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Standardization of 65Zn by 4πPC-γ coincidence counting method with efficiency extrapolation
ARTICLE IN PRESS
Applied Radiation and Isotopes 60 (2004) 423–427
Standardization of 65Zn by 4pPC-g coincidence counting method with efficiency extrapolation Maria Sahagiaa,*, C. Ivana, E.L. Grigorescua, M. Capognib, P. De Feliceb, A. Faziob a
National Institute of R&D for Physics and Nuclear Engineering ‘‘Horia Hulubei’’, IFIN-HH, POB MG-6, Bucharest RO-76900, Romania b E.N.E.A., Istituto Nazionale di Metrologia delle Radiazioni Ionizzanti, C.R. Casaccia, POB 2400, Rome A.D. I-00100, Italy
Abstract A 65Zn solution was standardized by the 4pPC–g efficiency-extrapolation coincidence counting method. Theoretical aspects of coincidence equations, efficiency equations and linearity conditions are reviewed. Experimental measurements were performed for two low level discrimination thresholds for the PC channel (counting K+L or K X-rays or Auger electrons from EC decay) and for three different settings of the g window. Requirements on g channel set-up for linear extrapolation were established by using a Pb absorber or by proper g window setting. The measured activity values were discussed and found in good agreement with those obtained with a calibrated ionization chamber. r 2003 Elsevier Ltd. All rights reserved. Keywords:
65
Zn; Coincidence-counting method; Efficiency extrapolation; Linearity conditions; Triangular decay scheme
1. Introduction
ment was set-up to practically accomplish the linearity conditions.
65
Zn is a radionuclide used for industrial and metrological purposes. It also occurs as an impurity in radionuclide production with cyclotrons or as environmental contamination radionuclide. 65Zn decays by electron capture to the 1115.6 keV exited level and by electron capture and beta plus emission to the ground state level of 65Cu (Fig. 1). The 4pPC–g coincidence counting method, in the variant of efficiency extrapolation, can be applied for 65Zn standardization but its peculiar decay scheme requires a theoretical investigation of the efficiency and coincidence equations. In particular, the fulfillment of linearity conditions in efficiency extrapolation for various experimental settings is an important aspect to obtain accurate extrapolated activity values. In this work, after a review on the main literature on this subject, a coincidence-counting equip-
*Corresponding author. Tel.: +401-404-2350; fax: +4021457-4440/+4021-457-4432. E-mail address: msahagia@ifin.nipne.ro (M. Sahagia).
2. Coincidence equations and decay scheme The well-known coincidence counting efficiencyextrapolation method is founded on the coincidence equations where the counting rates, N4pPC, Ng, Nc, respectively, in PC, g and coincidence channels, are functions of the source activity N0 and the detector efficiencies for different radiations. Generally from the coincidence equations one gets N0 ¼
N4pPC Ng 1 ; Nc 1 þ ð1 K0 Þ Ng =Nc 1
ð1Þ
where the counting rates are corrected for decay, backgrounds, dead times and accidental coincidences. A linear extrapolation of N4pPC Ng/Nc versus Ng/Nc is obtained only if the (1K0) term in Eq. (1) shows negligible dependence on Ng/Nc.
0969-8043/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2003.11.053
ARTICLE IN PRESS M. Sahagia et al. / Applied Radiation and Isotopes 60 (2004) 423–427
424 65
In these conditions (Grigorescu et al., 1996): ec1 eXA1 eXA2 1 K0 ¼ a1 ebg1 þ a2 1 eg7 1 eXA1 eXA1
Zn 243.9 d
a1 EC1
a2 EC2
a3 β+
1115.6 keV 511 keV γ1
γ± 65
Cu
a1=0.5075
a2= 0.4779
a3=0.0146
Fig. 1. 65Zn equivalent decay scheme. Nuclear data are taken from Coursol (1998).
In the special case of 65Zn the coincidence equations are (Grigorescu et al., 1996) N4pPC ¼ N0 fa1 ½eXA1 þ ð1 eXA1 Þebg1 þ a2 eXA2 þ a3 ebþ g; Ng ¼ N0 ða1 eg1 þ a3 eg7 Þ; Nc ¼ N0 fa1 ½eXA1 eg1 þ ð1 eXA1 Þec1 þ a3 ebþ eg7 g;
ð2Þ
where a1, a2, a3 are, respectively, the branching ratios for the two EC and b+ decay modes, eXA1 and eXA2 are, respectively, the PC detection efficiencies for X-rays or Auger electrons from EC1 and EC2 branches, eb+ is the positron detection efficiency, eg1 and eg7 are the detector efficiencies for g1 and the two annihilation quanta, respectively, e bg1 and ec1 are the efficiency of the PC detector and the efficiency of g selfcoincidences for g1 photons. These last effects are negligible for g7 radiations, due to the small value of a3, and have been ignored. The internal conversion coefficient for g1 is a ¼ 1:85 104 and may also be neglected. Specific considerations arising for different g-window settings are discussed in the following paragraphs. 2.1. Large g window and linearity conditions This situation is met when both g1 and g7 are detected in the g channel, that is, when a threshold lower than 511 keV is used. The linearity condition for efficiency extrapolation requires (Grigorescu et al., 1996): a1 eg1 1 ec1 =eg1 ¼ eg7 : ð3Þ a1 ð1 ebg1 Þ þ a2 ð1 eXA2 Þ=ð1 eXA1 Þ This may be approximated by a1 eg1 eg7 E a1 þ a2 that is eg7 E0:5eg1 when branching ratios from Coursol (1998) are taken.
