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Standardisation of 56Co and 57Co using software coincidence counting system
ARTICLE IN PRESS
Applied Radiation and Isotopes 66 (2008) 914–918 www.elsevier.com/locate/apradiso
Standardisation of 56Co and 57Co using software coincidence counting system Miroslav Havelka, Jana Sochorova´ Czech Metrology Institute, Inspectorate for Ionizing Radiation, Radiova´ 1, 102 00 Prague, Czech Republic
Abstract Activities of the radionuclides 56Co and 57Co were determined by the efficiency extrapolation method applied to 4p(PC)-g coincidence counting. Solutions of 56Co usually contain a significant amount of 57Co and 58Co, so the measured activity of 56Co requires correction. When the conventional coincidence method is used for 56Co standardisation, the corrections are derived from the dependence of Proportional Counter (PC) detection efficiencies for 57Co and 56Co measured using sources with mixture of 56Co and 57Co, which is complicated. These difficulties were reduced by means of a software coincidence method, with a HPGe detector in gamma channel, where the detection efficiencies were evaluated directly from the records of coincidence measurements of standardised sources. In the case of 57 Co standardisation, the software coincidence counting system was applied for the evaluation of optimal setting of coincidence parameters. The results obtained by software coincidence counting system were compared with those obtained by the conventional coincidence method. r 2008 Elsevier Ltd. All rights reserved. Keywords: 4pb-g coincidence counting; Software coincidence counting;
56
1. Introduction The radionuclides 56Co, 57Co and 58Co all decay by electron capture (EC). The decay scheme of 56Co is complicated, exhibiting ten EC(1–10) and two positron emission branches as shown in Fig. 1 (Be´ et al., 2004). All these branches after photon emissions proceed via the 847 keV level with a probability of 99.97%, thus the scheme for coincidence measurement with 847 keV photons may be considerably simplified. 57Co has a rather simple decay scheme, decaying by EC via the 136 keV level of 57Fe as shown in Fig. 2 (Be´ et al., 2004). The decay scheme of 58Co is also relatively simple; if the EC1 branch is neglected the decay scheme is similar to simplified 56Co decay scheme as shown in Fig. 3 (Be´ et al., 2004). The activities of both radionuclides were measured using the 4p(PC)-g coincidence counting efficiency extrapolation method. These standardisations can be realised by conventional (Campion, 1959), or by digital method (Buckman et al., 1998; Park et al., 2002; Keightley and Watt, 2002; Havelka et al., Corresponding author. Fax: +420 266020466.
E-mail address: [email protected] (M. Havelka). 0969-8043/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2008.02.034
Co standardisation;
57
Co standardisation
2002), that here profits from the possibility to evaluate the same data records with different coincidence parameter settings.
2. Experimental set-up Two detector systems have been used, the first for measurement with software coincidence counting, the second was connected to conventional coincidence modules and served as comparative system. The first system consisted from aluminium cylindrical proportional counter (PC) (60 mm inner-height and 52 mm inner-diameter) and a HPGe detector in the gamma channel. The sources were placed about 26 mm above the HPGe detector end cap. This system operated with a mixture of propane and butane at atmospheric pressure in a gas flow arrangement. In the second system the 4p detector was a stainlesssteel cylindrical proportional counter (two halves of 1 8 mm inner-height and 64 mm inner-diameter), using methane at atmospheric pressure in a gas flow arrangement. The g-ray detection assembly consisted of two opposing NaI(Tl) detectors mounted close to the PC. The
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
915
utilised the conventional method of altering the selfabsorption in the sources as well as the computer discrimination (CD) method (Smith, 1975) in the PC channel. The SCC system and the formulae used for data processing have been described in previous papers (Havelka et al., 2002, 2004, 2006).
56Co
EC(1-10) β+(1,2) γ 847 keV
3. Standardisation of
γ1
56Fe
Fig. 1. Simplified decay scheme of 56Co. The branching ratios for sum of EC and b+(1,2) branches are aEC ¼ 0.8042 and ab+(1) ¼ 0.0104, ab+(2) ¼ 0.1829.
57Co
56
Co
The coincidence measurement was carried out with a gamma window setting on the 847 keV peak, which simplified the standardisation, however, in spite of all branches proceeding via the level emitting 847 keV photons, the gamma detection efficiencies for g-rays are different for EC and positron branches due to summing effects. The coincidence equations (neglecting conversion electrons) are: N PC ¼ N 0 ½aEC ðXA þ ð1 XA ÞPCg Þ
EC
þ abþ ðbþ þ ð1 bþ ÞPCg Þ, N g ¼ N 0 ðaEC gðECÞ þ abþ gðbþÞ Þ,
136 keV
N C ¼ N 0 ½aEC ðXA gðECÞ þ ð1 XA ÞPCg 0gðECÞ Þ γ2
γ3
þ abþ ðbþ gðbþÞ þ ð1 bþ ÞPCg 0gðbþÞ Þ,
14 keV γ1 57Fe
Fig. 2. Simplified decay scheme of 57Co. The branching ratios for g2 (122 keV) and g3 (136 keV) branches are a1 ¼ 0.876 and a2 ¼ 0.123. The total internal conversion coefficients are aT14 ¼ 8.58, aT122 ¼ 0.0236 and aT136 ¼ 0.148.
