An Analytical Approach for Activity Determination of Extended Gas Ampoule Sources

Transcription

1 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt An Analytical Approach for Activity Determination of Extended Gas Ampoule ources herif. Nafee and Mahmoud I. Abbas Physics department, Faculty of cience, Alexandria University, Alexandria, Egypt mabbas@physicist.net ABTRACT The National Institute of tandards and Technology (NIT, Gaithersburg, MD 878, UA) uses different extended sources, such as ampoule sources filled with mixed noble gases ( 33 Xe and 85 Kr) to calibrate the detection systems in the nuclear power plants. Those noble gases are produced from the fission of the uranium and plutonium in the nuclear reactors. Accurate activity determination is needed for those radioactive sources to be used in the calibration process. A straight forward theoretical approach is presented here to determine the activity of the gas ampoule sources using the (NIT) hyper pure germanium (HPGe) cylindrical detectors. The validity of the present approach is tested through extensive comparisons with the activity values carried out in the (NIT). The calculated activities show discrepancies less than.5 % and less than % from the measured ones using the NIT gas counting system for the 33 Xe and 85 Kr, respectively. The comparisons indicate that the present analytical approach provides a useful methodology for traceability of radioactivity measurements to the fissionable radioactive sources and nuclear power facilities. Keywords: Ampoule sources; HPGe detector; Nuclear power facilities; Radioactivity measurements INTRODUCTION The use of extended sources in γ-ray spectrometry improves the sensitivity of detection, thus enabling the measurement of low-activity samples. To obtain reliable measurements of radionuclide activity, the knowledge of the detector absolute photopeak (full-energy peak) efficiency is required (). There is no universal method for the efficiency calibration of HPGe detectors; this is mainly because of two major factors, the extended dimensions and the self absorption of the source (). The most accurate method to determine the efficiency for the germanium crystal γ-ray spectrometer is the experimental method, where there is no need to make approximations. However, it is often require extensive and delicate laboratory work, both in terms of source preparation and measuring time (3, 4). For activity and impurity measurements of an unknown mixture of 85 Kr and 33 Xe gas sources, a full-energy-peak efficiency curve in the range from 8 kev to 3 kev is required since commonly found impurities for these gas mixtures are 3m Xe (63.9 kev) and 33m Xe

2 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt (35. kev). The calibration of high purity germanium (HPGe) detectors is crucial to determine the activity of these radioactive gamma ray sources in the nuclear power plants. The radioactive sources should be measured at high distances from the (NIT) high purity germanium (HPGe) detectors to have good statistics in the full energy peaks as they have high activities, and for the coincidence correction to be neglected (5). In the present work, we describe the experimental method employed to calibrate the National Institute of tandards and Technology (NIT) HPGe detectors used to determine the source activity of ampoule sources filled with a mixture of 85 Kr and 33 Xe noble gases. Experimental values are compared with those calculated by the present theoretical approach based on the elim and Abbas direct mathematical method that applied successfully before for obtaining the efficiencies of source - detector systems with different geometries (point source (6, 7), disk source (8-), cylindrical source (), Marinelli beaker (), parallelepiped source (3, 4) and NIT gas sphere source (5)). The calculated activities are also compared to those measured by the NIT gas counting system (6). The main contributions to the total uncertainties in the activity measurements for those radionuclides will be discussed in the results and discussion section. EXPERIMENTAL ETUP The absolute full-energy peak efficiency values are carried out for two n-type GMX Ortec HPGe detectors (models 7-P-A-Plus and 85-) of 38 and 8 cm 3 active volumes, with relative efficiencies at.33 MeV equal to 7% and %, labeled by Det. and Det., respectively. chematics from the manufacturers are illustrated in figures.a and.b, respectively, and the setup values are shown in table (). The ampoule is made of.6 ±.4 mm thick Pyrex with an external diameter of 6.5 ±.5 mm and bottom thickness of. ±.5 mm, and is filled with a mixture of 85 Kr and 33 Xe noble gases. The source to detector separations were.5 m and m from Det. and Det., respectively. The activities of the two noble gases are ((4.75 ±.59) 7 Bq) and ((.969 ±.6) 7 Bq), respectively, as measured by NIT gas counting system (6). The detectors were set-up according to the ANI standard (7). chematic diagram for the standard ampoule geometry and the counting arrangement in the measurements is shown in figure. The half-lives, gamma-ray emission probabilities and uncertainties used for the efficiency calibrations, activity and impurity measurements are available in (8) and (9), see table (). Efficiency measurements were generated by counting the source three times with each detector for one-day each to ensure an uncertainty from the statistical component to be less than.5%, and to ensure that each peak in the spectra have a net photopeak area of at least, counts. Measurements are carried out using multichannel analyzers (MCA) to obtain statistically significant main peaks in the spectra that were recorded and processed by IO 9 Genie data acquisition and analysis software made by Canberra (). The peak fitting is performed using a Gaussian shape with low energy tailing for HPGe spectra.

