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Two-parametric method for measuring the radioactive concentration of 22Na
Nuclear Instruments and Methods in Physics Research A312 (1992) 76-tt0 North-11olland
NUCLEAR INSTRUMENTS & METHODS
IN PHYSICS RESEARCH Svoion A
Two-parametric method for measuring the radioactive concentration of 22 Na A. Chylinski and T. Radoszewski
The Radioisotope Research Centre, 05-400 kvierk, Poland
A two-parametric method of absolute standardization employing coincidence and anticoincidence counting, is described as applied to the measurement of 22 Na . The results indicate that this method of counting gives a lower level of overall uncertainty and is more reliable than the other known methods. The special device used for these measurements as well as the method of analyzing the data is described.
1 . Introduction The main reason for the work prescated below was to prove that coincidence and anticoincidence methods can be combined with a two-parametic system in parallel measurements . The radionuclide in question was 22 Na and as detector a liquid scintillator was used . The advantage of the four obtained results, is shown.
(1) ß + particles with -y-photons of 1.275 MeV, (2) ß + particles with annihilation photons. In the first case the following notation is used :
2. The counting equipment The counting equipment comprises the four-fold scintillation head shown in fig. 1 and the electronic circuit in fig. 2. The four-fold scintillation head contains two photomultipliers looking into a counting vial filled with a liquid scintillator for ß-particle counting, and two scintillation counters for photon counting . The electronic circuit contains a two-stage coincidence system . The first-stage coincidence unit forms the 0-counting channel. The two scintillation counters with Nal(Tl) crystals working in sum mode form the -y-counting channel. The second-stage coincidence and anticoincidence units are connected to the output of these two counting channels .
3. The measurement of 22 Na 22
Na decays for 90% by emitting ß + particles and for 10% by EC, followed by emission of -y-photons of 1 .275 MeV. Additionally, photons of 511 keV are created in the annihilation process of the (3 + particles. We consider two types of coincidence involving -y-gates set in the 1 .275 MeV aid 0.511 MeV peaks respectively :
Fig. 1 . The four-fold scintillation head with counting vial filled with liquid scintillator and two Nal(TI) crystals . (1) Counting vial with liquid scintillator and radioactive sample ; (2) photomultipliers, (3) Nal (TI) crystal; (4) preamplifier ; (5) spring diaphragm holder; (6) vial lift : (7) spring diaphragm regulator; (ti) counting vial store; (9) light-tight sleeve ; (10) shield for counting vials; (11) photomultiplier for 0-counting .
0168-90(!2/9?/5()5 .()0 '"; 1992 - Elsevier Science Publishers B.V . All rights reserved
A. Chrlhiski. T Rados.rarski / Akeasacrtiam rachcxicttt e concentration
The relations (6) shoo%% that catr :apa,l~atiaaaa to mans extrapolation to f ` , * I %%hich i% inapproprwic and theref(ire a correction factor i-, introduced in the following equation : V NP, ) =-- Nj h(1-d))+a®j (1 - (t))+ (h N( . e yd
Fig . 2. Simplified block-diagram of two-stage coincidence system . (PW) preamplifier ; (W) amplifier: (A) analyser: dead-time unit : (K, . K r ) coincidence unit : (AK) anticoincidcnce unit.
a b
- probability of EC decay, - probability of ß + decay, EP - efficiency of ß + counting, - counting efficiency of -y-photons in liquid scintillator, Np counting rate in ß-channel, NY counting rate in -y-channel, EY efficiency of -y-photon counting, E, I - efficiency for sum effect of annihilation photons, N( , - coincidence counting rate, NA(, - anti-coincidence counting rate . With this notation the following relations can be prçsentcd : (1)
Nj~ -N [bEP + (1 - bf o )(b] ,
2
NY _ N, 1{aE y + b[E Y +' 1 - EY)E_ .J
3
we obtain Nc = No bEPE yd'
(4 )
After transformation of eqs. (1), (2) and (4) the following relation pan be obtained: r 1 - F,, h I [r nF Y + bF . .VP, IV bE13
1
Eyd
I.
(5)
., -> 1, we obtain After extrapolation N(/N bE~e,d
aé Y + ME Yd
I,
aE Eyd
(NY-NA( .)R1-
All the counting rates were corrected for dead time and for the resolving times of the coincidence and anticoincidcnce gates . Background was subtracted . In the second case, the ß + particles and annihilation photons in coincidence, additional notation is introduced: EA counting efficiency in the -y-channel for annihilation photons, E 5(counting efficiency in the -y-channel for scatter y-photons in the energy range of annihilation photons . The basic equations are as follow:
(5a)
(10)
(1 - be 1 ) ~b j,
( II)
- bEAESC I .