58Co
EC1 a1
1675 keV γ3
EC2 a2
γ2
β+ a3
810 keV γ1 58
Fe
Fig. 3. Decay scheme of 58Co. The branching ratios are a1 ¼ 0.0121, a2 ¼ 0.8379 and a3 ¼ 0.1500.
sources were prepared by deposition of 20–50 mg aliquots of active solution containing about 20 mg g1 carrier on 40–60 mg cm2 gold-coated VYNS foils or on gold-coated 850 mg cm2 Mylar films, treated with Ludox and insulin. All sources were treated in an atmosphere of NH3 to achieve higher PC detection efficiencies. The conventional coincidence system used the source self-absorption variation of PC efficiency via the addition of extra mass to the source. The software coincidence counting (SCC) system
(1)
where N0 is the source activity; NPC the (corrected) count rate in the proportional counter; Ng the (corrected) count rate in the gamma detector; Nc the (corrected) count rate of coincidences; aEC, ab+ are branching ratios for EC and positrons branches; eXA the efficiency of PC for X-rays and Auger electrons; eb+ the efficiency of PC for positrons; ePCg the efficiency of PC for g-rays; eg(EC), eg(b+) are the gamma detection efficiencies with an 847 keV window setting for g-rays corresponding EC and b+ branches; e0 g(EC), e0 g(b+) are the scattered gamma detection efficiencies which are already detected in the PC. Assuming that eb+ is a linear function of ePC as shown in Fig. 4 and for ePC-1 as eb+-1, e0 g(EC)Ee0 g(b+)E0 and eg(b+)E0.95eg(EC), we may express associated efficiency– extrapolation curve NPCNg/Nc in terms of the quantity (ePC Nc/Ng), which represents an estimate for the efficiency of the proportional counter to all events (positrons, X-rays, Auger-electrons and g-rays): N PC N g 1 PC N0 1 þ k , (2) Nc PC where the normalised extrapolation slope ‘‘k’’ is given by gðbþÞ k PCg þ abþ 1 . (3) gðECÞ The summing events are more frequent for positrons than for EC decay, mainly due to emission of annihilation photons. The 5% difference between the gamma detection efficiencies of the EC and positron branches caused an increase of the normalised extrapolation slope of about 1%, nevertheless the value N0 was not influenced. The real solutions always contain significant impurity levels of 57Co and 58Co, so NPC had to be corrected for
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
916
0.99
0.6 0.5
εPC (56Co)
0.98
εβ+
0.97 0.96
0.4 0.3 0.2 0.1
0.95 0.94 0.0
0.0 0.0 0.1
0.2
0.3
0.4
0.2
0.4
0.5
εPC Fig. 4. Dependence of eb+ on ePC for 56Co; calculated from software coincidence data using count rates of 511 keV peak area and corresponding coincidence count rates.
their contributions:
90 80
¼ N PCð56Coþ57Coþ58CoÞ N 57Co PCð57CoÞ N 58Co PCð58CoÞ ,
where N57Co, N58Co are activities of 57Co and 58Co measured by gamma ray spectrometry, ePC(57Co) and ePC(58Co) are the PC detection efficiencies. The efficiency ePC(57Co) can be calculated in case of digital coincidence counting from the ratios of the count rates of 122 and 136 keV peaks and the corresponding coincidence count rates according to the formula supposing that all conversion electrons arising from the internal conversion of the 122 and 136 keV photons of total probability (Pce ¼ 0.0360) are detected:
CD fitting region
70 Count rate (s-1)
(4)
PCð57CoÞ
0.8
Fig. 5. Variation of PC detection efficiency of 56Co on PC detection efficiency of 57Co; as calculated from software coincidence data. If ePC(57Co)o0.3, only positrons are detected in PC from 56Co decay. The similar graph can be obtained from measurements of sources with a mixture of both radionuclides.
N PC ¼ N PCð56Coþ57Coþ58CoÞ N PCð57CoÞ N PCð58CoÞ
N Cð122; 136Þ ð1 Pce Þ þ Pce . N gð122; 136Þ
0.6
εPC (57Co)
60 50 40 30 20 10 0 0
50
100 150 Channnel
200
250
Fig. 6. Pulse height spectra of PC channel pulses. The peak corresponds to 6 keV KX-electrons. The 56Co source activity was about 5 kBq.
