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New determination of the half-life of 121Te
Appl. Radiat. lsot. Vol. 46, No. 9, pp. 865-868, 1995 Copyright© 1995ElsevierScienceLtd 0969-8043(95)00187-5 Printed in Great Britain,All rights reserved 0969-8(M3/95 $9.50+ 0.00
Pergamon
New Determination of the Half-life of 121Te H. S I E G E R T Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany (Received 29 December 1994, in revised form 2 March 1995) After complete decay of the t23I activity of an aqueous solution, the y-emissions from the long-lived contaminating radionuclides t2tTe~ and t2tTe were followed simultaneously over a period of about 120 days. A revised value for the half-life Tj/2(t2tTe)= (19.16_ 0.05) days is deduced which differs appreciably from the value of 16.8 days adopted in the literature. The special influence of n~Tem nuclei in the decay chain 12tTe~12tTe--*t2tSb on the evaluation procedure is discussed in detail.
Introduction
Method
In the production process of t23I a highly pure Figure 1 shows a simplified scheme of the decay (>95.5%) gas target of '24Xe is bombarded in a chain '2~Tem~2~Te--*~2~Sb. There are several cyclotron with accelerated protons, leading to the branches for the decay of the radionuclide 12iTem. To main reaction 124Xe (p, 2n) '23Cs. The short-lived a minor extent (11.4%) the radionuclide 121Terndecays isotope 123Csdecays by electron capture via ~23Xeinto to the excited states of ~21Sb without populating the 123I. At the same time the unstable isotope ,2q is ground state of t2tTe. This decay mode has no effect produced by the alternative reaction n4Xe (p, ~t) nq. in this work. The majority (88.6%) of disintegrations This radionuclide decays by electron capture into of J2~Tempopulate the ground state of '2'Te, enabling J2~Te. So ~2JTe is one of the common contaminants of us to determine the half-life of ~2JTe by using a 123I solutions used in nuclear medicine for diagnostic calibrated HPGe spectrometer and following purposes. When calculating the integral dose applied simultaneously the count-rate of the two full-energy to a patient, the initial activities of all long-lived peaks at E?z = 212keV from t2tTern decay and at contaminants must be known, even if the activity E?2--573 keV from ~21Te decay during a period of ratio with respect to '23I during the medical treatment about 120days. Since our HPGe detector system may be only of the order of 10 -4 . For this purpose was routinely used during this time for other correct values of all the half-lives implicated are an measurements, too, we took care that our measuring important prerequisite. conditions did not occasionally change with time. In 1993 when examining an t23I solution with our The count-rate measurements reported here were HPGe detector system (Sch6tzig et al., 1992) in started after the '231 activity had decayed completely. order to establish the activities of all radionuclidic As the discrepancy between the old and the new contaminants, we found that the adopted value of half-life data of '2~Te is possibly related to measureabout 16.8 days for the half-life of '21Te (see Tamura meats with appreciably differing amounts of 121Ternin et al., 1991; Browne and Firestone, 1986) could not the t2~Te sources, the general formulas for the evalube correct. After the complete decay of the '23I ation of primarily acquired counting data are activity in the solution under investigation we then repeated here. followed the count rate of the full-energy peak at At a reference time to the relevant part (88.6%) of E~.2= 573 keV from 12'Te over a period of about 60 the activity of the parent nuclide ~2'Temis denoted as days, obtaining Tl/2(12'Te) = (19.39 _+ 0.20) days as a Al(to)=O.886.A['2'Tem(to)]. The activity of the preliminary result (Sch6tzig and Schrader, 1993). daughter nuclide '2~Te at reference time is written as After realizing the possible influence of the A20(t0). For the sake of brevity only the relevant part previously undetected impurity n'Tem decaying partly At(to) of the parent activity is considered in the to '2~Te with a half-life of 154 days, in 1994 we started following formulas. At(t ) at a measuring time t is a second set of measurements now giving special given by: attention to corrections caused by the amount of '2'Tern within the solution under investigation. At(t) = At(t0) e -~'l.... ~. 865
H. Siegert
866
y-ray peak is given by
with ).1 = In 2/Ti/2(12tTem).
