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Error in the absolute determination of disintegration rates of extended sources by coincidence counting with a single detector—Application to I-125 and Co-60
786
Technical notes
International JournalofAppliedRadiationand Isotopes,1967, Vol. 18, pp. 786-787. PergamonPressLtd. Printedin NorthernIreland
Error in the Absolute Determination of Disintegration Rates of Extended Sources by Coincidence Counting with a Single Detector -Application to I-125 and Co-60 (Received 3 JUJY 1967) IT HAS long been recognized that one condition for valid measurement of disintegration rates by the j3-/ coincidence method is that either the /?-detector or the y-detector be equally responsive to all parts of the source.(l) That a similar restriction applies to coincidence measurements of disintegration rates with a single detector apparently has not been generally recognized. BRINKMAN et a6.(2-5) developed the “sum peak” coincidence method for measuring the disintegration rates of radionuclides emitting gamma rays in coincidence, or positron annihilation radiation, using a single NaI(T1) detector. For a radionuclide emitting two gamma rays in coincidence, they derived the following relation for the disintegration rate:
hL++
T,
detectors by using the detection efficiencies computed and tabulated by GROSJEAN and BOSAERT.@) For example, relative values of the “disintegration rates” [right-hand sides of equations (1) and (2)] for 25-mm dia. weightless cylindrical sources of varying height, as they would be measured with a 3-in. dia. by 3-in. thick NaI(T1) detector, were calculated by numerical integration of the circular disk efficiencies obtained from the tables of GROSJEAN and BOSSAERT. The calculations were made for both I-125 and Co-60. The magnitude of the error was also determined experimentally by measuring the disintegration rate by the “sum peak” method as a function of the height of aqueous sample solution in a 25-mm dia. plastic vial centered on the face of a 3-m. by 3-m. NaI(T1) detector. The height of the sample solution was varied by successive dilutions. The measured and calculated values for Co-60 are given in Fig. 1. The measured and calculated values for I-125 are given in Fig. 2. Data of ELDRIDGE and CROWTHER for
Measured Colculoted
A -
(1)
12
,
where A, and A, are the areas of the photopeaks of y1 and y2, respectively, Al2 is the area under the sum peak, and T is the area under the whole spectrum. Independently, HARPER et al.(e), and HOUTERMAN@) developed a coincidence method for measuring the disintegration rate of I-125 with a single NaI(T1) detector. This method for I-125 is the subject of a paper by ELDRIDGE and CROWTHER.@) The disintegration rate of I-125 is: N
=
(A, + 2A1d2 4A
II
f
(2)
where AI is the area of the singles peak and An is the area of the sum peak. Equation (2) can be derived as a special case of equation (1) in which A, = A, = AI/~; T = AI + AII, and A,, = AII. A tacit assumption in the derivation of these equations is that the detector is equally responsive to all parts of the source. When the detection efficiency varies significantly for different parts of the source, there will be a significant error in the disintegration rate calculated from these equations. The magnitude of this error for a given sourcedetector combination can be estimated by numerical integration of the counting rate (or detection efficiency) over the dimensions of the source. Such calculations are greatly simplified for solid NaI(T1)
,
t
I
2
HEIGHT
I 3
OF
SOURCE
I
t
4
5
km)
1. Effects of finite source size on the Co-60 “disintegration rate” determined by the “sum peak” method (equation 1) for a 25-mm dia. cylindrical source centered on the face of a 3-in. by 3-in. NaI(Tl) detector.
FIG.
787
Technical notes
When this vial was nearly filled with 5 ml of solution the measured “disintegration rate” was only 42% of the true value. As ELDRIDGEand CROWTHERhave shown [Table 3 of reference (8)], the true value for the disintegration rate of an I-125 sample of this size can be obtained with little or no error by counting it in a NaI(T1) well detector. This is possible because a detector of this type is nearly equally responsive to all parts of a source when the source is counted in the well. In summary, the equations for obtaining the disintegration rate of a source by the “sum peak” method with a single detector are valid only when the detector is equally responsive to all parts 0; the source. Practically, this condition can be satisfied when using a solid detector by making the dimensions of the source as small as possible (i.e. by approximating a point source), or by counting samples of larger dimensions in a well-type detector.
A \A A\ A
I
I
I
I
I
3
I
3
4
5
HEIGHT
OF
LAUREL G. SUTHERLAND Isotopes Inc. JOHN D. BUCHANAN Palo Alto Laboratory 4062 Fabian Street Palo Alto, Califrnia 94303
SOURCE@)
FIG. 2. Effect of finite source size on the I-125
“disintegration rate” determined by the “sum peak” method (equation 2) for a 25-mm dia. cylindrical source centered on the face of a 3-in. by 3-in. NaI(T1) detector.