(5)
The efficiency ePC(57Co) may be also derived from the measured value of ePC(56Co) (the PC detection efficiency for 56 Co) by means of a correlation graph between ePC(56Co) and ePC(57Co) as shown in Fig. 5. This procedure in the case of conventional standardisation requires extra measurements of sources with a mixture of single radionuclides and usually results in less precise values. The efficiency ePC(58Co) was estimated from ePC(56Co) following the similarity of the PC channel pulse height spectra of 58Co and 56Co, and assuming the PC detection efficiency for positrons is approximately unity. In the case of a gamma window setting on the 847 keV peak, the presence of 57Co and 58Co in the sources has no significant influence on the gamma channel and coincidence count rates. Typical pulse height spectra from the PC channel with marked range for computer discrimination are presented in Figs. 6 and 7. The condition eb+-1 together with eXA1 when ePC -1 is fulfilled relatively easily for source selfabsorption variation of PC detection efficiency. In case of the CD method it is necessary to include into the fitting
region only the low part of pulse height spectra, in which positrons are not recorded. The activity results were compared to values obtained from the conventional coincidence standardisation, and differed by 0.36% for source self-absorption variation of the PC detection efficiency, and 0.01%, and 0.40% in case of computer discrimination methods applied on data from measurements on VYNS and Mylar foils. All results were considered in good agreement in relation to their measurement uncertainties (about 0.35%), of which the major contribution is due to the extrapolation procedure. 4. Standardisation of
57
Co
If the gamma windows are set to yield identical detection efficiencies for 122 and 136 keV photons, the activity standardisation of solution does not present any difficulties. This setting eliminates the difference in PC detection efficiencies of the two decay branches caused mainly by detection of particles originated from highly converted 14 keV transition. Regardless, the coincidence equations
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
16
140
14
84%
2%
120
14%
Count rate (s-1)
12 Count rate (s-1)
917
10 8 6
100 80 60
4
40
2
20
0
0 0
50
100 150 Channel
200
250
0
50
100 150 Channel
200
250
Fig. 7. Positrons pulse height spectrum of 5 kBq 56Co source. The count rates in the first 35 channels were practically zero, with only 2% of the total counts present below channel 40, which demonstrates that the lower part of spectra corresponds mainly to low-energy particles (up to 6 keV). This facilitates the use of computer discrimination extrapolation through the EC branch. Count rates in the range above channel 225 are affected by an electronic limiter.
Fig. 8. Total pulse height spectra of PC pulses. The peak corresponds to 6 keV KX-electrons. The computer discrimination fitting region ranged between channels 5 and 23. Pulses registered above channel 120 mainly correspond to 122 and 136 keV conversion electrons.
are simply: 1 XA1 N PC ¼ N 0 a1 XA1 þ ðaT122 ce122 þ PCg122 Þ 1 þ aT122 1 XA2 þa2 XA2 þ ðaT136 ce136 þ PCg136 Þ , 1 þ aT136 a1 a2 g122 þ g136 , Ng ¼ N0 1 þ aT122 1 þ aT136 a1 ½XA1 g122 þ ð1 XA1 ÞPCg122 0g122 NC ¼ N0 1 þ aT122 a2 0 þ ½XA2 g136 þ ð1 XA2 ÞPCg136 g136 , 1 þ aT136
where normalised extrapolation slope ‘‘k’’ is given by 0g122 a1 aT122 þ PCg122 1 k 1 þ aT122 g122 0g136 a2 þ aT136 þ PCg136 1 1 þ aT136 g136 ! 0 g122 Pce þ ð1 Pce ÞPCg122 1 . g122
(6) where N0, NPC, Ng and Nc are the same as for Eq. (1); a1, a2 are branching ratios of the g2 (122 keV) and g3 (136 keV) branches; aT122, aT136 are the total internal conversion coefficients for 122 and 136 keV g; eXA1 is the efficiency of PC for X-rays, Auger electrons and particles from 14 keV g transition for branch of g2 (122 keV); eXA2 is the efficiency of PC for X-rays and Auger electrons for branch of g2 (136 keV); ePCg122, ePCg136 are the efficiencies of PC for g-rays; ece122, ece136 are PC detection efficiencies for conversion electrons; eg122, eg136 are the gamma detection 0 0 efficiencies for 122 and 136 keV photons; eg122, eg136 are the scattered gamma detection efficiencies, for photons which were already detected in the PC. If eg122 ¼ eg136, e0 g122Ee0 g136, ePCg122EePCg136 and ece122Eece136-1 we may express NPCNg/Nc in terms of the quantity (ePC Nc/Ng), which represents an estimate for the efficiency of the proportional counter to all events (X-rays, Auger-electrons, conversion electrons and g-rays): N PC N g 1 PC N0 1 þ k , (7) Nc PC
(8)
