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Method of absolute gamma sources activity measurement using a scintillation counter in fixed geometry
NUCLEAR
INSTRUMENTS
AND METHODS
55 (1967) 329-332; ( ~ N O R T H - H O L L A N D
PUBLISHING
CO.
M E T H O D OF ABSOLUTE GAMMA SOURCES ACTIVITY MEASUREMENT USING A SCINTILLATION COUNTER IN FIXED GEOMETRY K. Z A R N O W I E C K I
Institute of Nuclear Research, Otwock, Swierk. Poland Received 23 May 1967 It has been calculated that the efficiency of a gamma scintillation counter is lower than the one obtained from a simple exponential formula. The influence of the escape of fluorescence X-rays and annihilation photons and the presence of low energy Compton electrons has been taken into account. It has been proved that a
counter in the collimated beam geometry can be used for absolute measurements of gamma source activity. The method of calculating the correction factors for filters, and a collimator permeability is given. The experimental results agree very well with theoretical calculations.
It is often supposed that every photon collision in a scintillator results in a count, and that the counter efficiency for a parallel beam is a simple exponential function of crystal thickness. On these grounds the efficiencies for convergent beams were also calculated for several crystal dimensions s- a). In the actual fact, scintillations smaller than the counter sensitivity threshold To are not registered and the counter effectiveness is always lower than 100 %. The sensitivity T O of the counter investigated corresponded to 10 keV electron energy absorbed in the NaI(Tl) crystal. To know exactly the counter efficiency, a detailed analysis of photon energy transfer to the scintillator has been made. In the case of photoelectric absorption, the whole photon energy is transferred to the crystal, except when an iodine X-ray photon escapes from the scintillator. In that case the pulse amplitude corresponds to the energy E~-K. When E y - K < T O the scintillation is not registered, an X-ray photon being escaped. It was calculated 4) that 1000 excited iodine atoms emit 155 photons K#(of energy 32.6 keV) and 707 photons K=(of energy 28.6 keV). So, in the energy range from 33.17 keV (iodine K excitation)to To+ +32.6 keV, the counter efficiency is lower than calculated with the exponential formula. That part of the X-ray photons escaping from the NaI(Tl) scintillator has been calculated from the formula 5):
simple exponential formula in the energy range from 33.17 to 38.6 keY and 4 % in the range from 38.6 to 42.6 keV.
m = 0.36711 - r In {(r+ 1)/r}],
(1)
where: m is the part of the photons escaped and r is the ratio of the attenuation coefficients for incident 7-rays and fluorescent X-rays. For T o = l0 keV, as can be seen in fig. 1, the counter efficiency is 23 to 20 ~ lower than calculated from a
/0C 9C
7C .6C •~ 56 ~C t~
2C
I(
i
Photon
energy, MeV
Fig. I. Counter efficiency for a crystal 50 mm high and l 0 keV sensibility threshold. I-crystal can only; 2-additional lucite filter 1 s/cm =.
A part of the continuous spectrum of Compton electrons involving the pulse amplitude below the sensitivity level corresponding to the electron energy To will also not be counted. The contribution of electrons having an energy T < T o = l0 keV in the Compton continuum has been calculated from several photon energies with the formula:
329
a=
fo
(do,/dT)dT // lrT,-== ( d ¢ , / d T ) d T IJo
,
(2)
330
K. 2 A R N O W I E C K I
with
dtrc/dT = {r~mcZ/(hv - T ) 2} X
x {[me 2T/(hv)2] 2 + 2 [ ( h v - T)/(hv)] 2 + (3)
+ [(hv- T)/(hv)3l[(T - mc2)2-(mc2)2]}.
