The activity concentration of 6 Ra in the selected reference samples. Sample code 6 Ra activity (Bq/kg) Density kg/l IAEA IAEA IAEA-A IAEA

10 64 W. F. Bakr etal Figure. The percent contribution of relative standard uncertainty of different elements on the calculated normalizing factor Figure 3. The percent contribution of the relative standard uncertainty of different elements on the calculated activity standard uncertainty ( NORM sample)

11 QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA 65 Figure 4. The percent contribution of U rel (net count) to the U rel(a) As seen from the results of the calculation it is shown that; the percent contribution of the standard uncertainty due to emission probability of 40 K has a great contribution on the calculated normalizing factor uncertainty, its value ranged from 3.7% for gamma energy kev to 87.0% for kev gamma line. It is a small variation in the percent contribution of KCl mass and it ranged from.7% to 3.6%. No significant variation in the contribution of counting statistic of KCl on the gamma energies of 6 Ra daughter and it ranged from 7.0% to 9.3% for 1460 kev gamma line. For the calculated standard uncertainty due to the activity calculation, the main contributors are the uncertainty due to the normalizing factor and the net counting statistics. The effect of uncertainty due to the mass of the samples is very low which is neglected. Due to the measuring of different samples with different activity concentrations and different masses, it is shown that the counting statistics effects on the total uncertainty due to the activity calculation ranged from 5.6 % for NORM sample to

12 66 W. F. Bakr etal 18.7 % for IAEA-1 sample. M. Herranz,,et al [13] found that, the contribution of counting statistics ranged from 0.3% to 8.0% in the determination of beta, gross alpha and alpha emitters determination. CONCLUSION The estimation of results uncertainty is the most important issue in analytical techniques especially in the determination of radioactivity in environmental samples in which their activity concentration is mainly low. Depending on the calibration procedure for gamma spectrometry discussed in this article, we can conclude that:- As the identical geometry for calibration and the measured sample with suitable distance from the detector was satisfied, the principal uncertainties are resulted from the uncertainty in the radiation intensity, the detector efficiency (calculated normalizing factor) and counting statistic. The conclusions derived from this work should only be applied to the measurement conditions considered in this work, that is, for different conditions, each laboratory should validate their own approximations, as done in this work. REFERENCES [1] IAEA TECDOC-1401, Quantifying Uncertainty in Nuclear Analytical Measurements, International Atomic Energy Authority, July (004). [] NIST Reference on Constants, Units, and Uncertainty, Physics.nist.gov/cuu/Uncertainty/basic.html [3] Khater, A. E. M. and Ebaid,.. "A Simplified Gamma-ray Selfattenuation Correction in Bulk Samples " Applied Radiation and Isotopes , (008). [4] Ebaid,.. "On the Use of Reference Materials in Gamma Ray Spectrometric Efficiency Calibration for Environmental Samples" Journal of Radioanalytical and Nuclear Chemistry Vol 80, No.1, 1-5, (009). [5] Farouk, M.A. and Souraya, A.M., Ra-6 as a Standard Source for Efficiency Calibration of Ge(Li) Detectors, Nuclear Instruments and Methods, (198). [6] El-Tahawy, M.S., Farouk, M.A., Hammad, F.H. and Ibrahiem., N.M., Natural Potassium as a Standard Source for the Absolute Efficiency Calibration of Ge Detectors, Nucl. Sci. J., (199).

13 QUANTIFICATION OF UNCERTAINTIES IN GAMMA RA 67 [7] International Commission on Radiation Units and Measurements, Measurement of Low Level Radioactivity, ICRU Report No., (1979). [8] N.N. Jibiri and H.U. Emelue (008), Soil Radionuclide Concentrations and Radiological Assessment in and Around a Refining and Petrochemical Company in Warri, Niger Delta, Nigeria, J. Radiol.Prot. 8(008) [9] Cember, H., Introduction to Health Physics, New ork: McGraw-Hill, Third Edition, (1996). [10] Guide to the Expression of Uncertainty in Measurement [GUM], ISO, Geneva, ISBN , (1995). [11] IAEA- X- Ray and Gamma Ray Decay Data Standards for Detector Calibration and other Applications, Volume 1, Recommended Decay Data High Energy Gamma Ray Standards and Angular Correlation Coefficient, IAEA, (007). [1] Al-Masri M.S., A. Aba., A proficiency Test for Some Laboratories in Arabic Countries for Determination of Naturally Occurring Radioactive Materials Contaminated Soil Reference Sample with Produced Water in Oil Field, AECS- PR/RSS 693 (006). [13] Herranz, M., R. Idoeta, F. Legarda "Evaluation of uncertainty and detection limits in radioactivity measurements" Nuclear Instruments and Methods in Physics Research A, , (008). التقدير الكمى لنسب الا رتياب لقياسات الجاما : دراسة حالة إن تقدیر المحتوى الا شعاعى فى أى عینة بیي یة یجب أن یرتبط بتقدیر نسب الا رتیاب المرتبطة بعملیة القیاس. فى ھذه الدراسة تم تقییم نسب الا رتیاب الناتجة من تعیین الكفاءة النسبیة لجھاز الجرمانیوم عالى النقاوة إلى جانب كافة العوامل المو ثرة فى عملیة القیاس ودراسة نسب تا ثیر كل ھذه العوامل على تركیز النشاط الا شعاعى للعینات. تم تطبیق طریقة التقییم ھذه على عینات مرجعیة من الوكالة الدولیة للطاقة الذریة.