- Email: [email protected]
Determination of corrections to true summations of photons for measurements in Marinelli beakers
Applied Radiation and Isotopes 56 (2002) 111–116
Determination of corrections to true summations of photons for measurements in Marinelli beakers Pavel Dryak*, Petr Kovar, Jiri Suran Inspectorate for Ionizing Radiation (CMI-IIR) Department, Czech Metrological Institute, Radiova! 1, 102 00 Prague 10, Czech Republic Accepted 22 August 2001
Abstract This paper describes a method of determination of correction factors for the true summation effect of photons for measurement of activity of radionuclides emitting gamma radiation. The method was tested with Marinelli beakers samples measured with coaxial germanium detectors. The advantage of this method is its simplicity since it is not necessary to determine the curves of total efficiency for each detector. The correction factor for the particular peak is determined by means of a detector index which is calculated from one of the measurements with a calibration standard. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Gamma spectrometry; True summations
1. Introduction
determining the ‘‘detector index’’ for which just one standard is sufficient.
The most common tools for the determination of the activity of radionuclides emitting gamma radiation in loose or liquid materials (e.g. environmental samples or food) are germanium detectors with samples contained in Marinelli beakers. This geometric arrangement is optimal with respect to high detection efficiency but, at the same time, the correction to true summation of photons becomes more important as it can reach as much as several tens per cent. Usually, the values of the correction factors are calculated on the basis of the decay scheme along with the knowledge of the peak and total efficiencies as a function of the energy of photons. This requires a complicated calibration for which at least four, and preferably more, calibration standards have to be used with ‘‘mono-energetic’’ radionuclides. When using this method, the total detection efficiency is assessed by
The most significant effect of true summations is the reduction of the area of the total absorption peak for photons g1 with energy E1 when, simultaneously (i.e. within the time resolution of the spectrometer) to photon g1 ; another photon g2 with energy E2 is also detected. In a simple case, the probability for an energy greater than E1 being deposited in the detector is given by
*Corresponding author. Tel.: +420-2-660-20497; fax: +4202-660-20466. E-mail address: [email protected] (P. Dryak).
S0 ðE1 Þ ¼ SðE1 Þ
2. Description of the effect of true summations of photons
p ¼ Ztot ðE2 Þpðg1 ; g2 Þ;
ð1Þ
where Ztot ðE2 Þ is the total detection efficiency of photons g2 and pðg1 ; g2 Þ is the probability of simultaneous emission of photons g1 and g2 : Therefore, the undistorted peak area, S0 ðE1 Þ; and the measured peak area, SðE1 Þ; are related by
0969-8043/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 1 ) 0 0 1 7 5 - 0
1 ; Kðg1 Þ
ð2Þ
112
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
where the correction factor Kðg1 Þ; by which the measured peak area SðE1 Þ has to be divided, is Kðg1 Þ ¼ 1 Ztot ðE2 Þpðg1 ; g2 Þ:
ð3Þ
For n photons being detected in coincidence, this factor becomes Kðg1 Þ ¼ 1
n X
geometric arrangement and the specifications of the detectors used are given in Table 1.
Ztot ðEi Þpðg1 ; gi Þ:
ð4Þ
i¼2
From relations (3) and (4), we can see that the correction to true summations depends on the value of the total detection efficiency of the coincident photons. In this work, the total detection efficiency is represented by the detector index, ND ; which is determined by measuring a standard source in the form of a Marinelli beaker. For this purpose, a standard for peak efficiency calibration of the particular detector may be used but it must contain either only one radionuclide, or several radionuclides all with similarl long half-lives, e.g. 152Eu and 133Ba.
