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Simultaneous estimation of several radioactive nuclides
Technical notes
230
the actual sample c o u n t c a n be o b t a i n e d from the s t a n d a r d q u e n c h i n g curve.
Acknowledgements--This work was s u p p o r t e d b y U.S. Public H e a l t h Service G r a n t C - 4 2 3 6 a n d was carried out w i t h the technical assistance of Louis J. PHILIPP.
Department of Biochemistry MILTON TOPOREK Jefferson Medical Co[le.~e Philadelphia, Pennsylvania, U.S.A. References 1. VAUGHAN M., STEINBERG D. a n d LOGAN J. Science 126, 446 (1957). 2. CHEN P. S. Jr. Proc. Soc. Exp. Biol., N.Y. 98, 546 (1958). 3. KERR V. N., HAYES F. N. a n d OTT D. G. Int. J. Appl. Rad. Isotopes 1, 284 (1957). 4. DAVIDSONJ. D. Liquid Scintillation Counting (Edited by BELL C. G. JR. a n d HAYES F. N.) p. 88, Perg a m o n Press, New York (1958). 5. KALLMAN H. a n d FURST M. Liquid Scintillation Counting (Edited b y BELL C. G. J m a n d HAYES F. N.) p. 3. P e r g a m o n Press, N e w York (1958). 6. TOPOREK M. 136th National Meeting of the American Chemical Society Abstracts p. 86C, S e p t e m b e r (1959). 7. HERBERG R. J . Analyt. Chem. 32, 42 (1960). 8. PASSMANNJ. iV[., RADIN N. S. a n d COOPERJ. A. D. Analyt. Chem. 28, 484 (1956). Note added in proof: Liquid scintillation counting is growing very rapidly. It is also shifting its field from the very low-energy/?-emitters such as C 14 and I-I3 where the technique is not so much "necessary" as "desirable". During the development of this technique, the concept of "quenching" has shifted from a pure electronic quenching as used in Geiger tubes and such devices, to a much more important concept of"quenching" which is determined by such things as the transfer of energy from the isotope through various chemical systems to the counting mechanism. The result, changed counting rates, is the same in chemical or in electronic quenching. However, the older definition of quenching is not vitiated. The newer concept of chemical quenching is probably not yet completely shifted. The importance of the article by TOPOREK lies in the description of a procedure for correction in the face of a changing concept of "quenching".
Simultaneous Estimation of Several Radioactive Nuclides
(First received2 March 1960 and in revisedform 11 April 1960) WHEN several radioactive species are used simultaneously in a tracer experiment, the activity of all the nuclides m u s t be m e a s u r e d in each sample. This
note describes a general m e t h o d of doing this, w h i c h is applicable to a n y n u m b e r of nuclides a n d in particular points out the simple way in w h i c h the calib r a t i o n c a n be m a d e . Several accounts h a v e b e e n given (1-9) of methods for analysing p a r t i c u l a r mixtures a n d in some cases they h a v e involved the solution of simultaneous equations for each sample. This is n o t necessary; the solution of simultaneous e q u a tions c a n be restricted to the calibration, a n d thereafter the m e a s u r e m e n t s of each sample c a n be reduced b y a simple calculation. I f n different radioactive tracers are b e i n g used, t h e n in order to d e t e r m i n e the activity of each nuclide it is necessary to measure each sample with a set of n r a d i a t i o n detectors w h i c h h a v e different sensitivities for each nuclide. Such detectors must h a v e a linear response to radiations (after correction if necessary) a n d m u s t be used u n d e r precisely defined conditions. T h e same i n s t r u m e n t m a y be used u n d e r two different conditions to provide two distinct detectors, as for example by using different absorbers, b y using scintillation counters at different parts of their spect r u m or by repeating the m e a s u r e m e n t s after a time interval. Let U z b e the set of n readings t h a t a sample causes in the set of n detectors, a n d let A k be the activities of the n different nuclides in the sample. Since r a d i a t i o n detectors respond i n d e p e n d e n t l y to the radiations from a n u m b e r of sources, t h e n the reading of each detector will be a linear sum of the activities of each of the n nuclides in the sample. This c a n be represented b y the following set of equations,
U s = EkbzkAk.