The contribution of Compton scattering to the total number of interactions is: b = a(E)/p(E),
(4)
where a ( E ) is the cross section for Compton scattering, and/~(E) is the sum of Compton-, photoelectric- and pair cross sections. The product of the probabilities a • b = c is the mean number of low energy electrons T < 10 keV for one photon collision in an NaI(TI) crystal containing 0.1 ~o of thallium 6). The results of the calculations are given in table 1.
and both annihilation photons escape. In such a case only the energy A is transferred to the crystal. When A -- 10 keV, the probability of pair production in Nal is negligible. The results of theoretical calculations have been compared to the measured dependence of the counting rate vs photomultiplier tension. Theoretical and experimental curves (normalized for calculated efficiency) for 6°Co and 19SAu are presented in fig. 2. Differences greater than the statistical error have not been observed. The increase of high tension above that corresponding to a counter sensitivity of a few keV, resulted in spurious counts following each pulse with an amplitude more than 500 times greater than the discrimination threshold. Thermal noise pulses of an EMI 9514 S photomultiplier are much lower than those, caused by l0 keV electrons, in an NaI(Tl) crystal. The energy calibration of the counter has been
TABH" 1 E (MeV)
0.056
0.1
[
0.2
0.3
0.4
0.5
0.6
0.8
1.0
a
1.00
0.41
i
0.14
0.08
0.054
0.034
0.026
0.017
0.012
0.004
0.020
0.087
[
0.34
0.58
0.74
0.82
0.87
0.91
0.94
0.99
0.011
0.004
;
2.0
0.020
0.036
[
0.048
0.046
0.040
]
0.028
0.023
0.015
0.035
0.26
i
0.88
1.45
1.71
[
1.85
1.93
2.00
2.09
2.19
K
ooo
ooo
I
oo1
o.13
0.26
I
0.35
0.41
0.48
0.53
0.67
d (/o) °/
0.00
0.00
I
0.05
0.60
1.04
l
0.98
0.94
0.72
0.58
0.27
£ (cm)
Photons which in the first collision have lost a little energy, can transfer to the crystal some more energy in a second collision inside the crystal. As these photons practically do not change their former direction, their supplementary attenuation is approximatively equal
done using 2°3Hg, 2 4 1 A m , l ° 9 C d and other sources of ?- and X-rays. The calculated efficiency of the above mentioned counter corresponds to a collimated beam geometry.
to:
k = exp ( - / ~ ( h - . ~ ) } ,
(5)
Z 1
where h is the height of the crystal and .£ is the mean free path of incident photons in the crystal of height h. Also, d = c • k is the difference (in ~o) between the counter effectiveness calculated above and that calculated on the grounds of a simple exponential formula. The values o f k and d, calculated for T o = l0 keV and a crystal height h = 5 cm are given in table 1. Pair production causes a remarkable scintillation while a photon of energy (1.02+ d ) M e V is absorbed
98 ~~b 95 ~. 9~ cz o
92 70 59 o
800
5ens, b / h t y threshold, 32 26 Id m
J
.
900 High tension,
keV I0 ~
tO00 '/
Fig. 2. Counter efficiency vs sensibility threshold. Curve: 1-6°Co calculated; Curve: 2 - ~ A u calculated. Experimental x-6°Co, • -19"Au, normalized for I0 keV.
ABSOLUTE GAMMA SOURCES ACTIVITY MEASUREMENT
In the case of a convergent beam, the paths of y-rays through the crystal are of various length and the exact calculation of the counter efficiency would be very complicated. Application of the simple exponential formula results in errors like those, given in line c of the table i. The crystal diameter and its position in the can is not always exactly known. The minor difference in source to crystal distance and its diameter results in an additional error of some percents 7). For avoiding these difficulties and for reaching the best possible precision in absolute measurements collimated beam geometry has been applied. The principle of the measurement is shown in fig. 3. Every coilima-
czA
J
V/A
Fig. 3. Measurement principle. 1-crystal; 2-photomultiplier; 3- removable lead cone; 4- lead collimator; 5- source.
tor is partly transparent for v-rays. As has been measured for a 7.5 cm thick lead collimator, 5 ~ of 6°Co and 0.7 ~o o f 137Cs V photons reached the crystal not through the collimator hole. For avoiding the error caused by collimator permeability, each measurement is repeated, using a supplementary lead shield of 15 cm thick. This shield (fig. 3) is the cone, which solid angle is exactly equal to that limited by collimator-source geometry. The background change due to the shield ought to be taken into account, calculating the true counting rate caused by the source. In the assembly used, the source to collimator distance was 217.75 mm, its dia. 27.86 mm, and the corresponding 7) solid angle co = 0.1015~. The angle of the collimator hole corresponds to 5 mm source diameter.