The efficiency–extrapolation curve (Fig. 9) is a linear function of (1ePC)/ePC and k is dominated by the total probability (Pce) of internal conversion of 122 and 136 keV photons, Pce ¼ 0.0360. Ten sources, with maximum ePC ¼ 0.8 were measured. The total number of recorded events was approximately 160 million (with approximately 150 million pulses in the PC channel). A typical pulse-height spectrum for 57Co in the PC channel is given in Fig. 8, and the efficiency extrapolation graph with a distribution of residuals in Fig. 9. The PC channel discrimination level cut off almost all L-capture events. The LLD in the gamma channel with HPGe detector was set at 30 keV, and the ULD was set at about 300 keV. The selected HPGe detector has insignificant (maximum 1%) differences in both peak and total detection efficiencies for 122 and 136 keV photons, which was demonstrated by the calculation of (NC/NPC) coincidence beta and total beta count rates ratios for parts of PC spectra, corresponding to both decay branches. Details of this procedure were given by Havelka et al. (2006). The results are summarised in Table 1. Considering the method with setting of upper level discrimination (ULD) in the PC channel to reduce the extrapolation slope only as a test, all other results exhibit slight variations. The CD extrapolation method gave lower values for the normalised extrapolation slope ‘k’ and about 0.12% higher activity
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
918
204 20 pts, Mylar +2 drops Al(OH)3 susp. R=0.29%
202 200
26 pts, Mylar +1 drop Al(OH)3 susp.
NPCNγ /Nc
198 196 194
Distribution of residuals
32 pts., Mylar 94 pts., VYNS R=0.21%
192 190 -0.6
188 0.0
0.5
-0.4
-0.2
0
1.0 (1-εPC)/εPC
0.2
0.4
1.5
0.6
2.0
Fig. 9. Efficiency extrapolation curve with sources prepared on VYNS or Mylar foils, modified by dropping of Al(OH)3 suspension. The graph of distribution of residuals includes relative differences from a least-squares fitted extrapolation curve for the first 94 points. Each point represents measurement with 1 million records of individual events, and its average relative residual (R) is about 0.21%. Table 1 57 Co standardisation results Standardisation method
Number of measured sources
A (kBq g1)
d (%)
Slope ‘k’
Conventional coincidence counting—methane SCC, source self-absorption, methane—(another solution) SCC, source self-absorption SCC, source self-absorption SCC, computer discrimination SCC, computer discrimination SCC, computer discrimination with ULD in PC channel
10 (VYNS) 5 (VYNS) 3 (Mylar) 8 (VYNS)+3 (Mylar) 3 (Mylar) 7 (VYNS) 3 (Mylar)
189.00 – 188.94 188.89 189.17 189.12 189.23
0.00 – 0.032 0.056 0.092 0.065 0.123
0.0391 0.0384 – 0.0344 0.0346 0.0189
results. These can be considered as acceptable values in contrast to measurement with PC using methane at atmospheric pressure, where 122 or 136 keV conversion electrons are counted in the same part of spectra as 5 keV electrons, hence the CD method is rendered inappropriate. 5. Conclusions Methods using a digital coincidence system for the standardisation of 56Co and 57Co were presented. These standardisations served as the first test of software coincidence systems connected to a HPGe detector and to the PC filled with a propane–butane mixture, which provided the possibility of application of the computer discrimination method. Furthermore, the advantages of the software coincidence system in setting and checking of the optimal counting parameters were demonstrated. The differences between results from SCC and conventional coincidence method did not exceed 0.4% and 0.1% for the 56 Co and 57Co standardisations respectively, which were less than corresponding uncertainties.
References Be´, M.M., Christe, V., Dulieu, C., Browne, E., Chechev, V., Kuzmenko, N., Helmer, R., Nichols, A., Schonfeld, E., Dersch, R., 2004. Table de Radionucleides. BIPM, France. Buckman, S.M., Keightley, J.D., Smith, D., Woods, M.J., 1998. The validation of a digital coincidence counting system. Appl. Radiat. Isot. 49, 1135–1140. Campion, P.J., 1959. The standardization of radioisotopes by the betagamma coincidence method using high efficiency detectors. Int. J. Appl. Radiat. Isot. 4, 232–248. Havelka, M., Auerbach, P., Sochorova, J., 2002. Software coincidence counting. Appl. Radiat. Isot. 56, 265–268. Havelka, M., Auerbach, P., Sochorova, J., 2004. Application of pulse mixing method in software coincidence counting. Appl. Radiat. Isot. 60, 409–413. Havelka, M., Auerbach, P., Sochorova, J., 2006. Standardisation of 54Mn and 65Zn using a software coincidence counting system. Appl. Radiat. Isot. 60, 409–413. Keightley, J.D., Watt, G.C., 2002. Digital coincidence counting (DCC) and its use in the corrections for out-of-channel gamma events in 4pb-g coincidence counting. Appl. Radiat. Isot. 56, 205–210. Park, T.S., Lee, J.M., Hwang, H.Y., 2002. Standardization of 152Eu and 88 Y. Appl. Radiat. Isot. 56, 275–280. Smith, D., 1975. An improved method of data collection for 4pb-g coincidence measurements. Metrologia 11, 73–77.
