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HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for cylindrical sources using compact analytical expressions
Radiation Physics and Chemistry 61 (2001) 429–431
HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for cylindrical sources using compact analytical expressions Mahmoud I. Abbasa,*, Younis S. Selima, M. Bassiounib a
Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt b Arab Academy for Science and Technology, Alexandria, Egypt
Abstract Total and full-energy peak efficiencies, coincidence correction factors and the source self-absorption of a p-type coaxial HPGe detector for cylindrical sources have been calculated using direct analytical expressions. In the experiments gamma aqueous sources containing several radionuclides covering the energy range from 60 to 1836 keV were used. By comparison, the theoretical and experimental full-energy peak efficiency values are in good agreement. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Photopeak efficiency; Cylindrical sources; HPGe detectors
1. Introduction In the field of activity measurement by means of gamma-ray spectrometry, the detection efficiencies, coincidence correction factors (which occur with radionuclides emitting more than one photon per decay) and the source self-absorption have been treated by several authors; Debertin and Grosswendt (1982), Wang et al. (1997), Selim et al. (1998), Selim and Abbas (2000) and Abbas (2001). For a given peak, the apparent full-energy peak efficiency (uncorrected for coincidence effects) must be multiplied by the coincidence correction factor C to get the true full-energy peak efficiency, Abbas (2001). For point sources, the detection efficiency is measurable without any difficulty. For extended sources, particularly for large volume sources close to the detector, the situation is difficult because to evaluate the correction factors it is necessary to know the spatial dependence of the detector efficiencies within the detector volume. The principle of this approach is described in a previous *Corresponding author. Tel.: +20-12-4445-131; fax:+2033911-794. E-mail address: [email protected] (M.I. Abbas).
work for Marinelli beaker sources, Abbas (2001). In the present work we applied it for another source detector geometrical configuration. In addition, the attenuation within the source volume (self-absorption) and by any other material between the source and the detector active volume will be taken into account.
2. Theoretical treatments 2.1. The efficiency determination The efficiency of a cylindrical detector, with radius R and height L, arising from a cylindrical source, with radius S ðSoRÞ and height H (see Fig. 1), is given by eC ¼
2 H S2
Z
h0 þH
Z
S
eðrpR; hÞr dr dh: h0
ð1Þ
0
The mathematical derivation of the efficiency eðrpR; hÞ is given in detail in a previous work, Selim et al. (1998). r and h are the lateral and source to detector distances, respectively.
0969-806X/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 1 ) 0 0 2 8 8 - 2
430
M.I. Abbas et al. / Radiation Physics and Chemistry 61 (2001) 429–431
Fig. 2. Simple decay scheme.
2.3. The self-absorption Fig. 1. Source detector configuration.
The attenuation of the photons by the source itself (self-absorption) or by any other material between the source and the detector active volume is indicated by ! X fatt ¼ exp @ mj dj ; ð5Þ
2.2. Coincidence effect corrections
j
The correction factor Ca of the full-energy peak for the photon ‘‘a’’ (see Fig. 2) for a cylindrical source with activity homogeneously distributed will be R h0 þH R S c epa r dr dh Ca ¼ R h0 þHh0R S 0 : c c ð2Þ h0 0 epa ð1@eTb Þr dr dh
where mj is the attenuation coefficient of the jth absorber for gamma-ray energy Eg , Hubbell and Seltzer (1995), and dj the path length of the gamma photon through the jth absorber. For the given cylindrical source and photon energy, the self-absorption is a function of the photon path length dS in the source medium. The photon path length dS is given by dS ¼
In addition, we have another two correction factors Cb and Cc for the photons ‘‘b’’ and ‘‘c’’, respectively R h0 þH R S c 0 epb r dr dh Cb ¼ R h0 þH R S h0 ; ð3Þ c c h0 0 epb ð1@Pga =Pgb eTa Þr dr dh R h0 þH R S Cc ¼ R h0 þH R S h0
0
h0
0
ecpc r dr dh
; ðecpc þ Pga =Pgc ecpa ecpb Þr dr dh
ð4Þ
where ecT and ecp are the total and full-energy peak efficiencies, respectively andPg is the photon emission probability, Abbas (2001).
h@h0 : cos W
ð6Þ
3. The experiment The full-energy peak efficiencies of a p-type coaxial HPGe detector (2R ¼ 6:99 cm and L ¼ 8:97 cm) for mixed radionuclides aqueous solutions, with volumes 10, 50, 100, 200 and 500 ml, placed in a cylindrical beaker (2S ¼ 6:96 cm) were measured. The active volume end is facing a 0.1 cm thick aluminum window of the detector housing at a distance of 0.4 cm. The cylinder is placed in contact with the detector endcap window. The correction factors of radionuclides 60Co
M.I. Abbas et al. / Radiation Physics and Chemistry 61 (2001) 429–431
431
correction and the source self-absorption have been introduced in the case of a coaxial HPGe detector and cylindrical sources.