3 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt MATHEMATICAL VIEWPOINT The efficiency of a gamma-ray detector, point, using an isotropic radiating non-axial point source (see figure 3) is defined as po int = g i, () where g is the geometrical efficiency = Ω / 4π; and Ω is the solid angle subtended by the detector at the source point, and i is the intrinsic efficiency: Ω = φ sin dφ d, () µ.d i = f att ( e ). (3) where µ is the attenuation coefficient of the detector active medium for a gamma-ray photon with energy E γ (). The factor determining the photon attenuation by the source container and the detector end cap materials, f att, is expressed as µ i. δ i i f att = e, (4) where µ i is the attenuation coefficient of the i th absorber for a gamma-ray photon with energy E γ (), and δ i is the average gamma-ray photon path length through the i th absorber. For the full - energy peak efficiency computation, µ is replaced in equation (3) by the peak attenuation coefficient for the detector s material µ p which represents the only part contributing to the fullenergy peak (photoelectric coefficient the fractions of the incoherent and pair production coefficients leading to the full-energy peak). The calculated fractions of the incoherent coefficients are reported by Abbas and elim (), whereas the calculated fractions of the pair production coefficients are reported by elim et al., (3) for cylindrical detector with respect to an axial point source. Finally, d is the average path length traveled by a photon through the detector active volume for an isotropic emission and is given by d = n ( j j Ω = φ Ω d ) dω dω = n ( j= d )sin dφ d j Ω. (5) where d, d,., d n are the photon path lengths traveled through the detector active volume (we will discuss them in details below). For each photon emitted from the point source, the probability of striking the point where the photon actually enters the detector active volume must be known to calculate d and consequently the detection efficiency. To calculate d, there are two main cases to be considered, the striking photon may enter the detector: i- upper face and emerge from its base L d =, (6) cos ii- upper face and emerge from its side ρ cosφ R ρ sin φ h d =, (7) sin cos 3

4 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt From equations 5, 6 and 7; d can be rewritten as d 3 I = π d and ' ( φ sin d π φ d sin Ω = π sin d = π ( cos ) π 4 ' d d sin dφ d sin dφ) d, sin dφ d φ sin d. φ 4 φ 4 d sin dφ d = I / Ω sin dφ d 3 ' ( φ, where, sin ' φ sin dφ) d, with, - R ρ - R ρ - R ρ - R ρ = tan, = tan, 3 = tan, 4 = tan, () h L h h L h - ρ R h tan ' - ρ R ( h L) tan φ = cos, φ = cos, () ρh tan ρ( h L)tan where, R is the detector circular face radius, ρ is the lateral distance of the source (ρ < R) and h is the non-axial point source to detector distance (as shown in figure 3). Homogenizing the core cavity with the other (active) part of the crystal material treats the attenuation of the penetrating gamma rays in the core cavity of the HPGe detector. Hence, the detector active volume consists of the detector crystal only and the density is artificially reduced to account for homogenization. That is (4) / V ' Vcore ρ Ge = ρge () V ' / where ρge and ρge are the original (5.33 g/cm 3 ()) and the corrected (5.869 g/cm 3 for detector Det. and 5.99 g/cm 3 for detector Det.) densities of the detector crystal, respectively. V' and V core are the active zone and the core cavity volumes of the detector, respectively. The gas ampoule source (as shown in figure ) is a volumetric source which can be treated as a cylindrical source of radius and height R s and h s h s '', respectively. Where h s and h s '' are the heights of the lower part of the ampoule of volume V low and the equivalent height of the upper part of the ampoule of volume V up. The ampoule is filled with a noble gas and sealed at some point. Then, the source consists of a group of point sources uniformly distributed; each one has an efficiency point, so that the efficiency of the entire volumetric source is given by dv po int V ampoule =, (3) Vequivalent (8) (9) 4