4. Calculations of correction coefficients for true summations of photons In order to obtain the correction coefficient KðX; EÞ as a function of the detector index ND for the selected radionuclide X at a photon energy E; the total efficiency curve and the probability of true coincidence of photons must have been determined for the tested geometric arrangement. In our case the total detection efficiency was determined by means of standards with 241Am, 57Co, 137 Cs and 60Co in Marinelli beakers of 450, 500 and 1000 cm3 (produced by CMI-IIR). The probabilities of true coincidences were calculated by Monte Carlo simulation and correction factors KðX; EÞ are given below, according to the following notation: Kð60 Co; 1173Þ ¼ 1 1:000Tð1332Þ;
3. Detector index determination In the present work, standards of 152Eu were used for obtaining the ‘‘detector index’’ values. The detector index was determined for each geometric arrangement of Marinelli beakers of 450, 500 and 1000 cm3 volume (produced by CMI-IIR). For Ge(Li) and HPGe coaxial detectors having relative efficiency 12–52% at 1332 keV, the detector indexes were determined according to ND ¼
Tð12; 1900Þ ; AðXÞt
ð5Þ
where Tð12; 1900Þ is the total number of impulses integrated in the 12–1900 keV region, AðXÞ is the activity of the radionuclide X in the standard used and t is the measuring time. The indexes for the above-mentioned
Kð60 Co; 1332Þ ¼ 1 0:998Tð1173Þ; Kð88 Y; 898Þ ¼ 1 1:000Tð1836Þ; Kð88 Y; 1836Þ ¼ 1 0:919Tð898Þ; Kð134 Cs; 604Þ ¼ 1 0:085Tð563Þ 0:868Tð795Þ 0:152Tð569Þ 0:072Tð802Þ 0:033Tð1365Þ; Kð134 Cs; 795Þ ¼ 1 0:994Tð604Þ 0:175Tð569Þ;
Table 1 Detector indexes ND and specification of detectors Det. no. Type
1 2 3 4 5 6
HPGe HPGe HPGe HPGe HPGe Ge(Li)
Manufacturer
CANBERRA CANBERRA CANBERRA ORTEC PGT CANBERRA
Rel. eff.a (%) 12.2 28.4 36.1 52.5 25.7 19.0
FWHMb (keV) 1.8 1.8 2.0 1.8 2.1 2.1
Index
(ND )c
450(Eu)
500(Eu)
1000(Eu)
0.08254 0.1263 0.1478 F 0.1169 0.1080
0.0816 0.1170 0.1353 0.1793 0.09859 0.1032
0.06115 0.09043 0.1052 0.1420 0.07858 0.07841
Size (mm)
47 33 53 60 60 53 Not provided 53 58 51 55
a
Efficiency compared to a 300 300 NaI(Tl) for 1332 keV. Resolution FWHM for 1332 keV. c 450(Eu), 500(Eu), 1000(Eu),... Marinelli 450, 500, 1000 cm3, radionuclide b
152
Eu.
113
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
K(X,E) 1.00
0.99
0.98
0.97
0.96
0.95
0.94 K(88Y,898) K(dRa,609) K(60Co,1173)
0.93
K(88Y,1836) 0.92
K(60Co,1332)
0.91
K(dRa,1120) K(dTh,583) K(134Cs,604)
0.90
K(134Cs,795) 0.89 K(dTh,2614) 0.88
(a)
0.05
0.10
0.15
ND
Fig. 1. (a) Correction coefficients versus detector index for 450 cm3 Marinelli beakers. (b) Correction coefficients versus detector index for 500 cm3 Marinelli beakers. (c) Correction coefficients versus detector index for 1000 cm3 Marinelli beakers.
114
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
K(X,E) 1.00
0.99
0.98
0.97
0.96
0.95
0.94
K(88Y,898)
0.93
K(dRa,609) K(60Co,1173) K(88Y,1836) K(60Co,1332)
0.92
0.91
0.90
K(dRa,1120) K(dTh,583)
0.89
K(134Cs,604)
0.88
K(134Cs,795) K(dTh,2614)
(b)
0.05
0.10 Fig. 1 (continued).
0.15
ND
115
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
K(X,E) 1.00
0.99
0.98
0.97
0.96
0.95
0.94 K(88Y,898) K(dRa,609) K(60Co,1173)
0.93
K(88Y,1836) K(60Co,1332)
0.92
K(dRa,1120) 0.91
K(dTh,583)
0.90
K(134Cs,604) K(134Cs,795)
0.89
K(dTh,2614)
0.88
(c)
0.05
0.10 Fig. 1 (continued).
0.15
ND
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P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
Kðd:226 Ra; 609Þ ¼ 1 0:098Tð768Þ 0:018Tð806Þ
standardized material in 450, 500 and 1000 cm3 Marinelli beakers.