(1)
Now, p r o v i d e d the d e t e r m i n a n t of the m a t r i x (b~) does not vanish, the A k c a n be written as a linear sum of the U~, A~ = Eza~U ~ (2) w h e r e the m a t r i x (ak~) is the inverse of the m a t r i x (bu~), a n d can be d e t e r m i n e d b y m e a s u r i n g a set of n k n o w n calibrating samples. I n dealing w i t h multiple tracers one should recognize t h a t the activity of each nuclide in a sample c a n be calculated simply as a linear sum of the readings of each detector, as shown b y e q u a t i o n (2), after the m a t r i x (ak~) has b e e n d e t e r m i n e d by a calibration procedure. T h e calibration should be m a d e b y suitable substitutions into e q u a t i o n (2) a n d n o reference need be m a d e to e q u a t i o n (1). i f the d e t e r m i n a n t of the m a t r i x (bz~) vanishes, t h e n equations (1) are n o t all i n d e p e n d e n t a n d t h a t set of detectors will not give e n o u g h information to determ i n e u n i q u e l y the activity of each nuclide in the sample. I n this case it will be found t h a t the calib r a t i o n m e t h o d described later will not give u n i q u e solutions for the m a t r i x (ak~).
231
Technical notes
T h e case for two tracer nuclides will be presented in detail a n d in a form t h a t c a n be readily e x t e n d e d to the general case. Consider the two isotopes Fe 59 a n d 32p, a n d the use of two detectors, a scintillation c o u n t e r a n d a Geiger counter, b o t h suitable for c o u n t i n g a 10 m l liquid sample. Let U s a n d Ug be the c o u n t i n g rates (less b a c k g r o u n d ) of a sample m e a s u r e d with tile scintillation a n d w i t h the Geiger counter, a n d A 1 a n d A~ the activities of the Fe 59 a n d the 32p in the sample. T h e n the general e q u a t i o n (2), enables the following to be written d o w n for this case, A.t -- a U s + b U g
(3)
Azo = c U s + d U g
where a, b, c a n d d are constants of the set of two counters a n d r e m a i n the same as long as the characteristics of b o t h counters r e m a i n u n c h a n g e d . W h e n once d e t e r m i n e d , the constants need only be checked at infrequent intervals, if the counter characteristics are stable. Now, equations (3) hold, with a p p r o p r i a t e constants, w h e n the activities of the nuclides A r a n d Av are m e a s u r e d in a n y valid set of units. T h e r e is one set of units, however, t h a t has the special p r o p e r t y of m a k i n g the c a l i b r a t i o n particularly simple a n d this is the set t h a t measures the activities in units of a detector reading. I t is p a r t i c u l a r l y f o r t u n a t e t h a t it is also a n a t u r a l way to measure the activities a n d is c o m m o n l y used in practice. D e n o t e the activities of the nuclides in these units b y F s a n d Po" T h u s a n activity o f F s units of Fe 59 will cause the scintillation c o u n t e r to give a c o u n t i n g rate o f F s counts p e r u n i t time, a n d similarly the Geiger c o u n t e r will give P g counts per u n i t time for Pg units of P 32. T h e equations (3) can n o w be w r i t t e n as F s = a U s + bU~,
(4)
Po = cUs + d U g
w h e r e the constants are a p p r o p r i a t e to these units of activity. T h e constants a, b, c a n d d in equations (4) can be d e t e r m i n e d simply b y c o u n t i n g with each counter, two c a l i b r a t i n g samples, one c o n t a i n i n g Fe 59 only
a n d the o t h e r p32 only. Because of the p a r t i c u l a r choice of units of activity, it is n o t necessary to p r e p a r e the samples w i t h k n o w n activities, except in so far as they should give convenient c o u n t i n g rates. Let the c o u n t i n g rates (less b a c k g r o u n d ) of the two calibrating samples by the two counters be f s , f g , Ps a n d pg. Because these samples contain one nuclide only, it follows from our choice of units of activity t h a t the activity of the two calibrating samples are f s a n d P o" Hence, b y substituting the c o u n t i n g rates for each sample into equations (4) a n d r e a r r a n g i n g them, two sets of simultaneous equations are obtained, f.~=afs +bfo 0 = aps + bpg 0 = cfs + d f g
and
Prt = cPs + dpg (5) from w h i c h the constants a, b, c a n d d can be calculated. T h e calibration for a particular pair of scintillation a n d Geiger counters t h a t was used in a biological investigation, was F s = U s + 0"004U s - 0-059Ug Pg ~ Ug ÷ 0"004Ug -- 0 ' 0 6 8 U s.