When we denote bE sc + bE A - bE AESC- = bEASC " eq. (11) can be expressed as follows:
(12)
NY = N,[bE ASC + aE sc I
(13)
and for coincidence N, = ]V bEtiEASC
(14)
After transformation of eqs . (10). (13) and (14) the following equation is obtained : N N
and further b(E p -1)=
Nu
Ny = Nll[ bEA + aEs(- + bE sc
EYd = IE Y + ( I - EY)E'-j,
= N I l +
N( . Rl
and for anticoincidcnce counting N,, NY
% =N,[bE i3 +
After the substitution
N(`
which arises from the relation (.5) given above . To establish the correction factor given in the square brackets one has to remember that (b is the slope of N,, NY /N, as a function of (I - N,/N},)l(N, /NY ) and can be obtained experimentally, e,, is obtained also from measurements. Effeeieney E,, can be calculated from eq. (3) having determined E-, ,, . Taking the correction factor in brackets in eq. (7) as R, one obtains for coincidence counting N1, NY N -
N, - decay rate in the sample,
(7)
N,
-IV
~1
1 +
1 - bE bE I3
i3 à j[ b+a
ESC EASC
j~ .
(15)
After extrapolation N,/N-, - 1 a relation is obtained that is similar to that in the first case:
b
1 1I(a) . COINCIDENCE METHODS
A. Chylhiski, T. Radoszctvski / Measuring radioactive concentratioll
78
511 keV
A
(1022 keV)
y 1275 keV
annihilation Fig. 3. Spectra of -y-radiations for
and further N13 NY N~
- NO [(b
+ a Esc
EASC )
(1 -
) +
J
(16)
is the coincidence efficiency of y-channel and can be experimentalltly determined by measuring scattered radiation from Co . EASC
Z `Na Na.
22
Taking the correction factor in the square brackets in eq . (16) as R-, the equation for coincidence counting can be obtained : N N (3 Y
N = N`
R
` ,
and for anticoincidence counting : No NY
Ao x 10
8
7,8
Fig. 4. Extrapolation carve `;, 7
second case of coincidence) .
(17)
A . CYtyfit"tski, . Rculoszewcski / Aleusurink rctdicxtrtN r concentration
79
Table I(a) Results of `= Nat measurements of coincidence and anticoincidence counting with the two-parametric system . fir%t case : y photon% ''
Source number
th
f (1
1
0 .8972411
0.897713 0.898463 0.892525 0.898703 0 .897733 0 .900122 0.900085
3 4 5 6 7 8 ~ R = 0 .9921) .
A, , jK
= 411 .16 kBq/g.
0 .1123813
0.023919 0.024211 0.024175 0.023965 0.0240116 0.024017 0.023963 AutAK
Coincidence A,lt; [kBq/gj"
0.11244 0.0302 0.0386 0.0384 0 .0291 11 .0357 0.0387 0.0366
411 .727 407.416 406.337 406.221 405.449 409.848 411 .666 408.234
Anticoincidence '~'IIAK
[kBq/gj r,
413.148 410.593 409.684 410.075 409.260 412.691 413.453 411 .394
= 414.23 kBq/g . J = 0.7r . A , = 412.69 kBq/g. t S,, = 0.W-~ . 6 = 0.l0rie .