ð4Þ
and depends on the PC channel counting efficiencies. This equation is more precise than Eq. (13) from Grigorescu et al. (1996). From Eqs. (2) and (3) one obtains the detection efficiency Nc/Ng as ebþ Nc 1 eXA1 ec1 a3 : ð5Þ Eða1 þ a2 ÞeXA1 1 þ þ Ng eXA1 eg1 a1 þ a2 eXA1 And therefore, from Eqs. (1) and (4) it follows: N4pPC Ng N0 ¼ Nc 1 ; 1 þ ð1 K Þ Ng =Nc 1 þ a2 eXA2 =eXA1 1 ec1 ð1 K Þ ¼ a1 ebg1 ; eg7
ð6Þ
ð7Þ
where (1K) is a constant value, expected to be low, may be negative, and the extrapolated value has to be corrected for the term a2 eXA2 =eXA1 1 generated by the pure EC branch. 2.2. Narrow g window and triangular decay scheme This situation is achieved when only g1 photons are detected in the g channel, that is, when a g threshold higher than 511 keV is used. A ‘‘triangular decay scheme’’ can be considered, as presented in various papers (Sahagia, 1979, Grigorescu et al., 1998) and treated extensively by Sahagia et al. (2002). According to these references it is possible to introduce a (1L) slope for the (n1) decays towards excited levels and a correction term for the nth direct transition to the ground state. The relation between (1L) and (1K0) slope is given by Ng : ð8Þ 1 K0 ¼ 1 L an ð1 ebn Þ Ng Nc In the
65
Zn specific case we have a2 a3 an ¼ a2 þ a3 ; ebn ¼ eXA2 þ e þ; a2 þ a3 a2 þ a3 b ec1 LEa1 1 ebg1 ; eg1
ð9Þ
where ec1/eg1 is lower than in the case 2.1. By the same approximation of Eq. (5), Eq. (6) is fulfilled if 1 ebþ ec1 ð1 K Þ ¼ a1 ebg1 þ a3 1 Ea3 ; eg1 1 eXA1 ð10Þ where (1K) is expected to be positive and approximately equal to a3=0.0146, as ð1 ebþ Þ=ð1 eXA1 Þ is a small, almost constant, term. From Eqs. (10) and (6) one
ARTICLE IN PRESS M. Sahagia et al. / Applied Radiation and Isotopes 60 (2004) 423–427
425
obtains the Eq. (5a) from the paper of DeRoost et al. (1972). They used a g-window of 800–1200 keV and counted only K-electron capture events.
where the efficiencies e4pPC are approximated by the experimental Nc/Ng values both for (K+L) an K events.
2.3. Efficiency equations
3. Experimental procedure
The application of Eq. (6) requires the estimation of the efficiency ratio eXA2 =eXA1 : The efficiency eXA, as a function of Auger electrons and X-rays efficiencies respectively for K and L capture events (eAK, eXK, eAL, eXL), were written by De Roost et al. (1972). Neglecting M electron capture events:
The 65Zn source was in the form of a solution of 560 mg g1 of ZnCl2 in 0.1 M HCl. An aliquot of 3.6 ml of solution was dispensed to a 5 ml BIPM-SIR ampoule which was flame sealed. A number of solid sources for absolute counting were also prepared from two different diluted solutions (dilution factors 4.0409 and 1.9252) of the original master solution. To this purpose accurately weighted aliquots of the diluted solutions were deposited onto gold-coated VYNS films treated with LUDOX 104 and dried under an infrared lamp. The ampoule source was measured in a CENTRONIC IG11/20A high pressure ionization chamber calibrated with standard solutions traceable to PTB and OMH. The resulting activity concentration A0=1958.5 kBq g1, with a combined standard uncertainty of 13.7 kBq g1 (0.7%), was assumed as reference value. The main uncertainty components arose from calibration of the standard solutions (0.6%) and the reproducibility of ionization chamber response (0.4%). Solid sources were measured in the ENEA-INMRI coincidence counting equipment based on a proportional counter working with a mixture of Ar–CH4 (90/10) at atmospheric pressure and a NaI(Tl) 7.5 cm