331
To cut the fl particles without remarkable attenuation in electromagnetic radiation, lucite filters ought to be used. One can suppose that the filter placed in the collimated v-ray beam involves a counting rate attenuation of
Nx/N =
exp
{-(z+mr)x},
(6)
where z is the photoelectric attenuation coefficient; tr, the Compton attenuation coefficient; n, the part of scattered photons not reaching the crystal and x, the filter thickness. The counting rate N (without) and Nx (with) filter has been measured for various ~ energies, filter thicknesses, and filter to scintillator distances. The value n obtained is n = 0.8 for a filter placed on the top of the collimator and n = 0.35 for a filter placed directly on the scintillator. The value of n shows only a slight dependence of the photon energy. Using formula (6), the correction factors for attenuation in air, lucite filters, aluminium can and MgO have been calculated. The total efficiency for photon registration by a scintillation counter with a crystal 5 cm in height and 10 keV registration threshold is presented in fig. I. For great 7 energies some positive error due to backscattering of photons passing the crystal without collision can be expected. The method described permits to measure the number of photons of known energy, emitted by the source, with high precision. When the decay scheme, the conversion coefficients and the fluorescence yield are well known, the source activity can also be determined. To prove experimentally the value of the method, the activities of some standard sources have been measured and the results obtained, are compared with those given in the IAEA certificate. For a comparison of the standard source activities, measured in the laboratories of IAEA and the results obtained using the method described, 6°Co, 137Cs and 5*Mn have been chosen. As can be seen in table 2, the differences between both measurements are of the order of l ~ , i.e., equal to the precision of IAEA standards itselves. The standards of 2°3Hg, 57Co, s a y and 22Na have also been measured. Calculating the activity, using decay branching and not very certain conversion data, can result in differences of the order of several percent. The measured activity of these standards, given in table 2 differ no more than 3 % with the figures given in the IAEA certificate.
332
K. ~ A R N O W I E C K I TABLE 2
Isotope
soCo
t*TCs S4Mn
Photon energy (keY) 1173.3 +0.3 1333.0 +0.3 661.59+0.076 32 36.5 835.0 :l:0.3
Photon yield per 100 desintegrations I00 I00
±0.012
IAEA overall error
(%)
Difference meas. act. and IAEA cert.
(%)
+i
+1.5
+2
--0.5
+l
--0.5
+0.00
84.6 +0.6 5.1 1.1 100
t0SHg
279.1 +0.05 72 83
81.55+0.15 10.6 3.0
±1
--3
s~Co
136.4 122.0 14.4
8.4 + 0 . 5 85.3 + 1.5 10.7 4-0.3
i2
--1.7
ssy
t,Na
897.5 +0.5 1836.2 +0.5 2734.1 +0.7
92 100 0.63+0.4
1274.6 +0.3 511
99.94 179.7 "+'0.8
Results of the measurements of the activity of gold foils, using the described method and the fl-~, coincidence method are also in excellent agreement within 1%.
:t:2
+3
_-hi
--I
mCi, while other absolute methods, permit only to determine the activity of solutions and need the preparation of special samples. References
Conclusions: The analysis of photon energy transfer to a crystal, permits to calculate the counter efficiency much more exactly than with the simple exponential formula. Using a counter of sensitivity of about 10 keV, with a crystal 2" x 2'% in a properly collimated beam geometry, one can reach a precision of absolute counting of photons of the order of 1-2 %. The method described permits to measure the activity of sources of small dimensions from 1 #Ci to 1
t) A. L. Stanford and W. K. Rivers, Rev. Sci. Instr. 29 (1958) 406. 2) j. H. Neiler and P. R. Bell, in Alpha-, beta- and gamma-ray spectroscopy (ed. K. Siegbahn; North-Holland Publishing Company, Amsterdam, 1965) p. 287. 3) N. A. Vartanov and P. S. Samoilov, Praktideskje metody scintiliacionnoj gamma-spektrometrji (Moskwa, 1964). 4) A. H. Wapstra, G. J. Nijgh and R. Van Li¢shout, Nuclear spectroscopy tables (North-Holland Publishing Company, Amsterdam, 1959). ,) P. Axel, Rev. Sci. Instr. 25 0954) 391. ,) G. W. Grodstein, NBS Circ. 583 (1957). ,) K. ~Mrnowigcki, IBJ 617/XIX/D (1965).