I-125 samples of the same diameter, and a detector of the same size, are also included in Fig. 2. The difference between the measured points and the calculated curve for the greater sample heights of I-125 results from neglecting sample self-absorption in the calculation. The magnitudes of the errors in the measured disintegration rates are similar for I-125 and Co-60 since the variation in detection efficiency, over the height of the cylindrical sample, results primarily from the variation in the physical geometry, which is the same for both nuclides in these examples. The error in the measured disintegration rate is about 25% for a 25-ml sample in a 25-mm dia. vial on the 3-in. by 3-m. detector. Even larger errors are obtained with other sourcedetector combinations. For example, we measured the “disintegration rate” of I-125 as a function of the height of a cylindrical sample by varying the volume of sample solution in a 16-mm dia. glass vial centered on a 31/32-in. dia., 0,0625-in. thick, NaI(T1) detector.
References
1. PUTMAN J. L. &it. J. Radial. 23, 46 (1950). 2. BRINKMAN G. A., ATEN A. H. W., JR. and VEENBOER J. TH. Int. J. appl. Radiat. Isotopes 14, 153 (1963). 3. BRINKMAN G. A. and ATEN A. H. W., JR. Int. J. appl. Radiat. Isotopes 14, 503 (1963). 4. BRM~MANG. A. and ATEN A. H. W., JR. Iti. J. apgl. Radiat. Isotojes 16, 177 (1965). G. A., ATEN A. H. W., JR., VEENBOER 5. BRIN~MAN J. TH. and ZIJLSTRAW. G. Proc. Symp. Radioisotope Sample Measurement Techniques in Medicine and BioLogy,Vienna, 24-28 May 1965, p. 581. I.A.E.A., Vienna ( 1965). HARPER P. V., SIEMENS W. D., LATHROP K. A.
and ENDLICH H. J. nucl. Med. 4, 277 (1963). HOUTERMANSH. Private communication to Eldridge and Crowther, ref. (8). ELDRIDGEJ. A. and CROWTHER P. Nucleonics 22, (6), 57 (1964). GROSJEAN C. C. and BOSSAERT W. Table of Absolute Detection Ejiciencies of Cylindrical Scintillation Gamma-Ray Detectors. Computing Laboratory of the University of Ghent, Ghent, Belgium (1965).
Technical notes
International JournalofAppliedRadiationand Isotopes,1967, Vol. 18, pp. 786-787. PergamonPressLtd. Printedin NorthernIreland
Error in the Absolute Determination of Disintegration Rates of Extended Sources by Coincidence Counting with a Single Detector -Application to I-125 and Co-60 (Received 3 JUJY 1967) IT HAS long been recognized that one condition for valid measurement of disintegration rates by the j3-/ coincidence method is that either the /?-detector or the y-detector be equally responsive to all parts of the source.(l) That a similar restriction applies to coincidence measurements of disintegration rates with a single detector apparently has not been generally recognized. BRINKMAN et a6.(2-5) developed the “sum peak” coincidence method for measuring the disintegration rates of radionuclides emitting gamma rays in coincidence, or positron annihilation radiation, using a single NaI(T1) detector. For a radionuclide emitting two gamma rays in coincidence, they derived the following relation for the disintegration rate:
hL++
T,
detectors by using the detection efficiencies computed and tabulated by GROSJEAN and BOSAERT.@) For example, relative values of the “disintegration rates” [right-hand sides of equations (1) and (2)] for 25-mm dia. weightless cylindrical sources of varying height, as they would be measured with a 3-in. dia. by 3-in. thick NaI(T1) detector, were calculated by numerical integration of the circular disk efficiencies obtained from the tables of GROSJEAN and BOSSAERT. The calculations were made for both I-125 and Co-60. The magnitude of the error was also determined experimentally by measuring the disintegration rate by the “sum peak” method as a function of the height of aqueous sample solution in a 25-mm dia. plastic vial centered on the face of a 3-m. by 3-m. NaI(T1) detector. The height of the sample solution was varied by successive dilutions. The measured and calculated values for Co-60 are given in Fig. 1. The measured and calculated values for I-125 are given in Fig. 2. Data of ELDRIDGE and CROWTHER for
Measured Colculoted
A -
(1)
12
,
where A, and A, are the areas of the photopeaks of y1 and y2, respectively, Al2 is the area under the sum peak, and T is the area under the whole spectrum. Independently, HARPER et al.(e), and HOUTERMAN@) developed a coincidence method for measuring the disintegration rate of I-125 with a single NaI(T1) detector. This method for I-125 is the subject of a paper by ELDRIDGE and CROWTHER.@) The disintegration rate of I-125 is: N
=
(A, + 2A1d2 4A
II
f
(2)
where AI is the area of the singles peak and An is the area of the sum peak. Equation (2) can be derived as a special case of equation (1) in which A, = A, = AI/~; T = AI + AII, and A,, = AII. A tacit assumption in the derivation of these equations is that the detector is equally responsive to all parts of the source. When the detection efficiency varies significantly for different parts of the source, there will be a significant error in the disintegration rate calculated from these equations. The magnitude of this error for a given sourcedetector combination can be estimated by numerical integration of the counting rate (or detection efficiency) over the dimensions of the source. Such calculations are greatly simplified for solid NaI(T1)
,
t
I
2
HEIGHT
I 3
OF
SOURCE
I
t
4
5
km)
1. Effects of finite source size on the Co-60 “disintegration rate” determined by the “sum peak” method (equation 1) for a 25-mm dia. cylindrical source centered on the face of a 3-in. by 3-in. NaI(Tl) detector.