(1)
ll + T
N~.l = P~,t~,,.l
fi
At(t0) e-~: .... ~dt.
The activity A2(t) of the daughter nuclide 12LTe at time t has two components:
Solving the integral of equation (5a) we obtain:
Az(t ) = A2o(t ) + A2i(t ).
N,: = P'4 E,,,IA l(to) e-~'(t'- t°)(1 - c -~' r)/2~
(2)
The first term, which is dominating for our source: A2o(t) = A2o(to ) e-~2(t-to)
N, 4 = p,:E,~lal(to) T e-~,(t, -to)
x [sinh().] T/2)/().l T/2)], ).2 = In 2/Tl/2(]21Te),
(3)
describes the decrease of the activity A20(t0) existing at the reference time to. The second term of equation
(2): A2] (t) = A 1(t0)).2 [e - ~ " ' - ,o) _ e-~( . . . . )]/().2 - ~ ),
(4) is related to the number of nuclei of 121Te that have been generated by the parent nuclide 121Tem since the reference time to [see, for example, Evans (1955) or D I N 6814, part 4 (1990)]. At the reference time to the component A2~(t) vanishes by definition. The product of the emission probability of 212 keV quanta per disintegration of )2lTe"~ and the detection probability of these quanta in our detection system may be denoted by Prl 6rl. The corresponding product of the emission probability of 573 keV quanta per disintegration of roTe and their detection probability may be pr2~>.2. If t] denotes the time at the beginning of a measurement running until (t) + T), then the number N : of acquired pulses within the 212 keV
0.114 /
121Tem
294.0
3+
~(0.886
~
I
212.2
154d
0.062
ns
1130.2_~ I
~.4_~ EC/~121Te /
1+
(5b)
Equation (5b) may be transformed identically into:
with
11" -'~
(5a)
I
0
19.16 d
(5c)
with t s = tl + T / 2 denoting the reference time of measurement. With the help of equations (5b) or (5c) the relevant part A I (to) of the activity of the parent nuclide t21Tem can be deduced from each data triple (Nyt, T, q ) for a given parameter ).1. If the product 0.1T/2) is small (due to a short counting interval), the term included in the brackets of equation (5c) has a value close to unity. The number Ny2 of simultaneously acquired pulses in the 573 keV y-ray peak is given by:
f
N,~2 = p,t2E,,~2 |
tl + T
0tl
(6a)
A2(t) dt.
When introducing expressions from equations (2), (3) and (4), we split up the number of counts attributed to the exponential terms with parameters ).2 and ).t: N~,2= P~2*r2[A 20(t0)/).2 - A i (t0)/().2
-- ).1
)]
x e -a2(', - tol(1 - e - a : ) + p;.2E,,,zA~ (to)2 2 × e -x"'' -'°)(1 - e -x' r)/{)., ().2 - ).1)}.
(6b)
The expression in the second line of equation (6b) is proportional to the measured quantity N;.I, see equation (Sb), and represents in our case only a small contribution to the measured count number N;.2. By subtracting this term from the measured number Nr2, an amount N ~ [first part of equation (6b)] remains: N~2 = U;.2 - {p;,2E;,2/(P,,.Ie;.. )} {).2/().2 -- ).t)}N;.I = p;.ze;.2[A2o(to)l).2 - AI (t0)/(22 - ).1 )1
x e -~2"' -'°)(1 - e - ~ : ) .
(7a)
By executing the same transformation of equation (7a) as with equation (5b), we get:
I+
0,*:2 =
~73.1y
p;.2~;.2[A2o(to)
-- Ax(to){).2/().2 - ).1)}IT
x e -~:', - '0~[sinh().2 T/2) (/1-2T/2)].
121Sb Fig.
1. Simplified
scheme
of
the
decay
chain
t21Tem--*t2~Te~2~Sb with energies, spins and parities taken from Tamura et al. (1991).