INSTRUMENTS
AND METHODS
55 (1967) 329-332; ( ~ N O R T H - H O L L A N D
PUBLISHING
CO.
M E T H O D OF ABSOLUTE GAMMA SOURCES ACTIVITY MEASUREMENT USING A SCINTILLATION COUNTER IN FIXED GEOMETRY K. Z A R N O W I E C K I
Institute of Nuclear Research, Otwock, Swierk. Poland Received 23 May 1967 It has been calculated that the efficiency of a gamma scintillation counter is lower than the one obtained from a simple exponential formula. The influence of the escape of fluorescence X-rays and annihilation photons and the presence of low energy Compton electrons has been taken into account. It has been proved that a
counter in the collimated beam geometry can be used for absolute measurements of gamma source activity. The method of calculating the correction factors for filters, and a collimator permeability is given. The experimental results agree very well with theoretical calculations.
It is often supposed that every photon collision in a scintillator results in a count, and that the counter efficiency for a parallel beam is a simple exponential function of crystal thickness. On these grounds the efficiencies for convergent beams were also calculated for several crystal dimensions s- a). In the actual fact, scintillations smaller than the counter sensitivity threshold To are not registered and the counter effectiveness is always lower than 100 %. The sensitivity T O of the counter investigated corresponded to 10 keV electron energy absorbed in the NaI(Tl) crystal. To know exactly the counter efficiency, a detailed analysis of photon energy transfer to the scintillator has been made. In the case of photoelectric absorption, the whole photon energy is transferred to the crystal, except when an iodine X-ray photon escapes from the scintillator. In that case the pulse amplitude corresponds to the energy E~-K. When E y - K < T O the scintillation is not registered, an X-ray photon being escaped. It was calculated 4) that 1000 excited iodine atoms emit 155 photons K#(of energy 32.6 keV) and 707 photons K=(of energy 28.6 keV). So, in the energy range from 33.17 keV (iodine K excitation)to To+ +32.6 keV, the counter efficiency is lower than calculated with the exponential formula. That part of the X-ray photons escaping from the NaI(Tl) scintillator has been calculated from the formula 5):
simple exponential formula in the energy range from 33.17 to 38.6 keY and 4 % in the range from 38.6 to 42.6 keV.
m = 0.36711 - r In {(r+ 1)/r}],
(1)
where: m is the part of the photons escaped and r is the ratio of the attenuation coefficients for incident 7-rays and fluorescent X-rays. For T o = l0 keV, as can be seen in fig. 1, the counter efficiency is 23 to 20 ~ lower than calculated from a
/0C 9C
7C .6C •~ 56 ~C t~
2C
I(
i
Photon
energy, MeV
Fig. I. Counter efficiency for a crystal 50 mm high and l 0 keV sensibility threshold. I-crystal can only; 2-additional lucite filter 1 s/cm =.
A part of the continuous spectrum of Compton electrons involving the pulse amplitude below the sensitivity level corresponding to the electron energy To will also not be counted. The contribution of electrons having an energy T < T o = l0 keV in the Compton continuum has been calculated from several photon energies with the formula:
329
a=
fo
(do,/dT)dT // lrT,-== ( d ¢ , / d T ) d T IJo
,
(2)
330
K. 2 A R N O W I E C K I
with
dtrc/dT = {r~mcZ/(hv - T ) 2} X
x {[me 2T/(hv)2] 2 + 2 [ ( h v - T)/(hv)] 2 + (3)
+ [(hv- T)/(hv)3l[(T - mc2)2-(mc2)2]}.
The contribution of Compton scattering to the total number of interactions is: b = a(E)/p(E),
(4)
where a ( E ) is the cross section for Compton scattering, and/~(E) is the sum of Compton-, photoelectric- and pair cross sections. The product of the probabilities a • b = c is the mean number of low energy electrons T < 10 keV for one photon collision in an NaI(TI) crystal containing 0.1 ~o of thallium 6). The results of the calculations are given in table 1.