0:070Tð934Þ 0:340Tð1120Þ 0:180Tð1238Þ 0:036Tð1281Þ0:035Tð1401Þ 0:060Tð1408Þ 0:055Tð1509Þ 0:09TðKXÞ; Kðd:226 Ra; 351Þ ¼ 1 0:009Tð487Þ; Kðd:226 Ra; 1120Þ ¼ 1 0:980Tð609Þ 0:016TðKXÞ; Kðd:232 Th; 583Þ ¼ 1 0:997Tð2614Þ 0:075Tð247Þ 0:247Tð511Þ 0:019Tð211Þ 0:060TðKXÞ; Kðd:232 Th; 2614Þ ¼ 1 0:856Tð583Þ 0:118Tð860Þ 0:066Tð277Þ 0:216Tð511Þ 0:016Tð763Þ 0:068TðKXÞ; where TðEÞ is the total efficiency of detection for coinciding photons of energy E ðkeVÞ; d:226 Ra represents the daughter radionuclides of 226Ra and d:232 Th represents the daughter radionuclides of 232Th. Fig. 1 shows the correction factor versus the detector index, which were determined by using a 152Eu
5. Conclusions The method described above is simple and makes it possible, for work places performing just routine measurement, to determine the correction factors of true summations of photons quite easily and quickly. Manufacturers of standards usually have much more extensive possibilities for determining detection efficiencies and correction factors for true summations of photons than users of the standards supplied by them. Therefore, they could use the method given in this contribution to draw curves of correction factors versus the detector index and provide them in appropriate cases (for example, measurement of low-activity samples with high detection efficiency) to their customers together with standards. Relative total uncertainty of correction factors should be better than 10% (K ¼ 2) in the case that the detector index has been determined with a standard in the same geometric arrangement which is used for measuring the samples. Future developments will test the possibilities of use of point standards for the determination of detector indexes.
Determination of corrections to true summations of photons for measurements in Marinelli beakers Pavel Dryak*, Petr Kovar, Jiri Suran Inspectorate for Ionizing Radiation (CMI-IIR) Department, Czech Metrological Institute, Radiova! 1, 102 00 Prague 10, Czech Republic Accepted 22 August 2001
Abstract This paper describes a method of determination of correction factors for the true summation effect of photons for measurement of activity of radionuclides emitting gamma radiation. The method was tested with Marinelli beakers samples measured with coaxial germanium detectors. The advantage of this method is its simplicity since it is not necessary to determine the curves of total efficiency for each detector. The correction factor for the particular peak is determined by means of a detector index which is calculated from one of the measurements with a calibration standard. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Gamma spectrometry; True summations
1. Introduction
determining the ‘‘detector index’’ for which just one standard is sufficient.
The most common tools for the determination of the activity of radionuclides emitting gamma radiation in loose or liquid materials (e.g. environmental samples or food) are germanium detectors with samples contained in Marinelli beakers. This geometric arrangement is optimal with respect to high detection efficiency but, at the same time, the correction to true summation of photons becomes more important as it can reach as much as several tens per cent. Usually, the values of the correction factors are calculated on the basis of the decay scheme along with the knowledge of the peak and total efficiencies as a function of the energy of photons. This requires a complicated calibration for which at least four, and preferably more, calibration standards have to be used with ‘‘mono-energetic’’ radionuclides. When using this method, the total detection efficiency is assessed by
The most significant effect of true summations is the reduction of the area of the total absorption peak for photons g1 with energy E1 when, simultaneously (i.e. within the time resolution of the spectrometer) to photon g1 ; another photon g2 with energy E2 is also detected. In a simple case, the probability for an energy greater than E1 being deposited in the detector is given by
*Corresponding author. Tel.: +420-2-660-20497; fax: +4202-660-20466. E-mail address: [email protected] (P. Dryak).