5 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt where, point is as identified before in equation, V equivalent is the volume of the equivalent cylinder of the ampoule source (=π R s (h s h s '')) and dv is the elementary volume of an element displaced by a lateral distance ρ from the detector axis and makes an angle ψ with the detector major axis. This elementary volume dv can be expressed as (by the use of the Cartesian coordinates system) dv = dx dy dh. (4) In the case of an isotropic radiating volumetric source, not all the emitted photons from its radioactive nuclei exit from the source volume with the same energy and sometimes part of them is absorbed totally in the source itself, affecting the efficiency calculations. The factor concerning this effect is called the self-absorption factor,, which is defined as µ a. t = e, (5) where µ a is the source medium attenuation coefficient, and t is the distance traveled by the photon inside the source material. The only possible path length covered by the photon inside the source medium and will hit the detector's top surface is given by equation 6, where the source detector separation is large; h h t =, (6) cos (The photon will exit from the source base and enters the top surface of the detector) Finally, the efficiency of a closed-end HPGe detector for a gas ampoule source is given by Cyl = h h h R ( h h ) R ο h ο point ρ dρ dα dh where, point, h s, h s '' and R are as identified before in equations and 5, respectively. The numerical evaluation of the double integrals is performed using the trapezoidal rule. A computer program is made to evaluate the efficiency of a cylindrical detector with respect to the previous source at any source-detector separation. Although the accuracy of the integration increases by increasing its intervals number n, the integration converges very well at n =. In this program, we define the source-detector geometry and the source-detector separation. Then the program runs to calculate the full-energy peak attenuation coefficient at a given energy, the self attenuation factor and then the efficiency. REULT AND DICUION The full energy peak efficiencies are calculated using the present approach and compared to the measured ones, (E), for the two HPGe detectors which are obtained from the following equation = N( E) ( E) C, (8) T A P( E) i s (7) 5

6 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt where, N(E) is the number of counts in the full-energy peak, T is the measuring time (in seconds), P(E) is the gamma-ray emission probability at energy E, C i are correction factors and A s is the activity of the source. The decay correction from the calibration source reference time to the middle of the run time C d is given by λ. T C d = e, (9) where λ is the decay constant and T is the time interval over which the source decays, corresponding to the run (or real) time. During measurements, count rates were kept lower than 8 counts per second to avoid pulse pile-up effects. The uncertainty of the full-energy-peak efficiency is obtained using uncertainty propagation and assuming that all measured quantities are independent. The uncertainty for the full-energy peak efficiency is given by σ = σ N σt σ A σ P σ λ, () N T A P λ where σ N, σ T, σ A, σ P, σ λ, are the uncertainties associated with the quantities N(E), T, A, P(E), λ, respectively, assuming that the only correction made is due to source decay. If other corrections are included in the efficiency calculation, their associated uncertainties are to be added in quadrate with the other uncertainty components. Due to the repetition of the measurement, the uncertainty in the full-energy peak efficiency, σ, is combined with the statistical component to obtain the combined standard uncertainty as [5] u = ( i ) ( ) i σ, (3) n n where the second term under the radical is the standard deviation of the mean where n is the number of measurements of the full-energy-peak efficiency and is the efficiency mean, and σ is given by equation. Note that all uncertainty values are given with a coverage factor k =. For the two radionuclides of interest ( 85 Kr and 33 Xe), the main contributions to the total uncertainty in the activity measurements are the uncertainty in the emission probability and in the efficiency value (5). For 85 Kr the uncertainty in the emission probability is approximately.3 %, in the efficiency is.4 %, in the positioning of the source.4 % and in the peak fitting and sample counting.3 % with a combined uncertainty of approximately.8 % when the smaller components are included. For 33 Xe the uncertainty in the emission probability is approximately.8 %, in the efficiency is.3 %, in the positioning of the source.4 % and in the peak fitting and sample counting. % with a combined uncertainty of approximately.3 % when the other components are included. The relatively high uncertainty contribution in the peak fitting component for 85 Kr is due to the difficulty in deconvoluting the unresolved 54 kev line (5). pectra acquired with Gamma Vision were 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 6