(7b)
In order to obtain count numbers with nearly the same statistical uncertainty at different measuring times, it was necessary to increase the measuring time to 400,000 s at high values of q. Therefore the expression in the last brackets of equation (7b) was no longer assumed to be constant (with the value of unity). Variations of this term were taken into account. As a consequence, according to equation (7b), an exponential fit of the measured data of N*2
Half-life of 12aTe
867
88 kBq 86 •
•
N
N
•
•
•
•
18.9d
~
N
19.0d
84
82 -
•
19.1 d
"
19.2d
80 ix
19.3d
78 19.4d 76
19.5 d
74 0
20
40
60
T i m e (t s - to)
80
100
d
120
=
Fig. 2. Variation of calculated activity value for ~2~Teat reference time to vs the elapsed time until the measurement with the tentative half-life of t2tTe taken as a parameter. with the given time delay (q = to) as a variable was not a suitable method for the evaluation of the parameter 22 from our measurement data. Alternatively, from equation (7b) the activity A2o(to) of the daughter nuclide ~21Te was calculated for each data triple (N~, T, t~ ) assuming fixed values for the parameters 22 and ).L:
half-life Ti/2(12~Te). We obtain T,2(121Te) = (19.16 _+ 0.05) days.
The given value of the standard uncertainty of the results reflects mainly the reproducibility of the geometry measuring conditions at different times of measurement. As can be seen from Fig. 2, the mean spread of data points belonging to one straight line A2o(to) = N*2 e +a21's-'°)/{[sinh(/.2 T/2)/(/. 2 T/2)] produces an uncertainty of the slope corresponding x P>.2',.2T} + Al(lo){/.2/(/. 2 --/.1)}. (8) to half the chosen step of the parameter T~/2. The contribution to the total uncertainty caused by the The first method adopted here to find the appropriate dead-time corrections of the counting procedure value for /-2 (and the half-life of roTe) utilizes (maximum rate less than 50 s-J) is negligible, as is the equation (8) by varying parameter/-2 until a consist- uncertainty of the time measurements. Changes of the ent value for A20(t0) independent of t, is found. This, detection probability with time in our detection naturally, is expected to occur when ).2 equals system are less than l0 -3 per year resulting in no In 2/TI/2 Q21Te). significant influence over 120 days. The spread which resulted from using two alternative methods for the peak area evaluation (Sch6tzig et al., 1973) was only Results AT~j2(121Te) = 0.01 days. JanBen (1993) had developed a special PC-code for Activity values A20(t0) of the daughter nuclide ~2~Te, calculated according to equation (8) from a set regression calculations with different model functions of I I consecutive measurements, are plotted in Fig. 2 applying the method of least squares adjustment of against the time delay ( t s - to) with respect to the several independent fit parameters. By introducing reference time to. The quantity In 2/22 is taken as a the nonlinear expression of equation (6b) as a model floating parameter. Numerical values of 1.83 x l0 -3 function in a special version of this code, it was for the product p;.j E;.j and 6.19 x l0 -4 for the product possible to check the given result also with the help p~.2E;,2were used. For a low uncertainty contribution of a second, more conventional method. For each from the counting statistics, a minimum of 2 x l05 net single measurement the data of the time t) at the pulses were acquired in a peak area to be evaluated. beginning of a measurement, its duration T, the Due to small additional systematic uncertainty number of peak pulses N,.2 counted and the standard components, the relative standard uncertainty of a uncertainty associated with N;.2 were taken as a four-fold experimental input data set. The activity given data point totals 0.3%. Within the parameter range of Fig. 2 the slopes of A j (t0) and the decay constant 2j of the parent nuclide the regression lines vary between positive and as well as the product p..2E;.2 were kept constant negative values. The value of the parameter In 2/). 2 during the fitting process. The activity A20(t0) at which belongs to a straight line with the slope the reference time to and the decay constant ";,2of the value zero represents the experimental result for the daughter nuclide were fitted by the program. The
H. Siegert
868
result calculated for the value of the half-life Tl/2(t21Te) was the same as above. By varying the values of the fixed input parameters within the range of the uncertainties given in this case, it was proved that the fixed parameters had no significant influence on the value of the half-life determined by the first method.