S0 ðE1 Þ ¼ SðE1 Þ
2. Description of the effect of true summations of photons
p ¼ Ztot ðE2 Þpðg1 ; g2 Þ;
ð1Þ
where Ztot ðE2 Þ is the total detection efficiency of photons g2 and pðg1 ; g2 Þ is the probability of simultaneous emission of photons g1 and g2 : Therefore, the undistorted peak area, S0 ðE1 Þ; and the measured peak area, SðE1 Þ; are related by
0969-8043/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 1 ) 0 0 1 7 5 - 0
1 ; Kðg1 Þ
ð2Þ
112
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
where the correction factor Kðg1 Þ; by which the measured peak area SðE1 Þ has to be divided, is Kðg1 Þ ¼ 1 Ztot ðE2 Þpðg1 ; g2 Þ:
ð3Þ
For n photons being detected in coincidence, this factor becomes Kðg1 Þ ¼ 1
n X
geometric arrangement and the specifications of the detectors used are given in Table 1.
Ztot ðEi Þpðg1 ; gi Þ:
ð4Þ
i¼2
From relations (3) and (4), we can see that the correction to true summations depends on the value of the total detection efficiency of the coincident photons. In this work, the total detection efficiency is represented by the detector index, ND ; which is determined by measuring a standard source in the form of a Marinelli beaker. For this purpose, a standard for peak efficiency calibration of the particular detector may be used but it must contain either only one radionuclide, or several radionuclides all with similarl long half-lives, e.g. 152Eu and 133Ba.
4. Calculations of correction coefficients for true summations of photons In order to obtain the correction coefficient KðX; EÞ as a function of the detector index ND for the selected radionuclide X at a photon energy E; the total efficiency curve and the probability of true coincidence of photons must have been determined for the tested geometric arrangement. In our case the total detection efficiency was determined by means of standards with 241Am, 57Co, 137 Cs and 60Co in Marinelli beakers of 450, 500 and 1000 cm3 (produced by CMI-IIR). The probabilities of true coincidences were calculated by Monte Carlo simulation and correction factors KðX; EÞ are given below, according to the following notation: Kð60 Co; 1173Þ ¼ 1 1:000Tð1332Þ;
3. Detector index determination In the present work, standards of 152Eu were used for obtaining the ‘‘detector index’’ values. The detector index was determined for each geometric arrangement of Marinelli beakers of 450, 500 and 1000 cm3 volume (produced by CMI-IIR). For Ge(Li) and HPGe coaxial detectors having relative efficiency 12–52% at 1332 keV, the detector indexes were determined according to ND ¼
Tð12; 1900Þ ; AðXÞt
ð5Þ
where Tð12; 1900Þ is the total number of impulses integrated in the 12–1900 keV region, AðXÞ is the activity of the radionuclide X in the standard used and t is the measuring time. The indexes for the above-mentioned
Kð60 Co; 1332Þ ¼ 1 0:998Tð1173Þ; Kð88 Y; 898Þ ¼ 1 1:000Tð1836Þ; Kð88 Y; 1836Þ ¼ 1 0:919Tð898Þ; Kð134 Cs; 604Þ ¼ 1 0:085Tð563Þ 0:868Tð795Þ 0:152Tð569Þ 0:072Tð802Þ 0:033Tð1365Þ; Kð134 Cs; 795Þ ¼ 1 0:994Tð604Þ 0:175Tð569Þ;
Table 1 Detector indexes ND and specification of detectors Det. no. Type
1 2 3 4 5 6
HPGe HPGe HPGe HPGe HPGe Ge(Li)
Manufacturer
CANBERRA CANBERRA CANBERRA ORTEC PGT CANBERRA
Rel. eff.a (%) 12.2 28.4 36.1 52.5 25.7 19.0
FWHMb (keV) 1.8 1.8 2.0 1.8 2.1 2.1
Index
(ND )c
450(Eu)
500(Eu)
1000(Eu)
0.08254 0.1263 0.1478 F 0.1169 0.1080
0.0816 0.1170 0.1353 0.1793 0.09859 0.1032
0.06115 0.09043 0.1052 0.1420 0.07858 0.07841
Size (mm)
47 33 53 60 60 53 Not provided 53 58 51 55
a
Efficiency compared to a 300 300 NaI(Tl) for 1332 keV. Resolution FWHM for 1332 keV. c 450(Eu), 500(Eu), 1000(Eu),... Marinelli 450, 500, 1000 cm3, radionuclide b
152
Eu.