and both annihilation photons escape. In such a case only the energy A is transferred to the crystal. When A -- 10 keV, the probability of pair production in Nal is negligible. The results of theoretical calculations have been compared to the measured dependence of the counting rate vs photomultiplier tension. Theoretical and experimental curves (normalized for calculated efficiency) for 6°Co and 19SAu are presented in fig. 2. Differences greater than the statistical error have not been observed. The increase of high tension above that corresponding to a counter sensitivity of a few keV, resulted in spurious counts following each pulse with an amplitude more than 500 times greater than the discrimination threshold. Thermal noise pulses of an EMI 9514 S photomultiplier are much lower than those, caused by l0 keV electrons, in an NaI(Tl) crystal. The energy calibration of the counter has been
TABH" 1 E (MeV)
0.056
0.1
[
0.2
0.3
0.4
0.5
0.6
0.8
1.0
a
1.00
0.41
i
0.14
0.08
0.054
0.034
0.026
0.017
0.012
0.004
0.020
0.087
[
0.34
0.58
0.74
0.82
0.87
0.91
0.94
0.99
0.011
0.004
;
2.0
0.020
0.036
[
0.048
0.046
0.040
]
0.028
0.023
0.015
0.035
0.26
i
0.88
1.45
1.71
[
1.85
1.93
2.00
2.09
2.19
K
ooo
ooo
I
oo1
o.13
0.26
I
0.35
0.41
0.48
0.53
0.67
d (/o) °/
0.00
0.00
I
0.05
0.60
1.04
l
0.98
0.94
0.72
0.58
0.27
£ (cm)
Photons which in the first collision have lost a little energy, can transfer to the crystal some more energy in a second collision inside the crystal. As these photons practically do not change their former direction, their supplementary attenuation is approximatively equal
done using 2°3Hg, 2 4 1 A m , l ° 9 C d and other sources of ?- and X-rays. The calculated efficiency of the above mentioned counter corresponds to a collimated beam geometry.
to:
k = exp ( - / ~ ( h - . ~ ) } ,
(5)
Z 1
where h is the height of the crystal and .£ is the mean free path of incident photons in the crystal of height h. Also, d = c • k is the difference (in ~o) between the counter effectiveness calculated above and that calculated on the grounds of a simple exponential formula. The values o f k and d, calculated for T o = l0 keV and a crystal height h = 5 cm are given in table 1. Pair production causes a remarkable scintillation while a photon of energy (1.02+ d ) M e V is absorbed
98 ~~b 95 ~. 9~ cz o
92 70 59 o
800
5ens, b / h t y threshold, 32 26 Id m
J
.
900 High tension,
keV I0 ~
tO00 '/
Fig. 2. Counter efficiency vs sensibility threshold. Curve: 1-6°Co calculated; Curve: 2 - ~ A u calculated. Experimental x-6°Co, • -19"Au, normalized for I0 keV.
ABSOLUTE GAMMA SOURCES ACTIVITY MEASUREMENT
In the case of a convergent beam, the paths of y-rays through the crystal are of various length and the exact calculation of the counter efficiency would be very complicated. Application of the simple exponential formula results in errors like those, given in line c of the table i. The crystal diameter and its position in the can is not always exactly known. The minor difference in source to crystal distance and its diameter results in an additional error of some percents 7). For avoiding these difficulties and for reaching the best possible precision in absolute measurements collimated beam geometry has been applied. The principle of the measurement is shown in fig. 3. Every coilima-
czA
J
V/A
Fig. 3. Measurement principle. 1-crystal; 2-photomultiplier; 3- removable lead cone; 4- lead collimator; 5- source.
tor is partly transparent for v-rays. As has been measured for a 7.5 cm thick lead collimator, 5 ~ of 6°Co and 0.7 ~o o f 137Cs V photons reached the crystal not through the collimator hole. For avoiding the error caused by collimator permeability, each measurement is repeated, using a supplementary lead shield of 15 cm thick. This shield (fig. 3) is the cone, which solid angle is exactly equal to that limited by collimator-source geometry. The background change due to the shield ought to be taken into account, calculating the true counting rate caused by the source. In the assembly used, the source to collimator distance was 217.75 mm, its dia. 27.86 mm, and the corresponding 7) solid angle co = 0.1015~. The angle of the collimator hole corresponds to 5 mm source diameter.