(6)
T a b l e 1 shows the calculations in full for a few typical samples as they a p p e a r in the working note book, a n d shows h o w simple they can be; a slide rule gives m o r e t h a n a d e q u a t e accuracy. O f p a r t i c u l a r interest to note is the sample 5 w h i c h was k n o w n to contain only the one isotope. H e r e m e a s u r e m e n t by the one counter only was needed a n d no a d j u s t m e n t was necessary. Also shown in the T a b l e are the c o u n t i n g rates for the two calibration samples from w h i c h the constants in equations (6) were calculated. I n bold type is shown the reduction of these c o u n t i n g rates b y equations (6) as t h o u g h they were o r d i n a r y samples, showing t h a t a correct result is obtained. This, of course, is only a check t h a t the constants in equations (6) were calculated correctly, b u t it is instructive in showing h o w the m e t h o d works, in particular w h y a a n d d are different from one.
TABLE 1. Specimen work sheet. U, and Ug counting rates (counts per minute less background) of scintillation and Geiger counters. F, and Pg counting rates due to Fe 59 and pm content of sample Sample No.
Uo + 0.004U, -- 0-059Ug 671 765 906 1447 1636
Calibration Calibration
1296 78
3 3 4 6
= Fs
Ug + 0.004Ug -- 0.068U,
= pg
--13 --21 --27 --11
661 747 883 1442 1636
222 354 458 191
1 1 2 1
--46 --52 --62 --98
177 303 398 94
5
--5
1296
0
--78
0
88 1324
0
5
--88 --5
0 1324
232
Technical notes
T h e merits of m e a s u r i n g the activities of the nuclides in the samples in units of a detector reading are t h a t the activities of the calibrating samples need n o t be known, t h a t in favourable circumstances the calculations b e c o m e very easy as shown by the example in equations (6) a n d t h a t if a sample is k n o w n to c o n t a i n only one nuclide only one m e a s u r e m e n t need be m a d e . I n m a n y tracer experiments the m e a s u r e m e n t of activities in a r b i t r a r y units is all t h a t is necessary t h o u g h t h e r e are a d v a n t a g e s in using the curie or its submultiples. Conversion to microcuries can be m a d e later if w a n t e d and, if the activities of the c a l i b r a t i n g samples are known, they c a n be used to provide the calibration necessary for this, b u t it is often m o r e c o n v e n i e n t to keep o t h e r sources for this purpose. T h e extension to n tracer nuclides is s t r a i g h t f o r w a r d ; n calibrating samples are needed, each c o n t a i n i n g one nuclide only. T h e solution of n sets of n simultaneous equations is n e e d e d to get the constants of e q u a t i o n (2), b u t thereafter the reduction of each sample requires only simple multiplication a n d addition. It is i m p o r t a n t to notice t h a t no accurate information is needed a b o u t the radiations given off by the nuclides or a b o u t the characteristics of the r a d i a t i o n detectors; the calibration procedure makes alI the m e a s u r e m e n t s t h a t are necessary. However, some knowledge of the properties of the radiations a n d the detectors is v a l u a b l e in deciding w h i c h is the best set of detectors to use. It is clearly desirable, as far as possible, to use the detectors in such a way as to give a big differentiation between each nuclide. This would be shown b y all b u t one of the constants in each of the equations (2) b e i n g small. This ideal c a n n o t always be o b t a i n e d a n d a n e x a m i n a t i o n of the constants of equations (2) will show h o w accurate the simultaneous estimation of the various nuclides is likely to be a n d