Table 1(b) Same as table la for the second case : 0'-annihilation photons `'
Source number 1
2 3 4 5 6 7 8
E~
E
0.962911 0.957345 0.956308 0.955905 0.956321 0.973680 0 .981497 0.976909
0.078622 0.079955 0.079907 0.080524 0.079376 0.068554 0.068093 0.066860
Coincidence A,,K [kBq/gj "
Y
0.0357 0.0434 0.0395 0.0487 0.0342 0.0406 0.0402 0.0555
384.571 382.805 382.452 380.289 380.212 379.485 378.280 374.904
Anticoincidence A OAK [kBq/gj " 386.117 385.569 384.890 384.862 383.034 382.097 379.419 377 .353
R, = 0 .9233, A ,K = 411 .08 kBq/g . A 2AK = 41473 kBq/g, A = 0 .8ri . A , = 412.91 kBq/g. t S,_ = 0.74ri. S = 0.10r'r . " J A 1. , = 0.05( . A = 412.80 kBq/g . t S, = 0.461-i . n = 011 (`i . ~'
4 . Results of
22 Na
activity measurements
Using the two-parametric methods described in the previous part, measurements of eight sources of 22 Na have been performed to establish the radioactive concentration of 22 Na solution . First the parameters for two-parametric spectra have to be fixed for the -y-channel . A typical spectrum is shown in fig . 3. For -y-rays of 1275 keV and for the annihilation photons of 1022 keV the analyzer window was fixed at 6 .2-10 V (the first case of coincidence) . For annihilation photons of 511 keV the analyzer window was fixed at 1 .8-3.8 V (the second case of coincidence). In the ß-channel only ß + particles were detertert (-7c=ro SC-nçitivity t(t F.Ç radiation)For each 22 Na source the extrapolation curve as a function of the ratio (1 - E~)/EGG was determined to be as shown in fig. 4. It was obtained by changing the high tension on the photomultipliers . Full results of the measurements are shown in table 1, together with all uncertainties, with the following notation : A , K = the mean value of radioactive: concentration in coincidence mode corrected with R, factor,
= the mean value of radioactive concentration in anti-coincidence mode corrected with R, factor, = the mean value of radioactive concentration A 02K in coincidence mode corrected with R, factor, A ,AK = the mean value of radioactive concentration in anti-coincidence mode corrected with R, factor, A = the mean value of corrected radioactive concentration for all measurements, S.,. = standard deviation . t S, = statistical error with a level of confidence of (1.99, = systematic error .
A0,AK
5 . Conclusion
The results with uncertainties of the two-parametric method shown in table 1 indicate that this method is better than others. The parallel coincidence and the anticoincidence counting in one measurement process gives four results instantly comparable with one another and in this way reduces the overall uncertainty . 111(x) . COINCIDENCE METHODS
80
A . Clhyliciski, 7: Rurloszewski / Measuring rurlicxuvi~c~ vollventratiutt
References [1) A. Chylinski and T. Radoszewski, Nucl . Instr. and Meth . 48 (1972) 109. [21 A. Chylinski and T. Radoszewski, Isotope npraxis, vol. 17 (Germany, 1980) HA, pp . 118-121.
[3j A. Chylinski and T. Radoszewski, Proc . Int. Symp. of Comecon Countries, Czopak, vol. 1 (Budapest, Ilungary, 1984) pp . 225-237 . [4] J. Legrand et al ., Table de Radionuclides, vol. l, LMR1, France (1975) .
NUCLEAR INSTRUMENTS & METHODS
IN PHYSICS RESEARCH Svoion A
Two-parametric method for measuring the radioactive concentration of 22 Na A. Chylinski and T. Radoszewski
The Radioisotope Research Centre, 05-400 kvierk, Poland
A two-parametric method of absolute standardization employing coincidence and anticoincidence counting, is described as applied to the measurement of 22 Na . The results indicate that this method of counting gives a lower level of overall uncertainty and is more reliable than the other known methods. The special device used for these measurements as well as the method of analyzing the data is described.
1 . Introduction The main reason for the work prescated below was to prove that coincidence and anticoincidence methods can be combined with a two-parametic system in parallel measurements . The radionuclide in question was 22 Na and as detector a liquid scintillator was used . The advantage of the four obtained results, is shown.
(1) ß + particles with -y-photons of 1.275 MeV, (2) ß + particles with annihilation photons. In the first case the following notation is used :
2. The counting equipment The counting equipment comprises the four-fold scintillation head shown in fig. 1 and the electronic circuit in fig. 2. The four-fold scintillation head contains two photomultipliers looking into a counting vial filled with a liquid scintillator for ß-particle counting, and two scintillation counters for photon counting . The electronic circuit contains a two-stage coincidence system . The first-stage coincidence unit forms the 0-counting channel. The two scintillation counters with Nal(Tl) crystals working in sum mode form the -y-counting channel. The second-stage coincidence and anticoincidence units are connected to the output of these two counting channels .
3. The measurement of 22 Na 22
Na decays for 90% by emitting ß + particles and for 10% by EC, followed by emission of -y-photons of 1 .275 MeV. Additionally, photons of 511 keV are created in the annihilation process of the (3 + particles. We consider two types of coincidence involving -y-gates set in the 1 .275 MeV aid 0.511 MeV peaks respectively :
Fig. 1 . The four-fold scintillation head with counting vial filled with liquid scintillator and two Nal(TI) crystals . (1) Counting vial with liquid scintillator and radioactive sample ; (2) photomultipliers, (3) Nal (TI) crystal; (4) preamplifier ; (5) spring diaphragm holder; (6) vial lift : (7) spring diaphragm regulator; (ti) counting vial store; (9) light-tight sleeve ; (10) shield for counting vials; (11) photomultiplier for 0-counting .