Discussion The measured T1/2(121Te) value deviates considerably from the values of Edwards and Pool (1946) (17+ l)days, Bhattacharyya and Shastry (1963) (17__+ 1)days and Karim (1973) (16.78+ 0.35) days. In contrast to the situation assumed to prevail during the earlier measurements, the primary conditions for carrying out these investigations were presumably more favorable now. The activity ratio A(t21Tem)/A(121Te) at our starting point was only 5 × 10 -4 increasing to less than 2.5 x 10 -2 after 120 days, so the contribution of 12~Tem nuclei made only very small corrections necessary in the present case. In earlier investigations with a higher content of 12~Tem nuclei it may have been overlooked that the decay curve according to equation (6b) is not just the sum of two exponential terms so that significant systematic uncertainties may have been introduced. The result of our preliminary measurement of the half-life of 121Te (Schftzig and Schrader, 1993) is in agreement with the new value within the standard uncertainties quoted. The half-life of J21Te~" used was taken from Tamura et al. (1991) and could not be checked precisely during these measurements, because the value of the primary activity A[~21Tem(t0)] was only about 40 Bq and the observation time of 120 days was too short. Even if 121Te as a contaminant of ~2~I solutions contributes very little to the integral dose applied to a patient for the period of medical treatment with 1231,as is normally the case for doses of other long-lived contaminants such as 12~Te~, 95Tcra and 96Tc, too, the dose contribution for the time interval after total decay of ~23I is not completely negligible. When assuming, for example, an initial activity ratio of A(~2JTe)/A(12~I) = (1.5 kBq ~21Te/1.0MBq
t23I) and half-lives of 19.16 days, respectively 0.55088 days, the time integral over the air kerma rate from t21Te amounts to about 12.9% of the time integral over the air kerma rate from t23I, in comparison to a fraction of only about 11.3%, if a half-life of 16.8 days for !21Te is chosen. Both figures may overestimate the relative extra doses from 12tTe which are really transferred to a patient. For a thorough calculation it would be necessary to discuss the spatial distribution of the incorporated radionuclides in the body and the dynamics of their biological excretion parallel to the physical decay process. This discussion is beyond the scope of this paper. Acknowledgement--The assistance of R. Def6r in carrying out the count-rate measurements and preparing the diagrams is gratefully acknowleged.
References Bhattacharyya R. and Shastry S. (1963) Positon-decay of 121Te and the excited states of 12tSb. Nucl. Phys. 41, 184. Browne E. and Firestone R. B. (1986) Table of Radioactive Isotopes (Shirley V.S., Ed.), p. 334. Wiley, New York. DIN 6814, Teil 4 (1990) Begriffe und Benennungen in der radiologischen Technik. Beuth, Berlin. Edwards J. E. and Pool M. L. (1946) Radioactive Te from Sb bombardment. Phys. Rev. 69, 140. Evans J. D. (1955) The Atomic Nucleus, p. 477. McGrawHill, New York. JanBen H. (1993) FIT9--Ein Dialogprogramm fiir Ausgleichsreehnungen nach der Methode der kleinsten Quadrate. Physikalisch-Technische Bundesanstalt, Braunschweig, Laborbericht 6.31-93-2. Karim H. M. A. (1973) Study of 4 GeV electron spallation products of iodine. Radiochim. Acta 19, 1. Sch6tzig U. and Schrader H. (1993) Halbwertszeiten und Emissionswahrscheinlichkeiten yon h/iufig verwendeten Radionukliden. Physikalisch-Technisehe Bundesanstalt, Braunschweig, Bericht PTB-Ra-16/4. Sch6tzig U., Debertin K. and Weil3 H. M. (1973) Bestimmung von Gammastrahlen-Emissionswahrscheinlichkeiten mit einem Ge(Li)-Spektrometer. PTBMitteilungen 83, 307. Sch6tzig U., Schrader H. and Debertin K. (1992) Precision measurements of radioactive decay data. In Proc. International Conference on "Nuclear Data for Science and Technology', Jfilich, Germany, p. 562. Springer, Berlin. Tamura T, Iimura H., Miyano K. and Ohya S. (1991) Nucl. Data Sheets 64, 335.