at w h a t level the activity of a n y one isotope is liable to s w a m p a n y of the others. I t is i m p o r t a n t that, w h e n the set of detectors has b e e n decided u p o n a n d calibrated, the characteristics of each detector in the set be m a i n t a i n e d strictly constant. I n particular, if differentiation b e t w e e n two nuclides of different half-life is m a d e b y c o u n t i n g the sample a g a i n after a time interval, t h e n w h e n once decided u p o n this time interval must be exactly the same for all samples, including the c a l i b r a t i o n samples. I n the same way, if the radioactive decay of a n y of the nuclides is not negligible d u r i n g the time t a k e n to measure the sample b y all the detectors, t h e n this effect can be completely t a k e n account of by m a k i n g the m e a s u r e m e n t s in a fixed order according to a n exact time schedule, again including the calib r a t i n g samples. C. W. GILBERT
Christie Hospital and Holt Radium Institute Manchester 20
References 1. ADAMS R., WOODWARD I. C. a n d HOLLOWAYJ. E. Int. J. Appl. Rad. Isotopes 3, 156 (1958). 2. ANTHONY D. S., CAMPBELLJ. E., HAOEE G. R. a n d ROBAJDEK E. S. Radiat. Res. 4, 286 (1956). 3. EsNouP M. P. Brit. d. Appl. Phys. 9, 161 (1958). 4. GROOM A. C., ROBERTS P. W. a n d ROWLANDS S.
Proceedings of the UNESCO Conference on Radioisotopes in Scientific Research, P a p e r 147 (1957). 5. GaooM A. C., ROBERTS P. W., ROWLANDS S. a n d THOMAS H. W. Brit. J. Radiol. 32, 641 (1959). 6. LmBY R. L. a n d HAND K. J. Lab. Clin. A.Ied. 48, 289 (1956). 7. MITCHELL T. G., SPENCER R. P. a n d KING ]~. R. Amer. d. Clin. Path. 28, 461 (1957). 8. MUNRO D. S., RENSCHLER H. a n d "VVILsON C. M. Phys. ~Ied. Biol. 2, 239 (1958). 9. ODEBALD E., MEURMAN L. a n d ZILIOTTO D. Acta Radiol. 44, 337 (1955).
S p e c t r o m 6 t r i e d u R a y o n n e m e n t X Excit6 par une Source Radioactive Emettrice de R a y o n n e r n e n t (Received 17 3/larch 1960) L'EXCITATION d u r a y o n n e m e n t X caractdristique d ' u n dldment p a r u n r a y o n n e m e n t [J dmis p a r u n e source radioactive a fait l'objet de n o m b r e u x t r a v a u x destinds 5~ mettre a u p o i n t des sources de rayons X portatives. O-4) COOK et al. (5) ont m o n t r d que la spectromdtrie d u r a y o n n e m e n t iX excitd p a r u n r a y o n n e m e n t /3 a u m o y e n d ' u n cristal dtait difficilem e n t applicable ~ l'analyse c h i m i q u e p a r fluorescence X p a r suite de son m a n q u e de sensibilitd; en effet: (1) L'intensit6 des sources radioactives actuellem e n t disponibles est faible si on la c o m p a r e ~ celle des tubes ~ rayons X utilisds en analye p a r fluorescence X-IX. (2) P a r suite de la forte absorption des r a y o n n e m e n t s t3 de faible dnergie, on est obligd d'utiliser des r a y o n n e m e n t s / ~ assez 6nergiques p o u r que le faisceau d'excitation ait u n e intensitd suffisante a u n i v e a u de l'dchantillon; dans ces conditions, le r a y o n n e m e n t X de freinage p r o d u i t dans l'dchantillon et l ' a p p a r e i l lage, d o n n e u n b r u i t de fond i m p o r t a n t . (3) Enfin, u n e p r o p o r t i o n i m p o r t a n t e d u r a y o n n e merit /~ est rdtrodiffusde p a r l'dchantillon et ce p h d n o m ~ n e contribue aussi ~ l ' a u g m e n t a t i o n d u b r u i t de fond. O n a pu, c e p e n d a n t , rdaliser u n a p p a r e i l de mesure d'dpaisseurs de ddp6ts et d'analyse c h i m i q u e p a r fluorescence /~-X e n effectuant la spectromdtrie d u
230
the actual sample c o u n t c a n be o b t a i n e d from the s t a n d a r d q u e n c h i n g curve.