0168-90(!2/9?/5()5 .()0 '"; 1992 - Elsevier Science Publishers B.V . All rights reserved
A. Chrlhiski. T Rados.rarski / Akeasacrtiam rachcxicttt e concentration
The relations (6) shoo%% that catr :apa,l~atiaaaa to mans extrapolation to f ` , * I %%hich i% inapproprwic and theref(ire a correction factor i-, introduced in the following equation : V NP, ) =-- Nj h(1-d))+a®j (1 - (t))+ (h N( . e yd
Fig . 2. Simplified block-diagram of two-stage coincidence system . (PW) preamplifier ; (W) amplifier: (A) analyser: dead-time unit : (K, . K r ) coincidence unit : (AK) anticoincidcnce unit.
a b
- probability of EC decay, - probability of ß + decay, EP - efficiency of ß + counting, - counting efficiency of -y-photons in liquid scintillator, Np counting rate in ß-channel, NY counting rate in -y-channel, EY efficiency of -y-photon counting, E, I - efficiency for sum effect of annihilation photons, N( , - coincidence counting rate, NA(, - anti-coincidence counting rate . With this notation the following relations can be prçsentcd : (1)
Nj~ -N [bEP + (1 - bf o )(b] ,
2
NY _ N, 1{aE y + b[E Y +' 1 - EY)E_ .J
3
we obtain Nc = No bEPE yd'
(4 )
After transformation of eqs. (1), (2) and (4) the following relation pan be obtained: r 1 - F,, h I [r nF Y + bF . .VP, IV bE13
1
Eyd
I.
(5)
., -> 1, we obtain After extrapolation N(/N bE~e,d
aé Y + ME Yd
I,
aE Eyd
(NY-NA( .)R1-
All the counting rates were corrected for dead time and for the resolving times of the coincidence and anticoincidcnce gates . Background was subtracted . In the second case, the ß + particles and annihilation photons in coincidence, additional notation is introduced: EA counting efficiency in the -y-channel for annihilation photons, E 5(counting efficiency in the -y-channel for scatter y-photons in the energy range of annihilation photons . The basic equations are as follow:
(5a)
(10)
(1 - be 1 ) ~b j,
( II)
- bEAESC I .
When we denote bE sc + bE A - bE AESC- = bEASC " eq. (11) can be expressed as follows:
(12)
NY = N,[bE ASC + aE sc I
(13)
and for coincidence N, = ]V bEtiEASC
(14)
After transformation of eqs . (10). (13) and (14) the following equation is obtained : N N
and further b(E p -1)=
Nu
Ny = Nll[ bEA + aEs(- + bE sc
EYd = IE Y + ( I - EY)E'-j,
= N I l +
N( . Rl
and for anticoincidcnce counting N,, NY
% =N,[bE i3 +
After the substitution
N(`
which arises from the relation (.5) given above . To establish the correction factor given in the square brackets one has to remember that (b is the slope of N,, NY /N, as a function of (I - N,/N},)l(N, /NY ) and can be obtained experimentally, e,, is obtained also from measurements. Effeeieney E,, can be calculated from eq. (3) having determined E-, ,, . Taking the correction factor in brackets in eq. (7) as R, one obtains for coincidence counting N1, NY N -
N, - decay rate in the sample,
(7)
N,
-IV
~1
1 +
1 - bE bE I3
i3 à j[ b+a
ESC EASC
j~ .
(15)
After extrapolation N,/N-, - 1 a relation is obtained that is similar to that in the first case:
b
1 1I(a) . COINCIDENCE METHODS
A. Chylhiski, T. Radoszctvski / Measuring radioactive concentratioll
78
511 keV
A
(1022 keV)
y 1275 keV
annihilation Fig. 3. Spectra of -y-radiations for
and further N13 NY N~
- NO [(b
+ a Esc
EASC )
(1 -
) +
J
(16)
is the coincidence efficiency of y-channel and can be experimentalltly determined by measuring scattered radiation from Co . EASC
Z `Na Na.
22
Taking the correction factor in the square brackets in eq . (16) as R-, the equation for coincidence counting can be obtained : N N (3 Y
N = N`
R
` ,
and for anticoincidence counting : No NY
Ao x 10
8
7,8
Fig. 4. Extrapolation carve `;, 7
second case of coincidence) .