Applied Radiation and Isotopes 66 (2008) 914–918 www.elsevier.com/locate/apradiso
Standardisation of 56Co and 57Co using software coincidence counting system Miroslav Havelka, Jana Sochorova´ Czech Metrology Institute, Inspectorate for Ionizing Radiation, Radiova´ 1, 102 00 Prague, Czech Republic
Abstract Activities of the radionuclides 56Co and 57Co were determined by the efficiency extrapolation method applied to 4p(PC)-g coincidence counting. Solutions of 56Co usually contain a significant amount of 57Co and 58Co, so the measured activity of 56Co requires correction. When the conventional coincidence method is used for 56Co standardisation, the corrections are derived from the dependence of Proportional Counter (PC) detection efficiencies for 57Co and 56Co measured using sources with mixture of 56Co and 57Co, which is complicated. These difficulties were reduced by means of a software coincidence method, with a HPGe detector in gamma channel, where the detection efficiencies were evaluated directly from the records of coincidence measurements of standardised sources. In the case of 57 Co standardisation, the software coincidence counting system was applied for the evaluation of optimal setting of coincidence parameters. The results obtained by software coincidence counting system were compared with those obtained by the conventional coincidence method. r 2008 Elsevier Ltd. All rights reserved. Keywords: 4pb-g coincidence counting; Software coincidence counting;
56
1. Introduction The radionuclides 56Co, 57Co and 58Co all decay by electron capture (EC). The decay scheme of 56Co is complicated, exhibiting ten EC(1–10) and two positron emission branches as shown in Fig. 1 (Be´ et al., 2004). All these branches after photon emissions proceed via the 847 keV level with a probability of 99.97%, thus the scheme for coincidence measurement with 847 keV photons may be considerably simplified. 57Co has a rather simple decay scheme, decaying by EC via the 136 keV level of 57Fe as shown in Fig. 2 (Be´ et al., 2004). The decay scheme of 58Co is also relatively simple; if the EC1 branch is neglected the decay scheme is similar to simplified 56Co decay scheme as shown in Fig. 3 (Be´ et al., 2004). The activities of both radionuclides were measured using the 4p(PC)-g coincidence counting efficiency extrapolation method. These standardisations can be realised by conventional (Campion, 1959), or by digital method (Buckman et al., 1998; Park et al., 2002; Keightley and Watt, 2002; Havelka et al., Corresponding author. Fax: +420 266020466.
E-mail address: [email protected] (M. Havelka). 0969-8043/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2008.02.034
Co standardisation;
57
Co standardisation
2002), that here profits from the possibility to evaluate the same data records with different coincidence parameter settings.
2. Experimental set-up Two detector systems have been used, the first for measurement with software coincidence counting, the second was connected to conventional coincidence modules and served as comparative system. The first system consisted from aluminium cylindrical proportional counter (PC) (60 mm inner-height and 52 mm inner-diameter) and a HPGe detector in the gamma channel. The sources were placed about 26 mm above the HPGe detector end cap. This system operated with a mixture of propane and butane at atmospheric pressure in a gas flow arrangement. In the second system the 4p detector was a stainlesssteel cylindrical proportional counter (two halves of 1 8 mm inner-height and 64 mm inner-diameter), using methane at atmospheric pressure in a gas flow arrangement. The g-ray detection assembly consisted of two opposing NaI(Tl) detectors mounted close to the PC. The
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
915
utilised the conventional method of altering the selfabsorption in the sources as well as the computer discrimination (CD) method (Smith, 1975) in the PC channel. The SCC system and the formulae used for data processing have been described in previous papers (Havelka et al., 2002, 2004, 2006).
56Co
EC(1-10) β+(1,2) γ 847 keV
3. Standardisation of
γ1
56Fe
Fig. 1. Simplified decay scheme of 56Co. The branching ratios for sum of EC and b+(1,2) branches are aEC ¼ 0.8042 and ab+(1) ¼ 0.0104, ab+(2) ¼ 0.1829.