Acknowledgements--This work was s u p p o r t e d b y U.S. Public H e a l t h Service G r a n t C - 4 2 3 6 a n d was carried out w i t h the technical assistance of Louis J. PHILIPP.
Department of Biochemistry MILTON TOPOREK Jefferson Medical Co[le.~e Philadelphia, Pennsylvania, U.S.A. References 1. VAUGHAN M., STEINBERG D. a n d LOGAN J. Science 126, 446 (1957). 2. CHEN P. S. Jr. Proc. Soc. Exp. Biol., N.Y. 98, 546 (1958). 3. KERR V. N., HAYES F. N. a n d OTT D. G. Int. J. Appl. Rad. Isotopes 1, 284 (1957). 4. DAVIDSONJ. D. Liquid Scintillation Counting (Edited by BELL C. G. JR. a n d HAYES F. N.) p. 88, Perg a m o n Press, New York (1958). 5. KALLMAN H. a n d FURST M. Liquid Scintillation Counting (Edited b y BELL C. G. J m a n d HAYES F. N.) p. 3. P e r g a m o n Press, N e w York (1958). 6. TOPOREK M. 136th National Meeting of the American Chemical Society Abstracts p. 86C, S e p t e m b e r (1959). 7. HERBERG R. J . Analyt. Chem. 32, 42 (1960). 8. PASSMANNJ. iV[., RADIN N. S. a n d COOPERJ. A. D. Analyt. Chem. 28, 484 (1956). Note added in proof: Liquid scintillation counting is growing very rapidly. It is also shifting its field from the very low-energy/?-emitters such as C 14 and I-I3 where the technique is not so much "necessary" as "desirable". During the development of this technique, the concept of "quenching" has shifted from a pure electronic quenching as used in Geiger tubes and such devices, to a much more important concept of"quenching" which is determined by such things as the transfer of energy from the isotope through various chemical systems to the counting mechanism. The result, changed counting rates, is the same in chemical or in electronic quenching. However, the older definition of quenching is not vitiated. The newer concept of chemical quenching is probably not yet completely shifted. The importance of the article by TOPOREK lies in the description of a procedure for correction in the face of a changing concept of "quenching".
Simultaneous Estimation of Several Radioactive Nuclides
(First received2 March 1960 and in revisedform 11 April 1960) WHEN several radioactive species are used simultaneously in a tracer experiment, the activity of all the nuclides m u s t be m e a s u r e d in each sample. This
note describes a general m e t h o d of doing this, w h i c h is applicable to a n y n u m b e r of nuclides a n d in particular points out the simple way in w h i c h the calib r a t i o n c a n be m a d e . Several accounts h a v e b e e n given (1-9) of methods for analysing p a r t i c u l a r mixtures a n d in some cases they h a v e involved the solution of simultaneous equations for each sample. This is n o t necessary; the solution of simultaneous e q u a tions c a n be restricted to the calibration, a n d thereafter the m e a s u r e m e n t s of each sample c a n be reduced b y a simple calculation. I f n different radioactive tracers are b e i n g used, t h e n in order to d e t e r m i n e the activity of each nuclide it is necessary to measure each sample with a set of n r a d i a t i o n detectors w h i c h h a v e different sensitivities for each nuclide. Such detectors must h a v e a linear response to radiations (after correction if necessary) a n d m u s t be used u n d e r precisely defined conditions. T h e same i n s t r u m e n t m a y be used u n d e r two different conditions to provide two distinct detectors, as for example by using different absorbers, b y using scintillation counters at different parts of their spect r u m or by repeating the m e a s u r e m e n t s after a time interval. Let U z b e the set of n readings t h a t a sample causes in the set of n detectors, a n d let A k be the activities of the n different nuclides in the sample. Since r a d i a t i o n detectors respond i n d e p e n d e n t l y to the radiations from a n u m b e r of sources, t h e n the reading of each detector will be a linear sum of the activities of each of the n nuclides in the sample. This c a n be represented b y the following set of equations,
U s = EkbzkAk.