Pergamon
New Determination of the Half-life of 121Te H. S I E G E R T Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany (Received 29 December 1994, in revised form 2 March 1995) After complete decay of the t23I activity of an aqueous solution, the y-emissions from the long-lived contaminating radionuclides t2tTe~ and t2tTe were followed simultaneously over a period of about 120 days. A revised value for the half-life Tj/2(t2tTe)= (19.16_ 0.05) days is deduced which differs appreciably from the value of 16.8 days adopted in the literature. The special influence of n~Tem nuclei in the decay chain 12tTe~12tTe--*t2tSb on the evaluation procedure is discussed in detail.
Introduction
Method
In the production process of t23I a highly pure Figure 1 shows a simplified scheme of the decay (>95.5%) gas target of '24Xe is bombarded in a chain '2~Tem~2~Te--*~2~Sb. There are several cyclotron with accelerated protons, leading to the branches for the decay of the radionuclide 12iTem. To main reaction 124Xe (p, 2n) '23Cs. The short-lived a minor extent (11.4%) the radionuclide 121Terndecays isotope 123Csdecays by electron capture via ~23Xeinto to the excited states of ~21Sb without populating the 123I. At the same time the unstable isotope ,2q is ground state of t2tTe. This decay mode has no effect produced by the alternative reaction n4Xe (p, ~t) nq. in this work. The majority (88.6%) of disintegrations This radionuclide decays by electron capture into of J2~Tempopulate the ground state of '2'Te, enabling J2~Te. So ~2JTe is one of the common contaminants of us to determine the half-life of ~2JTe by using a 123I solutions used in nuclear medicine for diagnostic calibrated HPGe spectrometer and following purposes. When calculating the integral dose applied simultaneously the count-rate of the two full-energy to a patient, the initial activities of all long-lived peaks at E?z = 212keV from t2tTern decay and at contaminants must be known, even if the activity E?2--573 keV from ~21Te decay during a period of ratio with respect to '23I during the medical treatment about 120days. Since our HPGe detector system may be only of the order of 10 -4 . For this purpose was routinely used during this time for other correct values of all the half-lives implicated are an measurements, too, we took care that our measuring important prerequisite. conditions did not occasionally change with time. In 1993 when examining an t23I solution with our The count-rate measurements reported here were HPGe detector system (Sch6tzig et al., 1992) in started after the '231 activity had decayed completely. order to establish the activities of all radionuclidic As the discrepancy between the old and the new contaminants, we found that the adopted value of half-life data of '2~Te is possibly related to measureabout 16.8 days for the half-life of '21Te (see Tamura meats with appreciably differing amounts of 121Ternin et al., 1991; Browne and Firestone, 1986) could not the t2~Te sources, the general formulas for the evalube correct. After the complete decay of the '23I ation of primarily acquired counting data are activity in the solution under investigation we then repeated here. followed the count rate of the full-energy peak at At a reference time to the relevant part (88.6%) of E~.2= 573 keV from 12'Te over a period of about 60 the activity of the parent nuclide ~2'Temis denoted as days, obtaining Tl/2(12'Te) = (19.39 _+ 0.20) days as a Al(to)=O.886.A['2'Tem(to)]. The activity of the preliminary result (Sch6tzig and Schrader, 1993). daughter nuclide '2~Te at reference time is written as After realizing the possible influence of the A20(t0). For the sake of brevity only the relevant part previously undetected impurity n'Tem decaying partly At(to) of the parent activity is considered in the to '2~Te with a half-life of 154 days, in 1994 we started following formulas. At(t ) at a measuring time t is a second set of measurements now giving special given by: attention to corrections caused by the amount of '2'Tern within the solution under investigation. At(t) = At(t0) e -~'l.... ~. 865
H. Siegert
866
y-ray peak is given by
with ).1 = In 2/Ti/2(12tTem).
(1)
ll + T
N~.l = P~,t~,,.l
fi
At(t0) e-~: .... ~dt.