57Co
56
Co
The coincidence measurement was carried out with a gamma window setting on the 847 keV peak, which simplified the standardisation, however, in spite of all branches proceeding via the level emitting 847 keV photons, the gamma detection efficiencies for g-rays are different for EC and positron branches due to summing effects. The coincidence equations (neglecting conversion electrons) are: N PC ¼ N 0 ½aEC ðXA þ ð1 XA ÞPCg Þ
EC
þ abþ ðbþ þ ð1 bþ ÞPCg Þ, N g ¼ N 0 ðaEC gðECÞ þ abþ gðbþÞ Þ,
136 keV
N C ¼ N 0 ½aEC ðXA gðECÞ þ ð1 XA ÞPCg 0gðECÞ Þ γ2
γ3
þ abþ ðbþ gðbþÞ þ ð1 bþ ÞPCg 0gðbþÞ Þ,
14 keV γ1 57Fe
Fig. 2. Simplified decay scheme of 57Co. The branching ratios for g2 (122 keV) and g3 (136 keV) branches are a1 ¼ 0.876 and a2 ¼ 0.123. The total internal conversion coefficients are aT14 ¼ 8.58, aT122 ¼ 0.0236 and aT136 ¼ 0.148.
58Co
EC1 a1
1675 keV γ3
EC2 a2
γ2
β+ a3
810 keV γ1 58
Fe
Fig. 3. Decay scheme of 58Co. The branching ratios are a1 ¼ 0.0121, a2 ¼ 0.8379 and a3 ¼ 0.1500.
sources were prepared by deposition of 20–50 mg aliquots of active solution containing about 20 mg g1 carrier on 40–60 mg cm2 gold-coated VYNS foils or on gold-coated 850 mg cm2 Mylar films, treated with Ludox and insulin. All sources were treated in an atmosphere of NH3 to achieve higher PC detection efficiencies. The conventional coincidence system used the source self-absorption variation of PC efficiency via the addition of extra mass to the source. The software coincidence counting (SCC) system
(1)
where N0 is the source activity; NPC the (corrected) count rate in the proportional counter; Ng the (corrected) count rate in the gamma detector; Nc the (corrected) count rate of coincidences; aEC, ab+ are branching ratios for EC and positrons branches; eXA the efficiency of PC for X-rays and Auger electrons; eb+ the efficiency of PC for positrons; ePCg the efficiency of PC for g-rays; eg(EC), eg(b+) are the gamma detection efficiencies with an 847 keV window setting for g-rays corresponding EC and b+ branches; e0 g(EC), e0 g(b+) are the scattered gamma detection efficiencies which are already detected in the PC. Assuming that eb+ is a linear function of ePC as shown in Fig. 4 and for ePC-1 as eb+-1, e0 g(EC)Ee0 g(b+)E0 and eg(b+)E0.95eg(EC), we may express associated efficiency– extrapolation curve NPCNg/Nc in terms of the quantity (ePC Nc/Ng), which represents an estimate for the efficiency of the proportional counter to all events (positrons, X-rays, Auger-electrons and g-rays): N PC N g 1 PC N0 1 þ k , (2) Nc PC where the normalised extrapolation slope ‘‘k’’ is given by gðbþÞ k PCg þ abþ 1 . (3) gðECÞ The summing events are more frequent for positrons than for EC decay, mainly due to emission of annihilation photons. The 5% difference between the gamma detection efficiencies of the EC and positron branches caused an increase of the normalised extrapolation slope of about 1%, nevertheless the value N0 was not influenced. The real solutions always contain significant impurity levels of 57Co and 58Co, so NPC had to be corrected for
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
916
0.99
0.6 0.5
εPC (56Co)
0.98
εβ+
0.97 0.96
0.4 0.3 0.2 0.1
0.95 0.94 0.0
0.0 0.0 0.1
0.2
0.3
0.4
0.2
0.4
0.5
εPC Fig. 4. Dependence of eb+ on ePC for 56Co; calculated from software coincidence data using count rates of 511 keV peak area and corresponding coincidence count rates.
their contributions:
90 80
¼ N PCð56Coþ57Coþ58CoÞ N 57Co PCð57CoÞ N 58Co PCð58CoÞ ,
where N57Co, N58Co are activities of 57Co and 58Co measured by gamma ray spectrometry, ePC(57Co) and ePC(58Co) are the PC detection efficiencies. The efficiency ePC(57Co) can be calculated in case of digital coincidence counting from the ratios of the count rates of 122 and 136 keV peaks and the corresponding coincidence count rates according to the formula supposing that all conversion electrons arising from the internal conversion of the 122 and 136 keV photons of total probability (Pce ¼ 0.0360) are detected:
CD fitting region
70 Count rate (s-1)
(4)
PCð57CoÞ
0.8
Fig. 5. Variation of PC detection efficiency of 56Co on PC detection efficiency of 57Co; as calculated from software coincidence data. If ePC(57Co)o0.3, only positrons are detected in PC from 56Co decay. The similar graph can be obtained from measurements of sources with a mixture of both radionuclides.