331
To cut the fl particles without remarkable attenuation in electromagnetic radiation, lucite filters ought to be used. One can suppose that the filter placed in the collimated v-ray beam involves a counting rate attenuation of
Nx/N =
exp
{-(z+mr)x},
(6)
where z is the photoelectric attenuation coefficient; tr, the Compton attenuation coefficient; n, the part of scattered photons not reaching the crystal and x, the filter thickness. The counting rate N (without) and Nx (with) filter has been measured for various ~ energies, filter thicknesses, and filter to scintillator distances. The value n obtained is n = 0.8 for a filter placed on the top of the collimator and n = 0.35 for a filter placed directly on the scintillator. The value of n shows only a slight dependence of the photon energy. Using formula (6), the correction factors for attenuation in air, lucite filters, aluminium can and MgO have been calculated. The total efficiency for photon registration by a scintillation counter with a crystal 5 cm in height and 10 keV registration threshold is presented in fig. I. For great 7 energies some positive error due to backscattering of photons passing the crystal without collision can be expected. The method described permits to measure the number of photons of known energy, emitted by the source, with high precision. When the decay scheme, the conversion coefficients and the fluorescence yield are well known, the source activity can also be determined. To prove experimentally the value of the method, the activities of some standard sources have been measured and the results obtained, are compared with those given in the IAEA certificate. For a comparison of the standard source activities, measured in the laboratories of IAEA and the results obtained using the method described, 6°Co, 137Cs and 5*Mn have been chosen. As can be seen in table 2, the differences between both measurements are of the order of l ~ , i.e., equal to the precision of IAEA standards itselves. The standards of 2°3Hg, 57Co, s a y and 22Na have also been measured. Calculating the activity, using decay branching and not very certain conversion data, can result in differences of the order of several percent. The measured activity of these standards, given in table 2 differ no more than 3 % with the figures given in the IAEA certificate.
332
K. ~ A R N O W I E C K I TABLE 2
Isotope
soCo
t*TCs S4Mn
Photon energy (keY) 1173.3 +0.3 1333.0 +0.3 661.59+0.076 32 36.5 835.0 :l:0.3
Photon yield per 100 desintegrations I00 I00
±0.012
IAEA overall error
(%)
Difference meas. act. and IAEA cert.
(%)
+i
+1.5
+2
--0.5
+l
--0.5
+0.00
84.6 +0.6 5.1 1.1 100
t0SHg
279.1 +0.05 72 83
81.55+0.15 10.6 3.0
±1
--3
s~Co
136.4 122.0 14.4
8.4 + 0 . 5 85.3 + 1.5 10.7 4-0.3
i2
--1.7
ssy
t,Na
897.5 +0.5 1836.2 +0.5 2734.1 +0.7
92 100 0.63+0.4
1274.6 +0.3 511
99.94 179.7 "+'0.8
Results of the measurements of the activity of gold foils, using the described method and the fl-~, coincidence method are also in excellent agreement within 1%.
:t:2
+3
_-hi
--I
mCi, while other absolute methods, permit only to determine the activity of solutions and need the preparation of special samples. References
Conclusions: The analysis of photon energy transfer to a crystal, permits to calculate the counter efficiency much more exactly than with the simple exponential formula. Using a counter of sensitivity of about 10 keV, with a crystal 2" x 2'% in a properly collimated beam geometry, one can reach a precision of absolute counting of photons of the order of 1-2 %. The method described permits to measure the activity of sources of small dimensions from 1 #Ci to 1
t) A. L. Stanford and W. K. Rivers, Rev. Sci. Instr. 29 (1958) 406. 2) j. H. Neiler and P. R. Bell, in Alpha-, beta- and gamma-ray spectroscopy (ed. K. Siegbahn; North-Holland Publishing Company, Amsterdam, 1965) p. 287. 3) N. A. Vartanov and P. S. Samoilov, Praktideskje metody scintiliacionnoj gamma-spektrometrji (Moskwa, 1964). 4) A. H. Wapstra, G. J. Nijgh and R. Van Li¢shout, Nuclear spectroscopy tables (North-Holland Publishing Company, Amsterdam, 1959). ,) P. Axel, Rev. Sci. Instr. 25 0954) 391. ,) G. W. Grodstein, NBS Circ. 583 (1957). ,) K. ~Mrnowigcki, IBJ 617/XIX/D (1965).