The activity A2(t) of the daughter nuclide 12LTe at time t has two components:
Solving the integral of equation (5a) we obtain:
Az(t ) = A2o(t ) + A2i(t ).
N,: = P'4 E,,,IA l(to) e-~'(t'- t°)(1 - c -~' r)/2~
(2)
The first term, which is dominating for our source: A2o(t) = A2o(to ) e-~2(t-to)
N, 4 = p,:E,~lal(to) T e-~,(t, -to)
x [sinh().] T/2)/().l T/2)], ).2 = In 2/Tl/2(]21Te),
(3)
describes the decrease of the activity A20(t0) existing at the reference time to. The second term of equation
(2): A2] (t) = A 1(t0)).2 [e - ~ " ' - ,o) _ e-~( . . . . )]/().2 - ~ ),
(4) is related to the number of nuclei of 121Te that have been generated by the parent nuclide 121Tem since the reference time to [see, for example, Evans (1955) or D I N 6814, part 4 (1990)]. At the reference time to the component A2~(t) vanishes by definition. The product of the emission probability of 212 keV quanta per disintegration of )2lTe"~ and the detection probability of these quanta in our detection system may be denoted by Prl 6rl. The corresponding product of the emission probability of 573 keV quanta per disintegration of roTe and their detection probability may be pr2~>.2. If t] denotes the time at the beginning of a measurement running until (t) + T), then the number N : of acquired pulses within the 212 keV
0.114 /
121Tem
294.0
3+
~(0.886
~
I
212.2
154d
0.062
ns
1130.2_~ I
~.4_~ EC/~121Te /
1+
(5b)
Equation (5b) may be transformed identically into:
with
11" -'~
(5a)
I
0
19.16 d
(5c)
with t s = tl + T / 2 denoting the reference time of measurement. With the help of equations (5b) or (5c) the relevant part A I (to) of the activity of the parent nuclide t21Tem can be deduced from each data triple (Nyt, T, q ) for a given parameter ).1. If the product 0.1T/2) is small (due to a short counting interval), the term included in the brackets of equation (5c) has a value close to unity. The number Ny2 of simultaneously acquired pulses in the 573 keV y-ray peak is given by:
f
N,~2 = p,t2E,,~2 |
tl + T
0tl
(6a)
A2(t) dt.
When introducing expressions from equations (2), (3) and (4), we split up the number of counts attributed to the exponential terms with parameters ).2 and ).t: N~,2= P~2*r2[A 20(t0)/).2 - A i (t0)/().2
-- ).1
)]
x e -a2(', - tol(1 - e - a : ) + p;.2E,,,zA~ (to)2 2 × e -x"'' -'°)(1 - e -x' r)/{)., ().2 - ).1)}.
(6b)
The expression in the second line of equation (6b) is proportional to the measured quantity N;.I, see equation (Sb), and represents in our case only a small contribution to the measured count number N;.2. By subtracting this term from the measured number Nr2, an amount N ~ [first part of equation (6b)] remains: N~2 = U;.2 - {p;,2E;,2/(P,,.Ie;.. )} {).2/().2 -- ).t)}N;.I = p;.ze;.2[A2o(to)l).2 - AI (t0)/(22 - ).1 )1
x e -~2"' -'°)(1 - e - ~ : ) .
(7a)
By executing the same transformation of equation (7a) as with equation (5b), we get:
I+
0,*:2 =
~73.1y
p;.2~;.2[A2o(to)
-- Ax(to){).2/().2 - ).1)}IT
x e -~:', - '0~[sinh().2 T/2) (/1-2T/2)].
121Sb Fig.
1. Simplified
scheme
of
the
decay
chain
t21Tem--*t2~Te~2~Sb with energies, spins and parities taken from Tamura et al. (1991).