113
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
K(X,E) 1.00
0.99
0.98
0.97
0.96
0.95
0.94 K(88Y,898) K(dRa,609) K(60Co,1173)
0.93
K(88Y,1836) 0.92
K(60Co,1332)
0.91
K(dRa,1120) K(dTh,583) K(134Cs,604)
0.90
K(134Cs,795) 0.89 K(dTh,2614) 0.88
(a)
0.05
0.10
0.15
ND
Fig. 1. (a) Correction coefficients versus detector index for 450 cm3 Marinelli beakers. (b) Correction coefficients versus detector index for 500 cm3 Marinelli beakers. (c) Correction coefficients versus detector index for 1000 cm3 Marinelli beakers.
114
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
K(X,E) 1.00
0.99
0.98
0.97
0.96
0.95
0.94
K(88Y,898)
0.93
K(dRa,609) K(60Co,1173) K(88Y,1836) K(60Co,1332)
0.92
0.91
0.90
K(dRa,1120) K(dTh,583)
0.89
K(134Cs,604)
0.88
K(134Cs,795) K(dTh,2614)
(b)
0.05
0.10 Fig. 1 (continued).
0.15
ND
115
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
K(X,E) 1.00
0.99
0.98
0.97
0.96
0.95
0.94 K(88Y,898) K(dRa,609) K(60Co,1173)
0.93
K(88Y,1836) K(60Co,1332)
0.92
K(dRa,1120) 0.91
K(dTh,583)
0.90
K(134Cs,604) K(134Cs,795)
0.89
K(dTh,2614)
0.88
(c)
0.05
0.10 Fig. 1 (continued).
0.15
ND
116
P. Dryak et al. / Applied Radiation and Isotopes 56 (2002) 111–116
Kðd:226 Ra; 609Þ ¼ 1 0:098Tð768Þ 0:018Tð806Þ
standardized material in 450, 500 and 1000 cm3 Marinelli beakers.
0:070Tð934Þ 0:340Tð1120Þ 0:180Tð1238Þ 0:036Tð1281Þ0:035Tð1401Þ 0:060Tð1408Þ 0:055Tð1509Þ 0:09TðKXÞ; Kðd:226 Ra; 351Þ ¼ 1 0:009Tð487Þ; Kðd:226 Ra; 1120Þ ¼ 1 0:980Tð609Þ 0:016TðKXÞ; Kðd:232 Th; 583Þ ¼ 1 0:997Tð2614Þ 0:075Tð247Þ 0:247Tð511Þ 0:019Tð211Þ 0:060TðKXÞ; Kðd:232 Th; 2614Þ ¼ 1 0:856Tð583Þ 0:118Tð860Þ 0:066Tð277Þ 0:216Tð511Þ 0:016Tð763Þ 0:068TðKXÞ; where TðEÞ is the total efficiency of detection for coinciding photons of energy E ðkeVÞ; d:226 Ra represents the daughter radionuclides of 226Ra and d:232 Th represents the daughter radionuclides of 232Th. Fig. 1 shows the correction factor versus the detector index, which were determined by using a 152Eu
5. Conclusions The method described above is simple and makes it possible, for work places performing just routine measurement, to determine the correction factors of true summations of photons quite easily and quickly. Manufacturers of standards usually have much more extensive possibilities for determining detection efficiencies and correction factors for true summations of photons than users of the standards supplied by them. Therefore, they could use the method given in this contribution to draw curves of correction factors versus the detector index and provide them in appropriate cases (for example, measurement of low-activity samples with high detection efficiency) to their customers together with standards. Relative total uncertainty of correction factors should be better than 10% (K ¼ 2) in the case that the detector index has been determined with a standard in the same geometric arrangement which is used for measuring the samples. Future developments will test the possibilities of use of point standards for the determination of detector indexes.