7.5 cm g-ray detector. A non-extendable fixed dead time of (8.0070.04) ms was imposed on both channels. The coincidence resolving time was (1.04070.004) ms. Two different integral discrimination thresholds were set for the PC channel: 0.4 keV (K and L events) and 1.1 keV (K events alone) according to the different situations considered under point 2 above. Both foil and threshold efficiency extrapolations were performed. With reference to the previous theoretical discussion the following settings of the g window were applied:
eXA ¼ ½eAL ð1 o % L fPL þ nKL PK % L Þ þ eXL o
½ð1 oK Þð1 eAK Þ þ oK ð1 eXK Þg þ ½eAK ð1 oK Þ þ eXK oK PK ;
ð11Þ
where PK, PL are the K and L capture probabilities, oK and o % L are fluorescence yields from K and L shells, nKL is the number of L vacancies produced as consequence of a K EC event. Taking nKL ¼ 1:36; oK ¼ 0:445; o %L ¼ 0:006; PK1 ¼ 0:879; PL1 ¼ 0:105; PK2 ¼ 0:886; PL2 ¼ 0:098; (Coursol, 1998), eXA1 and eXA2, for the two EC branches, can be written. Neglecting the very small contribution of ½eAL ð1 o % L Þ þ eXL o % L ½eAK ð1 oK Þ þ eXK oK the efficiency ratios eXA2/eXA1 are: (a) eXA2K =eXA1K ¼ 0:886 0:879 ¼ 1:0080 when only K radiations are counted or equivalently when a PC discrimination threshold of 1.1 keV is applied (Grigorescu et al., 1996); (b) eXA2ðKþLÞ eXA2K 0:994eAL þ 0:006eXL D 0:0118 ; eXA1ðKþLÞ eXA1K 0:555eAK þ 0:445eXK when (K+L) radiations are counted or when a PC discrimination threshold of 0.4 keV is applied. The second term in the last expression depends on the experimental setting. To this aim, combining Eq. (11) with Eq. (2) and rearranging the terms one obtains e4pPCðKþLÞ D 0:482eAK þ 0:387eXK þ 1:27eAL þ 0:0077eXL þ 0:015ebþ ðKþLÞ ;
ð12Þ
e4pPCK D0:482eAK þ 0:387eXK þ 0:015ebþ K : Neglecting the very small contribution of eXL term in Eq. (12) it follows: eAL ¼ 0:7874ðe4pPCðKþLÞ e4pPCK Þ 0:0118ðebþ ðKþLÞ ebþ K Þ;
ð13Þ
0:555eAK þ 0:445eXK ¼ 1:151ðe4pPCK 0:015ebþ K Þ; eXA2ðKþLÞ eXA2K D eXA1ðKþLÞ eXA1K 0:00802ðe4pPCðKþLÞ e4pPCK Þ 0:00012ðebþ ðKþLÞ ebþ K Þ ; e4pPCK 0:015ebþ K ð14Þ
(a) 400–1400 keV, corresponding to a large g window for detection of both g1 and g7. (b) 600–1400 keV, corresponding to detection of g1 quanta alone. (c) 511–1400 keV, corresponding to detection of g1 and half of g7. g efficiencies at 511 and 1116 keV were estimated with Na, 60Co and 65Zn commercially available standard point sources. Compton contribution was subtracted from the 460–562 keV gross counts to obtain the efficiency of the annihilation quanta. The efficiency ratio eg7 =eg1 ¼ 1:3 was obtained for the original system arrangement with setting (a). In order to accomplish the linearity condition of Eq. (3), a 7 mm Pb absorber was introduced between the proportional counter and the g detector for settings (a) and (b) above. The Pb absorber 22
ARTICLE IN PRESS M. Sahagia et al. / Applied Radiation and Isotopes 60 (2004) 423–427
426
was maintained, although not necessary, also in setting (b) in order to have comparable conditions with (a). An efficiency ratio eg7 =eg1 E0:63 is expected for setting (c) which means a partial accomplishment of the linearity condition. Data analysis was performed by using Eq. (6) with the (1 K) values from Eq. (7), for cases (a) and (c), and (10) for case (b). The measured data were analyzed by the SAHARA 2 and ETALON programs (Sahagia et al., 1976) for application of count-rate dependent effects. The terms in Eq. (14) were measured: ðNc =Ng ÞðKþLÞ ¼ 0:2393; ðNc =Ng ÞK ¼ 0:2063 and consequently e4pPCðKþLÞ e4pPCK D Nc =Ng
KþL
Nc =Ng
K
¼ 0:033:
Positron efficiencies for (K+L) and K events were evaluated by measurements of 60Co sources on VYNS films standardized by traditional 4pbg coincidence counting: ebþ ðKþLÞ D0:9; ebþ K D0:8: Introducing these values in Eq. (14) one gets eXA2ðKþLÞ =eXA1ðKþLÞ ¼ 1:0067: The N0 values were then calculated from Eq. (6) by applying the following values for the corrective term: a2 ðeXA2 =eXA1 1Þ ¼ 0:0032 for (K+L) detection and 0.0038 for K detection.