(7b)
In order to obtain count numbers with nearly the same statistical uncertainty at different measuring times, it was necessary to increase the measuring time to 400,000 s at high values of q. Therefore the expression in the last brackets of equation (7b) was no longer assumed to be constant (with the value of unity). Variations of this term were taken into account. As a consequence, according to equation (7b), an exponential fit of the measured data of N*2
Half-life of 12aTe
867
88 kBq 86 •
•
N
N
•
•
•
•
18.9d
~
N
19.0d
84
82 -
•
19.1 d
"
19.2d
80 ix
19.3d
78 19.4d 76
19.5 d
74 0
20
40
60
T i m e (t s - to)
80
100
d
120
=
Fig. 2. Variation of calculated activity value for ~2~Teat reference time to vs the elapsed time until the measurement with the tentative half-life of t2tTe taken as a parameter. with the given time delay (q = to) as a variable was not a suitable method for the evaluation of the parameter 22 from our measurement data. Alternatively, from equation (7b) the activity A2o(to) of the daughter nuclide ~21Te was calculated for each data triple (N~, T, t~ ) assuming fixed values for the parameters 22 and ).L:
half-life Ti/2(12~Te). We obtain T,2(121Te) = (19.16 _+ 0.05) days.
The given value of the standard uncertainty of the results reflects mainly the reproducibility of the geometry measuring conditions at different times of measurement. As can be seen from Fig. 2, the mean spread of data points belonging to one straight line A2o(to) = N*2 e +a21's-'°)/{[sinh(/.2 T/2)/(/. 2 T/2)] produces an uncertainty of the slope corresponding x P>.2',.2T} + Al(lo){/.2/(/. 2 --/.1)}. (8) to half the chosen step of the parameter T~/2. The contribution to the total uncertainty caused by the The first method adopted here to find the appropriate dead-time corrections of the counting procedure value for /-2 (and the half-life of roTe) utilizes (maximum rate less than 50 s-J) is negligible, as is the equation (8) by varying parameter/-2 until a consist- uncertainty of the time measurements. Changes of the ent value for A20(t0) independent of t, is found. This, detection probability with time in our detection naturally, is expected to occur when ).2 equals system are less than l0 -3 per year resulting in no In 2/TI/2 Q21Te). significant influence over 120 days. The spread which resulted from using two alternative methods for the peak area evaluation (Sch6tzig et al., 1973) was only Results AT~j2(121Te) = 0.01 days. JanBen (1993) had developed a special PC-code for Activity values A20(t0) of the daughter nuclide ~2~Te, calculated according to equation (8) from a set regression calculations with different model functions of I I consecutive measurements, are plotted in Fig. 2 applying the method of least squares adjustment of against the time delay ( t s - to) with respect to the several independent fit parameters. By introducing reference time to. The quantity In 2/22 is taken as a the nonlinear expression of equation (6b) as a model floating parameter. Numerical values of 1.83 x l0 -3 function in a special version of this code, it was for the product p;.j E;.j and 6.19 x l0 -4 for the product possible to check the given result also with the help p~.2E;,2were used. For a low uncertainty contribution of a second, more conventional method. For each from the counting statistics, a minimum of 2 x l05 net single measurement the data of the time t) at the pulses were acquired in a peak area to be evaluated. beginning of a measurement, its duration T, the Due to small additional systematic uncertainty number of peak pulses N,.2 counted and the standard components, the relative standard uncertainty of a uncertainty associated with N;.2 were taken as a four-fold experimental input data set. The activity given data point totals 0.3%. Within the parameter range of Fig. 2 the slopes of A j (t0) and the decay constant 2j of the parent nuclide the regression lines vary between positive and as well as the product p..2E;.2 were kept constant negative values. The value of the parameter In 2/). 2 during the fitting process. The activity A20(t0) at which belongs to a straight line with the slope the reference time to and the decay constant ";,2of the value zero represents the experimental result for the daughter nuclide were fitted by the program. The
H. Siegert
868
result calculated for the value of the half-life Tl/2(t21Te) was the same as above. By varying the values of the fixed input parameters within the range of the uncertainties given in this case, it was proved that the fixed parameters had no significant influence on the value of the half-life determined by the first method.