(17)
A . CYtyfit"tski, . Rculoszewcski / Aleusurink rctdicxtrtN r concentration
79
Table I(a) Results of `= Nat measurements of coincidence and anticoincidence counting with the two-parametric system . fir%t case : y photon% ''
Source number
th
f (1
1
0 .8972411
0.897713 0.898463 0.892525 0.898703 0 .897733 0 .900122 0.900085
3 4 5 6 7 8 ~ R = 0 .9921) .
A, , jK
= 411 .16 kBq/g.
0 .1123813
0.023919 0.024211 0.024175 0.023965 0.0240116 0.024017 0.023963 AutAK
Coincidence A,lt; [kBq/gj"
0.11244 0.0302 0.0386 0.0384 0 .0291 11 .0357 0.0387 0.0366
411 .727 407.416 406.337 406.221 405.449 409.848 411 .666 408.234
Anticoincidence '~'IIAK
[kBq/gj r,
413.148 410.593 409.684 410.075 409.260 412.691 413.453 411 .394
= 414.23 kBq/g . J = 0.7r . A , = 412.69 kBq/g. t S,, = 0.W-~ . 6 = 0.l0rie .
Table 1(b) Same as table la for the second case : 0'-annihilation photons `'
Source number 1
2 3 4 5 6 7 8
E~
E
0.962911 0.957345 0.956308 0.955905 0.956321 0.973680 0 .981497 0.976909
0.078622 0.079955 0.079907 0.080524 0.079376 0.068554 0.068093 0.066860
Coincidence A,,K [kBq/gj "
Y
0.0357 0.0434 0.0395 0.0487 0.0342 0.0406 0.0402 0.0555
384.571 382.805 382.452 380.289 380.212 379.485 378.280 374.904
Anticoincidence A OAK [kBq/gj " 386.117 385.569 384.890 384.862 383.034 382.097 379.419 377 .353
R, = 0 .9233, A ,K = 411 .08 kBq/g . A 2AK = 41473 kBq/g, A = 0 .8ri . A , = 412.91 kBq/g. t S,_ = 0.74ri. S = 0.10r'r . " J A 1. , = 0.05( . A = 412.80 kBq/g . t S, = 0.461-i . n = 011 (`i . ~'
4 . Results of
22 Na
activity measurements
Using the two-parametric methods described in the previous part, measurements of eight sources of 22 Na have been performed to establish the radioactive concentration of 22 Na solution . First the parameters for two-parametric spectra have to be fixed for the -y-channel . A typical spectrum is shown in fig . 3. For -y-rays of 1275 keV and for the annihilation photons of 1022 keV the analyzer window was fixed at 6 .2-10 V (the first case of coincidence) . For annihilation photons of 511 keV the analyzer window was fixed at 1 .8-3.8 V (the second case of coincidence). In the ß-channel only ß + particles were detertert (-7c=ro SC-nçitivity t(t F.Ç radiation)For each 22 Na source the extrapolation curve as a function of the ratio (1 - E~)/EGG was determined to be as shown in fig. 4. It was obtained by changing the high tension on the photomultipliers . Full results of the measurements are shown in table 1, together with all uncertainties, with the following notation : A , K = the mean value of radioactive: concentration in coincidence mode corrected with R, factor,
= the mean value of radioactive concentration in anti-coincidence mode corrected with R, factor, = the mean value of radioactive concentration A 02K in coincidence mode corrected with R, factor, A ,AK = the mean value of radioactive concentration in anti-coincidence mode corrected with R, factor, A = the mean value of corrected radioactive concentration for all measurements, S.,. = standard deviation . t S, = statistical error with a level of confidence of (1.99, = systematic error .
A0,AK
5 . Conclusion
The results with uncertainties of the two-parametric method shown in table 1 indicate that this method is better than others. The parallel coincidence and the anticoincidence counting in one measurement process gives four results instantly comparable with one another and in this way reduces the overall uncertainty . 111(x) . COINCIDENCE METHODS
80
A . Clhyliciski, 7: Rurloszewski / Measuring rurlicxuvi~c~ vollventratiutt
References [1) A. Chylinski and T. Radoszewski, Nucl . Instr. and Meth . 48 (1972) 109. [21 A. Chylinski and T. Radoszewski, Isotope npraxis, vol. 17 (Germany, 1980) HA, pp . 118-121.
[3j A. Chylinski and T. Radoszewski, Proc . Int. Symp. of Comecon Countries, Czopak, vol. 1 (Budapest, Ilungary, 1984) pp . 225-237 . [4] J. Legrand et al ., Table de Radionuclides, vol. l, LMR1, France (1975) .