7 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt spreadsheets that were used to perform the calculations necessary to generate the efficiency curves. Table (3) show the comparison between the calculated and the measured full-energy peak efficiency values as a function of the most probable photon energy for 33 Xe and 85 Kr gas ampoule source with the detector and detector, respectively. To investigate the accuracy of our present approach, the discrepancies between the calculated and the measured activities by the (NIT) gas counting system by equation 5 are also listed in table (3) Acalculated Ameasured A % =. (4) Acalculated The theoretical calculation of the full energy peak efficiency, (E), using the present approach leads to a direct evaluation for the activity of the gas ampoule source using equation 8, with discrepancies (.7 % and.8 %) and (.5 % and.77%) for the 33 Xe and 85 Kr gases with respect to Det. and Det., respectively. CONCLUION The analytical calculation of the full- energy peak efficiency of closed- end HPGe detectors in the case of using gas ampoule sources leads to a direct and fast estimation of the activities of 33 Xe and 85 Kr noble gases produced from the fission of uranium and plutonium in the nuclear reactors. This approach is based on the calculation of the average path length covered by an incident photon (consequently, the intrinsic efficiency) and the solid angle (consequently, the geometrical efficiency). The agreement between the calculated and the measured activities is very good. The highest discrepancy is less than % in comparison to the measured ones. The direct mathematical method can be used as a simple, fast and cheap method to calibrate the gamma ray detection systems in the nuclear power plants. ACKNOWLEDGEMENT The authors would like to thank the Authorities of the National Institute of tandards and Technology (NIT), Gaithersburg, MD 878, UA, for the allowing of carrying out the experimental measurements. FIGURE CAPTION Figure : chematic diagram of the (NIT) HPGe detectors: a- Det. and b- Det. used in these measurements. Figure : A chematic diagram for the counting arrangement in the measurements. Figure 3: chematic diagram of the non-axial point source to detector system. Table : The setup parameters for the NIT HPGe detectors, Det. and Det.. Table : The half-lives, gamma-ray emission probabilities and uncertainties used for the efficiency calibrations for 33 Xe and 85 Kr. 7

8 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt Table 3: The calculated, the measured full energy peak efficiencies, calculated, measured, the calculated, the measured activities for the 33 Xe and 85 Kr noble gases measured by the NIT gas counting system [5, 6], A calculated, A measured, and the discrepancies in the activities. REFERENCE () M. J. Daza, B. Quintana, M. García-Talavera, and F. Fernández, Nucl. Instr. and Meth.; A47, 5 (). () K. Debertin, and R. G. Helmer, Gamma- and X-ray pectrometry with emiconductor Detectors, Elsevier, North-Holland, Amsterdam, 988. (3) F. El-Daoushy, and R. Garcia-Tenorio, Nucl. Instr. and Meth.; A356, 376 (995). (4) O. ima, Nucl. Instr. and Meth.; A45, 98 (). (5) L. Pibida,.. Nafee, M. Unterweger, M. M. Hammond, L. Karam, and M. I. Abbas, Appl. Radiat. Isot.; 65, 5 (7). (6) Y.. elim, and M. I. Abbas, Radiat. Phys. Chem.; 44, (994). (7) Y.. elim, and M. I. Abbas, Radiat. Phys. Chem.; 48(), 3 (996). (8) Y.. elim, and M. I. Abbas, Radiat. Phys. Chem.; 58, 5 (). (9) M. I. Abbas, Y.. elim, and M. Bassiouni, Radiat. Phys and Chem.; 6, 43 (). () M. I. Abbas, Nucl. Instr. and Meth.; B56, 554 (7). () M. I. Abbas,.. Nafee, and Y.. elim, Appl. Radiat. Isot.; 64, 57 (6). () M. I. Abbas, Appl. Radiat. Isot.; 54, 76 (). (3) M. I. Abbas,.. Nafee, L. R. Karam, and Y.. elim, Transactions of the American Nuclear ociety; 94, 35 (6). (4).. Nafee, and M. I. Abbas, Nucl. Instr. and Meth.; A59 (-), 8 (8). (5) M. I. Abbas,.. Nafee, and Y.. elim, Egypt. J. of Phys.; 38, (6). (6) B. M. Coursey, J. M. R. Hutchinson, and M.P. Unterweger, Int. J. Appl. Radiat. Isot.; 8, 55 (977). (7) ANI N4, American National tandards for Calibration and Use of germanium pectrometers for Measurements of Gamma-ray Emission Rates of Radionuclides, [8]ENDF Nuclear Data heets, ( ( (9) IAEA NuclearData, ( ( () Canberra Industries web page, ( () J. H. Hubbell, and. M. eltzer, NITIR, UA; 563 (995). () M. I. Abbas, and Y.. elim, Egypt J. Phys.;, 5 (). (3) Y.. elim, M. A. Abdelzaher, M. A. El-Katib, and M. Bassiouny, Radiat. Phys. Chem.; 76, (7). (4) G. Haase, D. Tait, and A. Wiechen, Nucl. Instr. and Meth.; A39, 483 (993). (5) L. Pibida, E. Hsieh, A. Fuentes-Figueroa, M. M. Hammond, and L. R. Karam, Appl. Radiat. Isot.; 64, 33 (6). 8