4. Results and discussions Final results are reported in Table 1. The following comments can be made: (1) The (1K) values are practically the same within the stated uncertainties for the (K+L) and K counting
and they are in agreement with corresponding values predicted in Section 2. In setting (a) (Section 3) small, negative values 1K= 0.0096 and 0.0091, respectively, were obtained, although these values are a little higher than those reported by Grigorescu et al. (1996). In setting (b) (Section 3) the higher, positive values 1K= +0.0136 and +0.0129, respectively, are very close to a3, as predicted. In setting (c) (Section 3), a negative value 1K= 0.018 was obtained higher than in case (a) above. In contrast to De Roost, who prepared electro-deposed sources with eXA E0:5; in our case the extrapolation correction is higher, due to lower e4pPC E0:2: It is preferable to have lower extrapolation slopes, as it is in the linearity condition. (2) In all cases the A1 values determined from (K+L) counting are about 1% higher than the corresponding values obtained from K counting. They lie on both sides of the reference A0 value, in setting (a), they are systematically lower or higher in other settings. Although the (K+L) counting seems to provide more consistent results, the systematic differences between (K+L) and K events suggests the occurrence of some spurious pulses in the (K+L) counting due to the very low discrimination threshold used in PC channel. This was effectively confirmed with a careful analysis of time interval pulse distribution. (3) As a consequence of the above considerations a final A1 value from setting (a) in the variant of K counting result was chosen, namely: mean A1=1948.7 kBq g1 with combined standard uncertainty of 6.8 kBq g1 (0.35%). The type B uncertainty components were: background (0.02%), dead time
Table 1 Experimental results Source nr.
K threshold
(K+L) threshold Ng/Nc1 interval
A1 (kBq g1)
1K
Ng/Nc1 interval
A1(K+L)/A1K A1 (kBq g1)
1K
Setting (a) 400–1400 keV, 7 mm Pb absorber 87 181 187
4.3–11 1970712 4.1–6.8 1969716 3.9–16 1970.276.7 Mean A1=1969.677.0 D=+0.57%
87
4.8–15
183
3.3–15
1970713 D=+0.59% 1950.576.3 D= 0.41%
0.0097(9) 0.0097(15) 0.0093(4) 0.0096(6)
4.8–13 1947711 4.6–13 1946711 4.4–11 1953712 Mean A1 =1948.776.5 D= 0.50%
0.0086(7) 0.0087(8) 0.0101(8) 0.0091(4)
Setting (b) 600–1400 keV, 7 mm Pb absorber +0.0136(8) 5.6–18 1963713 +0.0129(6) D=+0.22% Setting (c) 511–1400 keV, no Pb absorber 0.0181(4) 3.8–29 1923.474.5 0.0179(1) D= 1.8%
1.012 1.012 1.009 1.011
1.004
1.014
For each source measured in the different experimental set-up, the resulting activity concentration values A1, the PC counting efficiency and the (1K) slopes are reported. The percent deviation D between A1 and A0 is also given as well as the ratio of the A1 values for (K+L) and K counting.
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(0.01%), resolving time (0.01%), Gandy effect (0.01%), weighing (0.03%), extrapolation (0.1%). Type A uncertainty components, mainly due to counting statistics (0.33%) are prevalent because of the low coincidence counting rates, due to both PC and g-low efficiencies. The corresponding difference from A0 is D=0.50% which is well within the combination (0.78%) of the uncertainties of A0 and A1.
427
Acknowledgements The authors are indebted to ENEA, for the research fellowship awarded to M. Sahagia and C. Ivan as well as to IFIN-HH and European Center of Excellence IDRANAP for the research fellowship awarded to M. Capogni.
References 5. Conclusions The standardization of 65Zn by the 4pPC–g efficiencyextrapolation coincidence counting method was investigated. The ratio of the 4pPC efficiencies for the two electron capture branches were calculated. Basic coincidence equations, valid for three different g windows such as linearity fulfillment, detection of the 1115.6 keV quanta as well as partial linearity accomplishment, were developed. The appropriate experimental conditions were established and the determinations were made in six variants: (K+L) and K counting conditions, and the three g counting conditions mentioned above. The results obtained were in good agreement with the theoretical predictions. The optimum conditions were chosen from six different cases: counting of the K electron capture radiations in the PC channel and linearity conditions in the g channel. The combined standard uncertainty was 0.35% and the difference between the determined activity and the reference value, based both on PTB and OMH standard, was 0.50%.
Coursol, N., 1998. Table des Radionucl!eides, BNM-CEA/ DTA/LNHB, France. DeRoost, E., Funck, E., Spernol, A., Vaninbroukx, R., 1972. The decay of 65Zn. Z. Physik 250, 395. Grigorescu, E.L., Sahagia, M., Razdolescu, A., Ivan, C., 1996. Standardization of some electron capture radionuclides. Nucl. Instrum. Methods A 369, 414. Grigorescu, E.L., Sahagia, M., Razdolescu, A.C., Luca, A., Radwan, R.M., 1998. Standardization of 110mAg and 75Se by the beta-efficiency extrapolation method. Appl. Radiat. Isot. 49 (9–11), 1165. Sahagia, M., 1979. Standardization of low energy beta emitters and beta-gamma emitters, decaying to the ground level, by the tracer and detection efficiency extrapolation, Russian, International Symposium, Methods of Obtaining and Measurement of Standard Sources and Solutions, Proceedings Marianske Lamne, Czech Republic, p. 180. Sahagia, M., Dumitrescu, R., Debert, C., 1976. Processing of the experimental data obtained at the absolute standardization. Res. Roum. Phys. 21, 7, 745. Sahagia, M., Razdolescu, A.C., Grigorescu, E.L., Luca, A., Ivan, C., 2002. Precise measurement of the activity of 186Re, 188 Re radiopharmaceuticals. Appl. Radiat. Isot. 56 (1–2), 349.