(1)
Now, p r o v i d e d the d e t e r m i n a n t of the m a t r i x (b~) does not vanish, the A k c a n be written as a linear sum of the U~, A~ = Eza~U ~ (2) w h e r e the m a t r i x (ak~) is the inverse of the m a t r i x (bu~), a n d can be d e t e r m i n e d b y m e a s u r i n g a set of n k n o w n calibrating samples. I n dealing w i t h multiple tracers one should recognize t h a t the activity of each nuclide in a sample c a n be calculated simply as a linear sum of the readings of each detector, as shown b y e q u a t i o n (2), after the m a t r i x (ak~) has b e e n d e t e r m i n e d by a calibration procedure. T h e calibration should be m a d e b y suitable substitutions into e q u a t i o n (2) a n d n o reference need be m a d e to e q u a t i o n (1). i f the d e t e r m i n a n t of the m a t r i x (bz~) vanishes, t h e n equations (1) are n o t all i n d e p e n d e n t a n d t h a t set of detectors will not give e n o u g h information to determ i n e u n i q u e l y the activity of each nuclide in the sample. I n this case it will be found t h a t the calib r a t i o n m e t h o d described later will not give u n i q u e solutions for the m a t r i x (ak~).
231
Technical notes
T h e case for two tracer nuclides will be presented in detail a n d in a form t h a t c a n be readily e x t e n d e d to the general case. Consider the two isotopes Fe 59 a n d 32p, a n d the use of two detectors, a scintillation c o u n t e r a n d a Geiger counter, b o t h suitable for c o u n t i n g a 10 m l liquid sample. Let U s a n d Ug be the c o u n t i n g rates (less b a c k g r o u n d ) of a sample m e a s u r e d with tile scintillation a n d w i t h the Geiger counter, a n d A 1 a n d A~ the activities of the Fe 59 a n d the 32p in the sample. T h e n the general e q u a t i o n (2), enables the following to be written d o w n for this case, A.t -- a U s + b U g
(3)
Azo = c U s + d U g
where a, b, c a n d d are constants of the set of two counters a n d r e m a i n the same as long as the characteristics of b o t h counters r e m a i n u n c h a n g e d . W h e n once d e t e r m i n e d , the constants need only be checked at infrequent intervals, if the counter characteristics are stable. Now, equations (3) hold, with a p p r o p r i a t e constants, w h e n the activities of the nuclides A r a n d Av are m e a s u r e d in a n y valid set of units. T h e r e is one set of units, however, t h a t has the special p r o p e r t y of m a k i n g the c a l i b r a t i o n particularly simple a n d this is the set t h a t measures the activities in units of a detector reading. I t is p a r t i c u l a r l y f o r t u n a t e t h a t it is also a n a t u r a l way to measure the activities a n d is c o m m o n l y used in practice. D e n o t e the activities of the nuclides in these units b y F s a n d Po" T h u s a n activity o f F s units of Fe 59 will cause the scintillation c o u n t e r to give a c o u n t i n g rate o f F s counts p e r u n i t time, a n d similarly the Geiger c o u n t e r will give P g counts per u n i t time for Pg units of P 32. T h e equations (3) can n o w be w r i t t e n as F s = a U s + bU~,
(4)
Po = cUs + d U g
w h e r e the constants are a p p r o p r i a t e to these units of activity. T h e constants a, b, c a n d d in equations (4) can be d e t e r m i n e d simply b y c o u n t i n g with each counter, two c a l i b r a t i n g samples, one c o n t a i n i n g Fe 59 only
a n d the o t h e r p32 only. Because of the p a r t i c u l a r choice of units of activity, it is n o t necessary to p r e p a r e the samples w i t h k n o w n activities, except in so far as they should give convenient c o u n t i n g rates. Let the c o u n t i n g rates (less b a c k g r o u n d ) of the two calibrating samples by the two counters be f s , f g , Ps a n d pg. Because these samples contain one nuclide only, it follows from our choice of units of activity t h a t the activity of the two calibrating samples are f s a n d P o" Hence, b y substituting the c o u n t i n g rates for each sample into equations (4) a n d r e a r r a n g i n g them, two sets of simultaneous equations are obtained, f.~=afs +bfo 0 = aps + bpg 0 = cfs + d f g
and
Prt = cPs + dpg (5) from w h i c h the constants a, b, c a n d d can be calculated. T h e calibration for a particular pair of scintillation a n d Geiger counters t h a t was used in a biological investigation, was F s = U s + 0"004U s - 0-059Ug Pg ~ Ug ÷ 0"004Ug -- 0 ' 0 6 8 U s.