9 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt Table etup Values amplifier MCA ADC Detector Label Det. Table Radionuclide Table 3 Det. Det. 85 Kr 33 Xe U. High rate Amp 973U Fine Gain:.5 Course Gain: Integrate Time: 3 µs Input: neg. Voltage Bias: -4, V haping Time: 3 µs Det. AFT Amp 5 Fine Gain: 8 Course Gain: Integrate Time: 4 µs Input: normal Voltage Bias: -3,3 V haping Time: 4 µs Radionuclid e (Energy) 85 Kr (54.67) 33 Xe (8.997) 85 Kr (54.67) 33 Xe (8.997) Half life, T /.756 years 5.43 days calculated Uncertainty of T /.8 years. days.53e-5 4.7E-5.635E-4.8E-4 measured.68e-5 5.4E-5.74E-4.98E-4 Energy, E (kev) PTRU-3 pectrum Master 99 Uncertainty of E (kev) Energy range: kev Channels: 89 Energy range: kev Channels: 6 Emission probability (P(E)) Uncertainty of P(E) A calculated (Bq) 4.64E7.787E E7.964E7 A measured (Bq) (5, 6) A measured (Bq) Corrected by gamma detection system A % 4.75E E E7 4.9E E7 4.7E E7 5.57E6.8 9

10 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt K L O M BAIC DETECTOR DIMENION Identifier Description Dimension (mm) M Detector diameter 7.4 K Detector length 86.4 J Detector end radius 8, nominal L Hole depth 79.3 O Hole diameter.6 MICELLANEOU DETECTOR AEMBLY DIMENION AND MATERIAL Identifier Description Dimension Material A Mount cap length 3 mm Aluminum B End cap to crystal gap 4 mm N.A. C Mount cup base 3. mm Aluminum D End cap window. mm Aluminum E Insulator/shield.5 mm Aluminized Mylar F Outside contact layer.3 Micron Boron G Hole contact layer 7 Micron Lithium H Mount cup wall.76 mm Aluminum I End cap wall. mm Aluminum HIELDING mm thick Lead Bricks 3.75 mm thick Cadmium.5 mm Copper sheet Figure.a: 3

11 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt K L O M BAIC DETECTOR DIMENION Identifier Description Dimension (mm) M Detector diameter 54.9 K Detector length 54. J Detector end radius 8, nominal L Hole depth 47. O Hole diameter MICELLANEOU DETECTOR AEMBLY DIMENION AND MATERIAL Identifier Description Dimension Material A Mount cap length 94 mm Copper B End cap to crystal gap 3 mm N.A. C Mount cup base 3. mm Copper D End cap window.5 mm Beryllium E Insulator/shield.5 mm Aluminized Mylar F Outside contact layer.3 Micron Boron G Hole contact layer Micron Lithium H Mount cup wall.76 mm Copper I End cap wall.3 mm Magnesium HIELDING mm thick Lead Bricks 3.75 mm thick Cadmium.5 mm Copper sheet Figure.b: 3

12 IX Radiation Physics & Protection Conference, 5-9 November 8, Nasr City - Cairo, Egypt Ampoule contains 33 Xe External diameter R s of 88 ±.5 h Diameter R' s of 6.7 ±.5 mm h s =37± mm Plastic holder mm Thickness Holder frame of hihh HPGe cylindrical d Figure : Figure 3: 3