Acknowledgements One of us, M. Abbas, would like to thank the Authorities of the Center for Ionizing Radiation Metrology, National Physical Laboratory (NPL), UK, for making it possible to carry out the measurements.
References Fig. 3. True full-energy peak efficiency curves: symbols represent experimental data, solid lines are the calculated values.
and 88Y were calculated using the present equations and have been taken into account to get the true full-energy peak efficiencies.
4. Results Fig. 3 shows the calculated and measured photopeak efficiencies of a HPGe detector using radionuclides aqueous sources placed in a cylindrical beaker, it can be clearly seen that there is a good agreement between the measured and the calculated values.
5. Conclusions In this paper, direct mathematical expressions to calculate the photopeak efficiency, the coincidence
Abbas, M.I., 2001. HPGe detector photopeak efficiencyyfor Marinelli beaker sources using compact analytical expressions. Appl. Radiat. Isotopes 54, 761–768. Debertin, K., Grosswendt, B., 1982. Efficiency calibration of semiconductor detectors byyM.C. calculations. Nucl. Instrum. Meth. 203, 343–352. Hubbell, J.H., Seltzer, S.M., 1995. Tables of X-ray mass attenuation coefficients and mass energy absorption coefficients 1 keV to 20 MeV for elements Z=1 to 92 and 48 additional substances of dosimetric interest. NISTIR-5632, USA. Selim, Y.S., Abbas, M.I., 2000. Analytical calculations of gamma scintillators efficiencies II: total efficiency for wide coaxial disk sources. Radiat. Phys. Chem. 58, 15–19. Selim, Y.S., Abbas, M.I., Fawzy, M.A., 1998. Analytical calculation of the efficiencies of gamma scintillators I: total efficiency for coaxial disk sources. Radiat. Phys. Chem. 53, 589–592. Wang, T.K., Ying, T.H., Mar, W.Y., Tseng, C.L., Liao, C.H., Wang, M.Y, 1997. HPGe detector true coincidence correction fory. Nucl. Instrum. Meth. A 376, 192–202.
HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for cylindrical sources using compact analytical expressions Mahmoud I. Abbasa,*, Younis S. Selima, M. Bassiounib a
Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt b Arab Academy for Science and Technology, Alexandria, Egypt
Abstract Total and full-energy peak efficiencies, coincidence correction factors and the source self-absorption of a p-type coaxial HPGe detector for cylindrical sources have been calculated using direct analytical expressions. In the experiments gamma aqueous sources containing several radionuclides covering the energy range from 60 to 1836 keV were used. By comparison, the theoretical and experimental full-energy peak efficiency values are in good agreement. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Photopeak efficiency; Cylindrical sources; HPGe detectors
1. Introduction In the field of activity measurement by means of gamma-ray spectrometry, the detection efficiencies, coincidence correction factors (which occur with radionuclides emitting more than one photon per decay) and the source self-absorption have been treated by several authors; Debertin and Grosswendt (1982), Wang et al. (1997), Selim et al. (1998), Selim and Abbas (2000) and Abbas (2001). For a given peak, the apparent full-energy peak efficiency (uncorrected for coincidence effects) must be multiplied by the coincidence correction factor C to get the true full-energy peak efficiency, Abbas (2001). For point sources, the detection efficiency is measurable without any difficulty. For extended sources, particularly for large volume sources close to the detector, the situation is difficult because to evaluate the correction factors it is necessary to know the spatial dependence of the detector efficiencies within the detector volume. The principle of this approach is described in a previous *Corresponding author. Tel.: +20-12-4445-131; fax:+2033911-794. E-mail address: [email protected] (M.I. Abbas).
work for Marinelli beaker sources, Abbas (2001). In the present work we applied it for another source detector geometrical configuration. In addition, the attenuation within the source volume (self-absorption) and by any other material between the source and the detector active volume will be taken into account.
2. Theoretical treatments 2.1. The efficiency determination The efficiency of a cylindrical detector, with radius R and height L, arising from a cylindrical source, with radius S ðSoRÞ and height H (see Fig. 1), is given by eC ¼
2 H S2
Z
h0 þH
Z
S
eðrpR; hÞr dr dh: h0
ð1Þ
0
The mathematical derivation of the efficiency eðrpR; hÞ is given in detail in a previous work, Selim et al. (1998). r and h are the lateral and source to detector distances, respectively.