(6)
T a b l e 1 shows the calculations in full for a few typical samples as they a p p e a r in the working note book, a n d shows h o w simple they can be; a slide rule gives m o r e t h a n a d e q u a t e accuracy. O f p a r t i c u l a r interest to note is the sample 5 w h i c h was k n o w n to contain only the one isotope. H e r e m e a s u r e m e n t by the one counter only was needed a n d no a d j u s t m e n t was necessary. Also shown in the T a b l e are the c o u n t i n g rates for the two calibration samples from w h i c h the constants in equations (6) were calculated. I n bold type is shown the reduction of these c o u n t i n g rates b y equations (6) as t h o u g h they were o r d i n a r y samples, showing t h a t a correct result is obtained. This, of course, is only a check t h a t the constants in equations (6) were calculated correctly, b u t it is instructive in showing h o w the m e t h o d works, in particular w h y a a n d d are different from one.
TABLE 1. Specimen work sheet. U, and Ug counting rates (counts per minute less background) of scintillation and Geiger counters. F, and Pg counting rates due to Fe 59 and pm content of sample Sample No.
Uo + 0.004U, -- 0-059Ug 671 765 906 1447 1636
Calibration Calibration
1296 78
3 3 4 6
= Fs
Ug + 0.004Ug -- 0.068U,
= pg
--13 --21 --27 --11
661 747 883 1442 1636
222 354 458 191
1 1 2 1
--46 --52 --62 --98
177 303 398 94
5
--5
1296
0
--78
0
88 1324
0
5
--88 --5
0 1324
232
Technical notes
T h e merits of m e a s u r i n g the activities of the nuclides in the samples in units of a detector reading are t h a t the activities of the calibrating samples need n o t be known, t h a t in favourable circumstances the calculations b e c o m e very easy as shown by the example in equations (6) a n d t h a t if a sample is k n o w n to c o n t a i n only one nuclide only one m e a s u r e m e n t need be m a d e . I n m a n y tracer experiments the m e a s u r e m e n t of activities in a r b i t r a r y units is all t h a t is necessary t h o u g h t h e r e are a d v a n t a g e s in using the curie or its submultiples. Conversion to microcuries can be m a d e later if w a n t e d and, if the activities of the c a l i b r a t i n g samples are known, they c a n be used to provide the calibration necessary for this, b u t it is often m o r e c o n v e n i e n t to keep o t h e r sources for this purpose. T h e extension to n tracer nuclides is s t r a i g h t f o r w a r d ; n calibrating samples are needed, each c o n t a i n i n g one nuclide only. T h e solution of n sets of n simultaneous equations is n e e d e d to get the constants of e q u a t i o n (2), b u t thereafter the reduction of each sample requires only simple multiplication a n d addition. It is i m p o r t a n t to notice t h a t no accurate information is needed a b o u t the radiations given off by the nuclides or a b o u t the characteristics of the r a d i a t i o n detectors; the calibration procedure makes alI the m e a s u r e m e n t s t h a t are necessary. However, some knowledge of the properties of the radiations a n d the detectors is v a l u a b l e in deciding w h i c h is the best set of detectors to use. It is clearly desirable, as far as possible, to use the detectors in such a way as to give a big differentiation between each nuclide. This would be shown b y all b u t one of the constants in each of the equations (2) b e i n g small. This ideal c a n n o t always be o b t a i n e d a n d a n e x a m i n a t i o n of the constants of equations (2) will show h o w accurate the simultaneous