Discussion The measured T1/2(121Te) value deviates considerably from the values of Edwards and Pool (1946) (17+ l)days, Bhattacharyya and Shastry (1963) (17__+ 1)days and Karim (1973) (16.78+ 0.35) days. In contrast to the situation assumed to prevail during the earlier measurements, the primary conditions for carrying out these investigations were presumably more favorable now. The activity ratio A(t21Tem)/A(121Te) at our starting point was only 5 × 10 -4 increasing to less than 2.5 x 10 -2 after 120 days, so the contribution of 12~Tem nuclei made only very small corrections necessary in the present case. In earlier investigations with a higher content of 12~Tem nuclei it may have been overlooked that the decay curve according to equation (6b) is not just the sum of two exponential terms so that significant systematic uncertainties may have been introduced. The result of our preliminary measurement of the half-life of 121Te (Schftzig and Schrader, 1993) is in agreement with the new value within the standard uncertainties quoted. The half-life of J21Te~" used was taken from Tamura et al. (1991) and could not be checked precisely during these measurements, because the value of the primary activity A[~21Tem(t0)] was only about 40 Bq and the observation time of 120 days was too short. Even if 121Te as a contaminant of ~2~I solutions contributes very little to the integral dose applied to a patient for the period of medical treatment with 1231,as is normally the case for doses of other long-lived contaminants such as 12~Te~, 95Tcra and 96Tc, too, the dose contribution for the time interval after total decay of ~23I is not completely negligible. When assuming, for example, an initial activity ratio of A(~2JTe)/A(12~I) = (1.5 kBq ~21Te/1.0MBq
t23I) and half-lives of 19.16 days, respectively 0.55088 days, the time integral over the air kerma rate from t21Te amounts to about 12.9% of the time integral over the air kerma rate from t23I, in comparison to a fraction of only about 11.3%, if a half-life of 16.8 days for !21Te is chosen. Both figures may overestimate the relative extra doses from 12tTe which are really transferred to a patient. For a thorough calculation it would be necessary to discuss the spatial distribution of the incorporated radionuclides in the body and the dynamics of their biological excretion parallel to the physical decay process. This discussion is beyond the scope of this paper. Acknowledgement--The assistance of R. Def6r in carrying out the count-rate measurements and preparing the diagrams is gratefully acknowleged.
References Bhattacharyya R. and Shastry S. (1963) Positon-decay of 121Te and the excited states of 12tSb. Nucl. Phys. 41, 184. Browne E. and Firestone R. B. (1986) Table of Radioactive Isotopes (Shirley V.S., Ed.), p. 334. Wiley, New York. DIN 6814, Teil 4 (1990) Begriffe und Benennungen in der radiologischen Technik. Beuth, Berlin. Edwards J. E. and Pool M. L. (1946) Radioactive Te from Sb bombardment. Phys. Rev. 69, 140. Evans J. D. (1955) The Atomic Nucleus, p. 477. McGrawHill, New York. JanBen H. (1993) FIT9--Ein Dialogprogramm fiir Ausgleichsreehnungen nach der Methode der kleinsten Quadrate. Physikalisch-Technische Bundesanstalt, Braunschweig, Laborbericht 6.31-93-2. Karim H. M. A. (1973) Study of 4 GeV electron spallation products of iodine. Radiochim. Acta 19, 1. Sch6tzig U. and Schrader H. (1993) Halbwertszeiten und Emissionswahrscheinlichkeiten yon h/iufig verwendeten Radionukliden. Physikalisch-Technisehe Bundesanstalt, Braunschweig, Bericht PTB-Ra-16/4. Sch6tzig U., Debertin K. and Weil3 H. M. (1973) Bestimmung von Gammastrahlen-Emissionswahrscheinlichkeiten mit einem Ge(Li)-Spektrometer. PTBMitteilungen 83, 307. Sch6tzig U., Schrader H. and Debertin K. (1992) Precision measurements of radioactive decay data. In Proc. International Conference on "Nuclear Data for Science and Technology', Jfilich, Germany, p. 562. Springer, Berlin. Tamura T, Iimura H., Miyano K. and Ohya S. (1991) Nucl. Data Sheets 64, 335.