0969-806X/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 1 ) 0 0 2 8 8 - 2
430
M.I. Abbas et al. / Radiation Physics and Chemistry 61 (2001) 429–431
Fig. 2. Simple decay scheme.
2.3. The self-absorption Fig. 1. Source detector configuration.
The attenuation of the photons by the source itself (self-absorption) or by any other material between the source and the detector active volume is indicated by ! X fatt ¼ exp @ mj dj ; ð5Þ
2.2. Coincidence effect corrections
j
The correction factor Ca of the full-energy peak for the photon ‘‘a’’ (see Fig. 2) for a cylindrical source with activity homogeneously distributed will be R h0 þH R S c epa r dr dh Ca ¼ R h0 þHh0R S 0 : c c ð2Þ h0 0 epa ð1@eTb Þr dr dh
where mj is the attenuation coefficient of the jth absorber for gamma-ray energy Eg , Hubbell and Seltzer (1995), and dj the path length of the gamma photon through the jth absorber. For the given cylindrical source and photon energy, the self-absorption is a function of the photon path length dS in the source medium. The photon path length dS is given by dS ¼
In addition, we have another two correction factors Cb and Cc for the photons ‘‘b’’ and ‘‘c’’, respectively R h0 þH R S c 0 epb r dr dh Cb ¼ R h0 þH R S h0 ; ð3Þ c c h0 0 epb ð1@Pga =Pgb eTa Þr dr dh R h0 þH R S Cc ¼ R h0 þH R S h0
0
h0
0
ecpc r dr dh
; ðecpc þ Pga =Pgc ecpa ecpb Þr dr dh
ð4Þ
where ecT and ecp are the total and full-energy peak efficiencies, respectively andPg is the photon emission probability, Abbas (2001).
h@h0 : cos W
ð6Þ
3. The experiment The full-energy peak efficiencies of a p-type coaxial HPGe detector (2R ¼ 6:99 cm and L ¼ 8:97 cm) for mixed radionuclides aqueous solutions, with volumes 10, 50, 100, 200 and 500 ml, placed in a cylindrical beaker (2S ¼ 6:96 cm) were measured. The active volume end is facing a 0.1 cm thick aluminum window of the detector housing at a distance of 0.4 cm. The cylinder is placed in contact with the detector endcap window. The correction factors of radionuclides 60Co
M.I. Abbas et al. / Radiation Physics and Chemistry 61 (2001) 429–431
431
correction and the source self-absorption have been introduced in the case of a coaxial HPGe detector and cylindrical sources.
Acknowledgements One of us, M. Abbas, would like to thank the Authorities of the Center for Ionizing Radiation Metrology, National Physical Laboratory (NPL), UK, for making it possible to carry out the measurements.
References Fig. 3. True full-energy peak efficiency curves: symbols represent experimental data, solid lines are the calculated values.
and 88Y were calculated using the present equations and have been taken into account to get the true full-energy peak efficiencies.
4. Results Fig. 3 shows the calculated and measured photopeak efficiencies of a HPGe detector using radionuclides aqueous sources placed in a cylindrical beaker, it can be clearly seen that there is a good agreement between the measured and the calculated values.
5. Conclusions In this paper, direct mathematical expressions to calculate the photopeak efficiency, the coincidence
Abbas, M.I., 2001. HPGe detector photopeak efficiencyyfor Marinelli beaker sources using compact analytical expressions. Appl. Radiat. Isotopes 54, 761–768. Debertin, K., Grosswendt, B., 1982. Efficiency calibration of semiconductor detectors byyM.C. calculations. Nucl. Instrum. Meth. 203, 343–352. Hubbell, J.H., Seltzer, S.M., 1995. Tables of X-ray mass attenuation coefficients and mass energy absorption coefficients 1 keV to 20 MeV for elements Z=1 to 92 and 48 additional substances of dosimetric interest. NISTIR-5632, USA. Selim, Y.S., Abbas, M.I., 2000. Analytical calculations of gamma scintillators efficiencies II: total efficiency for wide coaxial disk sources. Radiat. Phys. Chem. 58, 15–19. Selim, Y.S., Abbas, M.I., Fawzy, M.A., 1998. Analytical calculation of the efficiencies of gamma scintillators I: total efficiency for coaxial disk sources. Radiat. Phys. Chem. 53, 589–592. Wang, T.K., Ying, T.H., Mar, W.Y., Tseng, C.L., Liao, C.H., Wang, M.Y, 1997. HPGe detector true coincidence correction fory. Nucl. Instrum. Meth. A 376, 192–202.