N PC ¼ N PCð56Coþ57Coþ58CoÞ N PCð57CoÞ N PCð58CoÞ
N Cð122; 136Þ ð1 Pce Þ þ Pce . N gð122; 136Þ
0.6
εPC (57Co)
60 50 40 30 20 10 0 0
50
100 150 Channnel
200
250
Fig. 6. Pulse height spectra of PC channel pulses. The peak corresponds to 6 keV KX-electrons. The 56Co source activity was about 5 kBq.
(5)
The efficiency ePC(57Co) may be also derived from the measured value of ePC(56Co) (the PC detection efficiency for 56 Co) by means of a correlation graph between ePC(56Co) and ePC(57Co) as shown in Fig. 5. This procedure in the case of conventional standardisation requires extra measurements of sources with a mixture of single radionuclides and usually results in less precise values. The efficiency ePC(58Co) was estimated from ePC(56Co) following the similarity of the PC channel pulse height spectra of 58Co and 56Co, and assuming the PC detection efficiency for positrons is approximately unity. In the case of a gamma window setting on the 847 keV peak, the presence of 57Co and 58Co in the sources has no significant influence on the gamma channel and coincidence count rates. Typical pulse height spectra from the PC channel with marked range for computer discrimination are presented in Figs. 6 and 7. The condition eb+-1 together with eXA1 when ePC -1 is fulfilled relatively easily for source selfabsorption variation of PC detection efficiency. In case of the CD method it is necessary to include into the fitting
region only the low part of pulse height spectra, in which positrons are not recorded. The activity results were compared to values obtained from the conventional coincidence standardisation, and differed by 0.36% for source self-absorption variation of the PC detection efficiency, and 0.01%, and 0.40% in case of computer discrimination methods applied on data from measurements on VYNS and Mylar foils. All results were considered in good agreement in relation to their measurement uncertainties (about 0.35%), of which the major contribution is due to the extrapolation procedure. 4. Standardisation of
57
Co
If the gamma windows are set to yield identical detection efficiencies for 122 and 136 keV photons, the activity standardisation of solution does not present any difficulties. This setting eliminates the difference in PC detection efficiencies of the two decay branches caused mainly by detection of particles originated from highly converted 14 keV transition. Regardless, the coincidence equations
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
16
140
14
84%
2%
120
14%
Count rate (s-1)
12 Count rate (s-1)
917
10 8 6
100 80 60
4
40
2
20
0
0 0
50
100 150 Channel
200
250
0
50
100 150 Channel
200
250
Fig. 7. Positrons pulse height spectrum of 5 kBq 56Co source. The count rates in the first 35 channels were practically zero, with only 2% of the total counts present below channel 40, which demonstrates that the lower part of spectra corresponds mainly to low-energy particles (up to 6 keV). This facilitates the use of computer discrimination extrapolation through the EC branch. Count rates in the range above channel 225 are affected by an electronic limiter.
Fig. 8. Total pulse height spectra of PC pulses. The peak corresponds to 6 keV KX-electrons. The computer discrimination fitting region ranged between channels 5 and 23. Pulses registered above channel 120 mainly correspond to 122 and 136 keV conversion electrons.