Applied Radiation and Isotopes 60 (2004) 423–427
Standardization of 65Zn by 4pPC-g coincidence counting method with efficiency extrapolation Maria Sahagiaa,*, C. Ivana, E.L. Grigorescua, M. Capognib, P. De Feliceb, A. Faziob a
National Institute of R&D for Physics and Nuclear Engineering ‘‘Horia Hulubei’’, IFIN-HH, POB MG-6, Bucharest RO-76900, Romania b E.N.E.A., Istituto Nazionale di Metrologia delle Radiazioni Ionizzanti, C.R. Casaccia, POB 2400, Rome A.D. I-00100, Italy
Abstract A 65Zn solution was standardized by the 4pPC–g efficiency-extrapolation coincidence counting method. Theoretical aspects of coincidence equations, efficiency equations and linearity conditions are reviewed. Experimental measurements were performed for two low level discrimination thresholds for the PC channel (counting K+L or K X-rays or Auger electrons from EC decay) and for three different settings of the g window. Requirements on g channel set-up for linear extrapolation were established by using a Pb absorber or by proper g window setting. The measured activity values were discussed and found in good agreement with those obtained with a calibrated ionization chamber. r 2003 Elsevier Ltd. All rights reserved. Keywords:
65
Zn; Coincidence-counting method; Efficiency extrapolation; Linearity conditions; Triangular decay scheme
1. Introduction
ment was set-up to practically accomplish the linearity conditions.
65
Zn is a radionuclide used for industrial and metrological purposes. It also occurs as an impurity in radionuclide production with cyclotrons or as environmental contamination radionuclide. 65Zn decays by electron capture to the 1115.6 keV exited level and by electron capture and beta plus emission to the ground state level of 65Cu (Fig. 1). The 4pPC–g coincidence counting method, in the variant of efficiency extrapolation, can be applied for 65Zn standardization but its peculiar decay scheme requires a theoretical investigation of the efficiency and coincidence equations. In particular, the fulfillment of linearity conditions in efficiency extrapolation for various experimental settings is an important aspect to obtain accurate extrapolated activity values. In this work, after a review on the main literature on this subject, a coincidence-counting equip-
*Corresponding author. Tel.: +401-404-2350; fax: +4021457-4440/+4021-457-4432. E-mail address: msahagia@ifin.nipne.ro (M. Sahagia).
2. Coincidence equations and decay scheme The well-known coincidence counting efficiencyextrapolation method is founded on the coincidence equations where the counting rates, N4pPC, Ng, Nc, respectively, in PC, g and coincidence channels, are functions of the source activity N0 and the detector efficiencies for different radiations. Generally from the coincidence equations one gets N0 ¼
N4pPC Ng 1 ; Nc 1 þ ð1 K0 Þ Ng =Nc 1
ð1Þ
where the counting rates are corrected for decay, backgrounds, dead times and accidental coincidences. A linear extrapolation of N4pPC Ng/Nc versus Ng/Nc is obtained only if the (1K0) term in Eq. (1) shows negligible dependence on Ng/Nc.
0969-8043/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2003.11.053
ARTICLE IN PRESS M. Sahagia et al. / Applied Radiation and Isotopes 60 (2004) 423–427
424 65
In these conditions (Grigorescu et al., 1996): ec1 eXA1 eXA2 1 K0 ¼ a1 ebg1 þ a2 1 eg7 1 eXA1 eXA1
Zn 243.9 d
a1 EC1
a2 EC2
a3 β+
1115.6 keV 511 keV γ1
γ± 65
Cu
a1=0.5075
a2= 0.4779
a3=0.0146
Fig. 1. 65Zn equivalent decay scheme. Nuclear data are taken from Coursol (1998).
In the special case of 65Zn the coincidence equations are (Grigorescu et al., 1996) N4pPC ¼ N0 fa1 ½eXA1 þ ð1 eXA1 Þebg1 þ a2 eXA2 þ a3 ebþ g; Ng ¼ N0 ða1 eg1 þ a3 eg7 Þ; Nc ¼ N0 fa1 ½eXA1 eg1 þ ð1 eXA1 Þec1 þ a3 ebþ eg7 g;
ð2Þ
where a1, a2, a3 are, respectively, the branching ratios for the two EC and b+ decay modes, eXA1 and eXA2 are, respectively, the PC detection efficiencies for X-rays or Auger electrons from EC1 and EC2 branches, eb+ is the positron detection efficiency, eg1 and eg7 are the detector efficiencies for g1 and the two annihilation quanta, respectively, e bg1 and ec1 are the efficiency of the PC detector and the efficiency of g selfcoincidences for g1 photons. These last effects are negligible for g7 radiations, due to the small value of a3, and have been ignored. The internal conversion coefficient for g1 is a ¼ 1:85 104 and may also be neglected. Specific considerations arising for different g-window settings are discussed in the following paragraphs. 2.1. Large g window and linearity conditions This situation is met when both g1 and g7 are detected in the g channel, that is, when a threshold lower than 511 keV is used. The linearity condition for efficiency extrapolation requires (Grigorescu et al., 1996): a1 eg1 1 ec1 =eg1 ¼ eg7 : ð3Þ a1 ð1 ebg1 Þ þ a2 ð1 eXA2 Þ=ð1 eXA1 Þ This may be approximated by a1 eg1 eg7 E a1 þ a2 that is eg7 E0:5eg1 when branching ratios from Coursol (1998) are taken.