estimation of the various nuclides is likely to be a n d at w h a t level the activity of a n y one isotope is liable to s w a m p a n y of the others. I t is i m p o r t a n t that, w h e n the set of detectors has b e e n decided u p o n a n d calibrated, the characteristics of each detector in the set be m a i n t a i n e d strictly constant. I n particular, if differentiation b e t w e e n two nuclides of different half-life is m a d e b y c o u n t i n g the sample a g a i n after a time interval, t h e n w h e n once decided u p o n this time interval must be exactly the same for all samples, including the c a l i b r a t i o n samples. I n the same way, if the radioactive decay of a n y of the nuclides is not negligible d u r i n g the time t a k e n to measure the sample b y all the detectors, t h e n this effect can be completely t a k e n account of by m a k i n g the m e a s u r e m e n t s in a fixed order according to a n exact time schedule, again including the calib r a t i n g samples. C. W. GILBERT
Christie Hospital and Holt Radium Institute Manchester 20
References 1. ADAMS R., WOODWARD I. C. a n d HOLLOWAYJ. E. Int. J. Appl. Rad. Isotopes 3, 156 (1958). 2. ANTHONY D. S., CAMPBELLJ. E., HAOEE G. R. a n d ROBAJDEK E. S. Radiat. Res. 4, 286 (1956). 3. EsNouP M. P. Brit. d. Appl. Phys. 9, 161 (1958). 4. GROOM A. C., ROBERTS P. W. a n d ROWLANDS S.
Proceedings of the UNESCO Conference on Radioisotopes in Scientific Research, P a p e r 147 (1957). 5. GaooM A. C., ROBERTS P. W., ROWLANDS S. a n d THOMAS H. W. Brit. J. Radiol. 32, 641 (1959). 6. LmBY R. L. a n d HAND K. J. Lab. Clin. A.Ied. 48, 289 (1956). 7. MITCHELL T. G., SPENCER R. P. a n d KING ]~. R. Amer. d. Clin. Path. 28, 461 (1957). 8. MUNRO D. S., RENSCHLER H. a n d "VVILsON C. M. Phys. ~Ied. Biol. 2, 239 (1958). 9. ODEBALD E., MEURMAN L. a n d ZILIOTTO D. Acta Radiol. 44, 337 (1955).
S p e c t r o m 6 t r i e d u R a y o n n e m e n t X Excit6 par une Source Radioactive Emettrice de R a y o n n e r n e n t (Received 17 3/larch 1960) L'EXCITATION d u r a y o n n e m e n t X caractdristique d ' u n dldment p a r u n r a y o n n e m e n t [J dmis p a r u n e source radioactive a fait l'objet de n o m b r e u x t r a v a u x destinds 5~ mettre a u p o i n t des sources de rayons X portatives. O-4) COOK et al. (5) ont m o n t r d que la spectromdtrie d u r a y o n n e m e n t iX excitd p a r u n r a y o n n e m e n t /3 a u m o y e n d ' u n cristal dtait difficilem e n t applicable ~ l'analyse c h i m i q u e p a r fluorescence X p a r suite de son m a n q u e de sensibilitd; en effet: (1) L'intensit6 des sources radioactives actuellem e n t disponibles est faible si on la c o m p a r e ~ celle des tubes ~ rayons X utilisds en analye p a r fluorescence X-IX. (2) P a r suite de la forte absorption des r a y o n n e m e n t s t3 de faible dnergie, on est obligd d'utiliser des r a y o n n e m e n t s / ~ assez 6nergiques p o u r que le faisceau d'excitation ait u n e intensitd suffisante a u n i v e a u de l'dchantillon; dans ces conditions, le r a y o n n e m e n t X de freinage p r o d u i t dans l'dchantillon et l ' a p p a r e i l lage, d o n n e u n b r u i t de fond i m p o r t a n t . (3) Enfin, u n e p r o p o r t i o n i m p o r t a n t e d u r a y o n n e merit /~ est rdtrodiffusde p a r l'dchantillon et ce p h d n o m ~ n e contribue aussi ~ l ' a u g m e n t a t i o n d u b r u i t de fond. O n a pu, c e p e n d a n t , rdaliser u n a p p a r e i l de mesure d'dpaisseurs de ddp6ts et d'analyse c h i m i q u e p a r fluorescence /~-X e n effectuant la spectromdtrie d u