are simply: 1 XA1 N PC ¼ N 0 a1 XA1 þ ðaT122 ce122 þ PCg122 Þ 1 þ aT122 1 XA2 þa2 XA2 þ ðaT136 ce136 þ PCg136 Þ , 1 þ aT136 a1 a2 g122 þ g136 , Ng ¼ N0 1 þ aT122 1 þ aT136 a1 ½XA1 g122 þ ð1 XA1 ÞPCg122 0g122 NC ¼ N0 1 þ aT122 a2 0 þ ½XA2 g136 þ ð1 XA2 ÞPCg136 g136 , 1 þ aT136
where normalised extrapolation slope ‘‘k’’ is given by 0g122 a1 aT122 þ PCg122 1 k 1 þ aT122 g122 0g136 a2 þ aT136 þ PCg136 1 1 þ aT136 g136 ! 0 g122 Pce þ ð1 Pce ÞPCg122 1 . g122
(6) where N0, NPC, Ng and Nc are the same as for Eq. (1); a1, a2 are branching ratios of the g2 (122 keV) and g3 (136 keV) branches; aT122, aT136 are the total internal conversion coefficients for 122 and 136 keV g; eXA1 is the efficiency of PC for X-rays, Auger electrons and particles from 14 keV g transition for branch of g2 (122 keV); eXA2 is the efficiency of PC for X-rays and Auger electrons for branch of g2 (136 keV); ePCg122, ePCg136 are the efficiencies of PC for g-rays; ece122, ece136 are PC detection efficiencies for conversion electrons; eg122, eg136 are the gamma detection 0 0 efficiencies for 122 and 136 keV photons; eg122, eg136 are the scattered gamma detection efficiencies, for photons which were already detected in the PC. If eg122 ¼ eg136, e0 g122Ee0 g136, ePCg122EePCg136 and ece122Eece136-1 we may express NPCNg/Nc in terms of the quantity (ePC Nc/Ng), which represents an estimate for the efficiency of the proportional counter to all events (X-rays, Auger-electrons, conversion electrons and g-rays): N PC N g 1 PC N0 1 þ k , (7) Nc PC
(8)
The efficiency–extrapolation curve (Fig. 9) is a linear function of (1ePC)/ePC and k is dominated by the total probability (Pce) of internal conversion of 122 and 136 keV photons, Pce ¼ 0.0360. Ten sources, with maximum ePC ¼ 0.8 were measured. The total number of recorded events was approximately 160 million (with approximately 150 million pulses in the PC channel). A typical pulse-height spectrum for 57Co in the PC channel is given in Fig. 8, and the efficiency extrapolation graph with a distribution of residuals in Fig. 9. The PC channel discrimination level cut off almost all L-capture events. The LLD in the gamma channel with HPGe detector was set at 30 keV, and the ULD was set at about 300 keV. The selected HPGe detector has insignificant (maximum 1%) differences in both peak and total detection efficiencies for 122 and 136 keV photons, which was demonstrated by the calculation of (NC/NPC) coincidence beta and total beta count rates ratios for parts of PC spectra, corresponding to both decay branches. Details of this procedure were given by Havelka et al. (2006). The results are summarised in Table 1. Considering the method with setting of upper level discrimination (ULD) in the PC channel to reduce the extrapolation slope only as a test, all other results exhibit slight variations. The CD extrapolation method gave lower values for the normalised extrapolation slope ‘k’ and about 0.12% higher activity
ARTICLE IN PRESS M. Havelka, J. Sochorova´ / Applied Radiation and Isotopes 66 (2008) 914–918
918
204 20 pts, Mylar +2 drops Al(OH)3 susp. R=0.29%
202 200
26 pts, Mylar +1 drop Al(OH)3 susp.
NPCNγ /Nc
198 196 194
Distribution of residuals
32 pts., Mylar 94 pts., VYNS R=0.21%
192 190 -0.6
188 0.0
0.5
-0.4
-0.2
0
1.0 (1-εPC)/εPC
0.2
0.4
1.5
0.6
2.0
Fig. 9. Efficiency extrapolation curve with sources prepared on VYNS or Mylar foils, modified by dropping of Al(OH)3 suspension. The graph of distribution of residuals includes relative differences from a least-squares fitted extrapolation curve for the first 94 points. Each point represents measurement with 1 million records of individual events, and its average relative residual (R) is about 0.21%. Table 1 57 Co standardisation results Standardisation method
Number of measured sources
A (kBq g1)
d (%)
Slope ‘k’
Conventional coincidence counting—methane SCC, source self-absorption, methane—(another solution) SCC, source self-absorption SCC, source self-absorption SCC, computer discrimination SCC, computer discrimination SCC, computer discrimination with ULD in PC channel
10 (VYNS) 5 (VYNS) 3 (Mylar) 8 (VYNS)+3 (Mylar) 3 (Mylar) 7 (VYNS) 3 (Mylar)
189.00 – 188.94 188.89 189.17 189.12 189.23
0.00 – 0.032 0.056 0.092 0.065 0.123
0.0391 0.0384 – 0.0344 0.0346 0.0189
results. These can be considered as acceptable values in contrast to measurement with PC using methane at atmospheric pressure, where 122 or 136 keV conversion electrons are counted in the same part of spectra as 5 keV electrons, hence the CD method is rendered inappropriate. 5. Conclusions Methods using a digital coincidence system for the standardisation of 56Co and 57Co were presented. These standardisations served as the first test of software coincidence systems connected to a HPGe detector and to the PC filled with a propane–butane mixture, which provided the possibility of application of the computer discrimination method. Furthermore, the advantages of the software coincidence system in setting and checking of the optimal counting parameters were demonstrated. The differences between results from SCC and conventional coincidence method did not exceed 0.4% and 0.1% for the 56 Co and 57Co standardisations respectively, which were less than corresponding uncertainties.
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