ð4Þ
and depends on the PC channel counting efficiencies. This equation is more precise than Eq. (13) from Grigorescu et al. (1996). From Eqs. (2) and (3) one obtains the detection efficiency Nc/Ng as ebþ Nc 1 eXA1 ec1 a3 : ð5Þ Eða1 þ a2 ÞeXA1 1 þ þ Ng eXA1 eg1 a1 þ a2 eXA1 And therefore, from Eqs. (1) and (4) it follows: N4pPC Ng N0 ¼ Nc 1 ; 1 þ ð1 K Þ Ng =Nc 1 þ a2 eXA2 =eXA1 1 ec1 ð1 K Þ ¼ a1 ebg1 ; eg7
ð6Þ
ð7Þ
where (1K) is a constant value, expected to be low, may be negative, and the extrapolated value has to be corrected for the term a2 eXA2 =eXA1 1 generated by the pure EC branch. 2.2. Narrow g window and triangular decay scheme This situation is achieved when only g1 photons are detected in the g channel, that is, when a g threshold higher than 511 keV is used. A ‘‘triangular decay scheme’’ can be considered, as presented in various papers (Sahagia, 1979, Grigorescu et al., 1998) and treated extensively by Sahagia et al. (2002). According to these references it is possible to introduce a (1L) slope for the (n1) decays towards excited levels and a correction term for the nth direct transition to the ground state. The relation between (1L) and (1K0) slope is given by Ng : ð8Þ 1 K0 ¼ 1 L an ð1 ebn Þ Ng Nc In the
65
Zn specific case we have a2 a3 an ¼ a2 þ a3 ; ebn ¼ eXA2 þ e þ; a2 þ a3 a2 þ a3 b ec1 LEa1 1 ebg1 ; eg1
ð9Þ
where ec1/eg1 is lower than in the case 2.1. By the same approximation of Eq. (5), Eq. (6) is fulfilled if 1 ebþ ec1 ð1 K Þ ¼ a1 ebg1 þ a3 1 Ea3 ; eg1 1 eXA1 ð10Þ where (1K) is expected to be positive and approximately equal to a3=0.0146, as ð1 ebþ Þ=ð1 eXA1 Þ is a small, almost constant, term. From Eqs. (10) and (6) one
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425
obtains the Eq. (5a) from the paper of DeRoost et al. (1972). They used a g-window of 800–1200 keV and counted only K-electron capture events.
where the efficiencies e4pPC are approximated by the experimental Nc/Ng values both for (K+L) an K events.
2.3. Efficiency equations
3. Experimental procedure
The application of Eq. (6) requires the estimation of the efficiency ratio eXA2 =eXA1 : The efficiency eXA, as a function of Auger electrons and X-rays efficiencies respectively for K and L capture events (eAK, eXK, eAL, eXL), were written by De Roost et al. (1972). Neglecting M electron capture events:
The 65Zn source was in the form of a solution of 560 mg g1 of ZnCl2 in 0.1 M HCl. An aliquot of 3.6 ml of solution was dispensed to a 5 ml BIPM-SIR ampoule which was flame sealed. A number of solid sources for absolute counting were also prepared from two different diluted solutions (dilution factors 4.0409 and 1.9252) of the original master solution. To this purpose accurately weighted aliquots of the diluted solutions were deposited onto gold-coated VYNS films treated with LUDOX 104 and dried under an infrared lamp. The ampoule source was measured in a CENTRONIC IG11/20A high pressure ionization chamber calibrated with standard solutions traceable to PTB and OMH. The resulting activity concentration A0=1958.5 kBq g1, with a combined standard uncertainty of 13.7 kBq g1 (0.7%), was assumed as reference value. The main uncertainty components arose from calibration of the standard solutions (0.6%) and the reproducibility of ionization chamber response (0.4%). Solid sources were measured in the ENEA-INMRI coincidence counting equipment based on a proportional counter working with a mixture of Ar–CH4 (90/10) at atmospheric pressure and a NaI(Tl) 7.5 cm