FIG.
787
Technical notes
When this vial was nearly filled with 5 ml of solution the measured “disintegration rate” was only 42% of the true value. As ELDRIDGEand CROWTHERhave shown [Table 3 of reference (8)], the true value for the disintegration rate of an I-125 sample of this size can be obtained with little or no error by counting it in a NaI(T1) well detector. This is possible because a detector of this type is nearly equally responsive to all parts of a source when the source is counted in the well. In summary, the equations for obtaining the disintegration rate of a source by the “sum peak” method with a single detector are valid only when the detector is equally responsive to all parts 0; the source. Practically, this condition can be satisfied when using a solid detector by making the dimensions of the source as small as possible (i.e. by approximating a point source), or by counting samples of larger dimensions in a well-type detector.
A \A A\ A
I
I
I
I
I
3
I
3
4
5
HEIGHT
OF
LAUREL G. SUTHERLAND Isotopes Inc. JOHN D. BUCHANAN Palo Alto Laboratory 4062 Fabian Street Palo Alto, Califrnia 94303
SOURCE@)
FIG. 2. Effect of finite source size on the I-125
“disintegration rate” determined by the “sum peak” method (equation 2) for a 25-mm dia. cylindrical source centered on the face of a 3-in. by 3-in. NaI(T1) detector.
I-125 samples of the same diameter, and a detector of the same size, are also included in Fig. 2. The difference between the measured points and the calculated curve for the greater sample heights of I-125 results from neglecting sample self-absorption in the calculation. The magnitudes of the errors in the measured disintegration rates are similar for I-125 and Co-60 since the variation in detection efficiency, over the height of the cylindrical sample, results primarily from the variation in the physical geometry, which is the same for both nuclides in these examples. The error in the measured disintegration rate is about 25% for a 25-ml sample in a 25-mm dia. vial on the 3-in. by 3-m. detector. Even larger errors are obtained with other sourcedetector combinations. For example, we measured the “disintegration rate” of I-125 as a function of the height of a cylindrical sample by varying the volume of sample solution in a 16-mm dia. glass vial centered on a 31/32-in. dia., 0,0625-in. thick, NaI(T1) detector.
References
1. PUTMAN J. L. &it. J. Radial. 23, 46 (1950). 2. BRINKMAN G. A., ATEN A. H. W., JR. and VEENBOER J. TH. Int. J. appl. Radiat. Isotopes 14, 153 (1963). 3. BRINKMAN G. A. and ATEN A. H. W., JR. Int. J. appl. Radiat. Isotopes 14, 503 (1963). 4. BRM~MANG. A. and ATEN A. H. W., JR. Iti. J. apgl. Radiat. Isotojes 16, 177 (1965). G. A., ATEN A. H. W., JR., VEENBOER 5. BRIN~MAN J. TH. and ZIJLSTRAW. G. Proc. Symp. Radioisotope Sample Measurement Techniques in Medicine and BioLogy,Vienna, 24-28 May 1965, p. 581. I.A.E.A., Vienna ( 1965). HARPER P. V., SIEMENS W. D., LATHROP K. A.
and ENDLICH H. J. nucl. Med. 4, 277 (1963). HOUTERMANSH. Private communication to Eldridge and Crowther, ref. (8). ELDRIDGEJ. A. and CROWTHER P. Nucleonics 22, (6), 57 (1964). GROSJEAN C. C. and BOSSAERT W. Table of Absolute Detection Ejiciencies of Cylindrical Scintillation Gamma-Ray Detectors. Computing Laboratory of the University of Ghent, Ghent, Belgium (1965).