7.5 cm g-ray detector. A non-extendable fixed dead time of (8.0070.04) ms was imposed on both channels. The coincidence resolving time was (1.04070.004) ms. Two different integral discrimination thresholds were set for the PC channel: 0.4 keV (K and L events) and 1.1 keV (K events alone) according to the different situations considered under point 2 above. Both foil and threshold efficiency extrapolations were performed. With reference to the previous theoretical discussion the following settings of the g window were applied:
eXA ¼ ½eAL ð1 o % L fPL þ nKL PK % L Þ þ eXL o
½ð1 oK Þð1 eAK Þ þ oK ð1 eXK Þg þ ½eAK ð1 oK Þ þ eXK oK PK ;
ð11Þ
where PK, PL are the K and L capture probabilities, oK and o % L are fluorescence yields from K and L shells, nKL is the number of L vacancies produced as consequence of a K EC event. Taking nKL ¼ 1:36; oK ¼ 0:445; o %L ¼ 0:006; PK1 ¼ 0:879; PL1 ¼ 0:105; PK2 ¼ 0:886; PL2 ¼ 0:098; (Coursol, 1998), eXA1 and eXA2, for the two EC branches, can be written. Neglecting the very small contribution of ½eAL ð1 o % L Þ þ eXL o % L ½eAK ð1 oK Þ þ eXK oK the efficiency ratios eXA2/eXA1 are: (a) eXA2K =eXA1K ¼ 0:886 0:879 ¼ 1:0080 when only K radiations are counted or equivalently when a PC discrimination threshold of 1.1 keV is applied (Grigorescu et al., 1996); (b) eXA2ðKþLÞ eXA2K 0:994eAL þ 0:006eXL D 0:0118 ; eXA1ðKþLÞ eXA1K 0:555eAK þ 0:445eXK when (K+L) radiations are counted or when a PC discrimination threshold of 0.4 keV is applied. The second term in the last expression depends on the experimental setting. To this aim, combining Eq. (11) with Eq. (2) and rearranging the terms one obtains e4pPCðKþLÞ D 0:482eAK þ 0:387eXK þ 1:27eAL þ 0:0077eXL þ 0:015ebþ ðKþLÞ ;
ð12Þ
e4pPCK D0:482eAK þ 0:387eXK þ 0:015ebþ K : Neglecting the very small contribution of eXL term in Eq. (12) it follows: eAL ¼ 0:7874ðe4pPCðKþLÞ e4pPCK Þ 0:0118ðebþ ðKþLÞ ebþ K Þ;
ð13Þ
0:555eAK þ 0:445eXK ¼ 1:151ðe4pPCK 0:015ebþ K Þ; eXA2ðKþLÞ eXA2K D eXA1ðKþLÞ eXA1K 0:00802ðe4pPCðKþLÞ e4pPCK Þ 0:00012ðebþ ðKþLÞ ebþ K Þ ; e4pPCK 0:015ebþ K ð14Þ
(a) 400–1400 keV, corresponding to a large g window for detection of both g1 and g7. (b) 600–1400 keV, corresponding to detection of g1 quanta alone. (c) 511–1400 keV, corresponding to detection of g1 and half of g7. g efficiencies at 511 and 1116 keV were estimated with Na, 60Co and 65Zn commercially available standard point sources. Compton contribution was subtracted from the 460–562 keV gross counts to obtain the efficiency of the annihilation quanta. The efficiency ratio eg7 =eg1 ¼ 1:3 was obtained for the original system arrangement with setting (a). In order to accomplish the linearity condition of Eq. (3), a 7 mm Pb absorber was introduced between the proportional counter and the g detector for settings (a) and (b) above. The Pb absorber 22
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was maintained, although not necessary, also in setting (b) in order to have comparable conditions with (a). An efficiency ratio eg7 =eg1 E0:63 is expected for setting (c) which means a partial accomplishment of the linearity condition. Data analysis was performed by using Eq. (6) with the (1 K) values from Eq. (7), for cases (a) and (c), and (10) for case (b). The measured data were analyzed by the SAHARA 2 and ETALON programs (Sahagia et al., 1976) for application of count-rate dependent effects. The terms in Eq. (14) were measured: ðNc =Ng ÞðKþLÞ ¼ 0:2393; ðNc =Ng ÞK ¼ 0:2063 and consequently e4pPCðKþLÞ e4pPCK D Nc =Ng
KþL
Nc =Ng
K
¼ 0:033:
Positron efficiencies for (K+L) and K events were evaluated by measurements of 60Co sources on VYNS films standardized by traditional 4pbg coincidence counting: ebþ ðKþLÞ D0:9; ebþ K D0:8: Introducing these values in Eq. (14) one gets eXA2ðKþLÞ =eXA1ðKþLÞ ¼ 1:0067: The N0 values were then calculated from Eq. (6) by applying the following values for the corrective term: a2 ðeXA2 =eXA1 1Þ ¼ 0:0032 for (K+L) detection and 0.0038 for K detection.
4. Results and discussions Final results are reported in Table 1. The following comments can be made: (1) The (1K) values are practically the same within the stated uncertainties for the (K+L) and K counting
and they are in agreement with corresponding values predicted in Section 2. In setting (a) (Section 3) small, negative values 1K= 0.0096 and 0.0091, respectively, were obtained, although these values are a little higher than those reported by Grigorescu et al. (1996). In setting (b) (Section 3) the higher, positive values 1K= +0.0136 and +0.0129, respectively, are very close to a3, as predicted. In setting (c) (Section 3), a negative value 1K= 0.018 was obtained higher than in case (a) above. In contrast to De Roost, who prepared electro-deposed sources with eXA E0:5; in our case the extrapolation correction is higher, due to lower e4pPC E0:2: It is preferable to have lower extrapolation slopes, as it is in the linearity condition. (2) In all cases the A1 values determined from (K+L) counting are about 1% higher than the corresponding values obtained from K counting. They lie on both sides of the reference A0 value, in setting (a), they are systematically lower or higher in other settings. Although the (K+L) counting seems to provide more consistent results, the systematic differences between (K+L) and K events suggests the occurrence of some spurious pulses in the (K+L) counting due to the very low discrimination threshold used in PC channel. This was effectively confirmed with a careful analysis of time interval pulse distribution. (3) As a consequence of the above considerations a final A1 value from setting (a) in the variant of K counting result was chosen, namely: mean A1=1948.7 kBq g1 with combined standard uncertainty of 6.8 kBq g1 (0.35%). The type B uncertainty components were: background (0.02%), dead time
Table 1 Experimental results Source nr.
K threshold
(K+L) threshold Ng/Nc1 interval
A1 (kBq g1)
1K
Ng/Nc1 interval
A1(K+L)/A1K A1 (kBq g1)
1K
Setting (a) 400–1400 keV, 7 mm Pb absorber 87 181 187
4.3–11 1970712 4.1–6.8 1969716 3.9–16 1970.276.7 Mean A1=1969.677.0 D=+0.57%
87
4.8–15
183
3.3–15
1970713 D=+0.59% 1950.576.3 D= 0.41%
0.0097(9) 0.0097(15) 0.0093(4) 0.0096(6)
4.8–13 1947711 4.6–13 1946711 4.4–11 1953712 Mean A1 =1948.776.5 D= 0.50%
0.0086(7) 0.0087(8) 0.0101(8) 0.0091(4)
Setting (b) 600–1400 keV, 7 mm Pb absorber +0.0136(8) 5.6–18 1963713 +0.0129(6) D=+0.22% Setting (c) 511–1400 keV, no Pb absorber 0.0181(4) 3.8–29 1923.474.5 0.0179(1) D= 1.8%
1.012 1.012 1.009 1.011
1.004
1.014
For each source measured in the different experimental set-up, the resulting activity concentration values A1, the PC counting efficiency and the (1K) slopes are reported. The percent deviation D between A1 and A0 is also given as well as the ratio of the A1 values for (K+L) and K counting.
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(0.01%), resolving time (0.01%), Gandy effect (0.01%), weighing (0.03%), extrapolation (0.1%). Type A uncertainty components, mainly due to counting statistics (0.33%) are prevalent because of the low coincidence counting rates, due to both PC and g-low efficiencies. The corresponding difference from A0 is D=0.50% which is well within the combination (0.78%) of the uncertainties of A0 and A1.
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Acknowledgements The authors are indebted to ENEA, for the research fellowship awarded to M. Sahagia and C. Ivan as well as to IFIN-HH and European Center of Excellence IDRANAP for the research fellowship awarded to M. Capogni.
References 5. Conclusions The standardization of 65Zn by the 4pPC–g efficiencyextrapolation coincidence counting method was investigated. The ratio of the 4pPC efficiencies for the two electron capture branches were calculated. Basic coincidence equations, valid for three different g windows such as linearity fulfillment, detection of the 1115.6 keV quanta as well as partial linearity accomplishment, were developed. The appropriate experimental conditions were established and the determinations were made in six variants: (K+L) and K counting conditions, and the three g counting conditions mentioned above. The results obtained were in good agreement with the theoretical predictions. The optimum conditions were chosen from six different cases: counting of the K electron capture radiations in the PC channel and linearity conditions in the g channel. The combined standard uncertainty was 0.35% and the difference between the determined activity and the reference value, based both on PTB and OMH standard, was 0.50%.
Coursol, N., 1998. Table des Radionucl!eides, BNM-CEA/ DTA/LNHB, France. DeRoost, E., Funck, E., Spernol, A., Vaninbroukx, R., 1972. The decay of 65Zn. Z. Physik 250, 395. Grigorescu, E.L., Sahagia, M., Razdolescu, A., Ivan, C., 1996. Standardization of some electron capture radionuclides. Nucl. Instrum. Methods A 369, 414. Grigorescu, E.L., Sahagia, M., Razdolescu, A.C., Luca, A., Radwan, R.M., 1998. Standardization of 110mAg and 75Se by the beta-efficiency extrapolation method. Appl. Radiat. Isot. 49 (9–11), 1165. Sahagia, M., 1979. Standardization of low energy beta emitters and beta-gamma emitters, decaying to the ground level, by the tracer and detection efficiency extrapolation, Russian, International Symposium, Methods of Obtaining and Measurement of Standard Sources and Solutions, Proceedings Marianske Lamne, Czech Republic, p. 180. Sahagia, M., Dumitrescu, R., Debert, C., 1976. Processing of the experimental data obtained at the absolute standardization. Res. Roum. Phys. 21, 7, 745. Sahagia, M., Razdolescu, A.C., Grigorescu, E.L., Luca, A., Ivan, C., 2002. Precise measurement of the activity of 186Re, 188 Re radiopharmaceuticals. Appl. Radiat. Isot. 56 (1–2), 349.