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Precise energy determinations of γ-rays from 66Ga
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Nuclear Physics A132 (1969) 195--203; ~ ) North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprint or microfilmwithout written permission from the publisher
PRECISE ENERGY D E T E R M I N A T I O N S OF ?-RAYS F R O M 66Ga M. G. STRAUSS and F. R. LENKSZUS Argonne National Laboratory, Argonne, Illinois 60439 USA * Received 24 March 1969
Abstract: A simple and precise technique for energy calibration of Ge(Li) 7-ray spectrometers has been developed. The technique, which is particularly useful in studies of decay schemes, was used in measuring the energies of the 7-rays present in the decay of 9.5 h 66Ga. The highenergy lines were measured to a precision of 0.25 keV which is a significant improvement over previous measurements in which the uncertainties are 0.9-1.5 keV. The accuracy is demonstrated in a measurement of equal energy intervals of 2moc 2 as a function of 7-ray energy. The standard deviation of the eight measured 2moc 2 intervals was only 0.08 keV. The largest deviation from the mean was about 0.1 keV or less than 0.1 channel. The four high-energy 7-rays are particularly useful as calibration lines. Their energies in keV are 4086.18:L0.25, 4295.6l :L0.25, 4461.59±0.25 and 4806.58±0.25. E I
RADIOACTIVITY 66Ga [fr°m 64Zn(c~' I N2n)]; target. ameasured t E7" u 66Zn r deduced a l levels"
1. Introduction A precise c a l i b r a t i o n technique for m e a s u r i n g 7-ray energies a n d G e ( L i ) d e t e c t o r linearity has been recently d e v e l o p e d 1). A m p l i f i e r - a n a l y s e r non-linearity is c o r r e c t e d for by the system differential response o b t a i n e d with a sliding pulse g e n e r a t o r 1,z) whose i n c r e m e n t a l n o n - l i n e a r i t y is 0.005-0.01%. The technique is simple, fast a n d virtually a u t o m a t i c . The m e t h o d was evaluated b y m e a s u r i n g y-ray energies (0.272.75 M e V ) from the following sources: Z°3Hg, 51Cr, 137Cs, 54Mn, 2°7Bi, 22Na, 6OCo ' SSy, T h C " a n d / 4 N a . T h e results are in a g r e e m e n t with previously r e p o r t e d a n d generally accepted values to within 40-110 eV. The y-rays p r e s e n t in the decay o f 66Ga were initially used to study the linearity o f a coaxial G e ( L i ) d e t e c t o r a). Since there are n o t m a n y y-ray s t a n d a r d s a b o v e 3 M e V p a r t i c u l a r l y in source form, 66Ga could serve as a high-energy (up to 4.8 M e V ) y-ray c a l i b r a t i o n source. W i d e s p r e a d interest in m o r e precise d e t e r m i n a t i o n s o f the energies o f 7-rays f r o m the decay o f this nucleide p r o m p t e d further m e a s u r e m e n t s . The 7-ray energies f r o m 66Ga have been recently m e a s u r e d with a G e ( L i ) s p e c t r o m eter by Cot6 et al. 3), F r e e d m a n el al. 4) a n d C a m p 5). Their values for the h i g h - e n e r g y lines have an assigned u n c e r t a i n t y o f 0.9-1.5 keV. Based on our linearity m e a s u r e ments 1) a n d the results o b t a i n e d at energies b e l o w 3 MeV, we felt t h a t with the use o f the sliding p u l s e r c a l i b r a t i o n technique these uncertainties could be r e d u c e d a p p r e ciably. * Work performed under the auspices of the U.S. Atomic Energy Commission. 195
196
M. G. STRAUSSAND F. R. LENKSZUS
2. Principle of energy calibration technique l'he differential response of an amplifier-multi-channel analyser system is measured by applying signals to the input of the preamplifier from a sliding pulse generator ~' 2) whose output amplitude increases linearly with time. A hypothetical response with an exaggerated non-linearity is shown in fig. l(b). The counts in each channel are proportional to the channel width and therefore also to the energy/channel. The (a) ENERGY SPECTRUM El
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Fig. 1. Implementation of sliding pulser energy calibration technique. A calibration constant N, 2/A.E12 in counts/keV is computed on the basis o f the two calibration energies E1 and E2 and the differential response o f the amplifier-multi-channel analyser system. The u n k n o w n energy interval AE2,, is equal to the integral N2x divided by this calibration constant.
integral of the differential response with respect to counts is an absolutely linear function of energy provided the sliding pulser is perfectly linear. To use this linear function for energy calibration, the relationship between the number of counts and the channels of interest must be established. Suppose that in the spectrum shown in fig. 1(a), it is desired to determine the energy Ex on the basis of the known calibration energies E1 and E2. Since peaks E1 and Ex lie in the non-linear regions of the analyser, the observed centroids must be corrected. The correct energy is determined
7-RAYS FROM 66Ga
197
from the differential response shown in fig. l(b). The counts between the channel numbers [in fig. 1 (b)] corresponding to the peaks E1 and E2 [in fig. l(a)] are integrated. The integral N12 divided by the energy difference AEI2 is the calibration constant (counts/keV) which is independent of channel number. The unknown energy interval AE2x is then equal to the integral N2x divided by the calibration constant. The differential response [fig. l(b)] serves the same purpose as a gain correction curve obtained with a conventional pulse generator or with radioactive sources, namely, to correct the experimental data for the non-linearity of the amplifier-analyser system. However, the differential response is obtained from a direct measurement carried out by using a simple and rather effortless process, whereas the gain correction curve is obtained indirectly from a tedious point-by-point (usually not contiguous) measurement. This calibration method is particularly useful in studies of decay schemes, as it essentially consists of determining relative energies rather than absolute energies. The accuracy of this technique depends only on the linearity of the sliding pulser and the Ge(Li) detector. In comparisons with standard 7-ray energies, our results routinely show agreements within 40 eV at a gain of 0.4 keV/channel and 110 eV at 0.8 keV/channel, thus attesting to the linearity of both components. In fact, even if high precision is not required, the simplicity and speed with which the differential response can be measured merit the use of the sliding pulser technique for energy calibration. 3. Energy measurements The nucleide 66Ga is a relatively convenient high-energy source with a half-life of 9.5 h and y-rays extending to 4.8 MeV. It can be produced by bombarding natural zinc with protons 3, 5), deuterons 4) or a-particles 6). Subsequent chemical separation is not necessary. We have utilized the last two methods, but, herein report the results of the last one only. Zinc foil of ~ 0.06 mm thickness was bombarded with 35 MeV a-particles from the Argonne 1.5 m cyclotron for about 1 h at a rate of 30 I~A/h. Short half-life activities were allowed to decay for about 5 h before the measurement began. Prior to taking data, a 4 h background run was taken to insure that the 66Ga spectrum would be free of contamination. Gamma rays fi'om SSy and ThC" were used for energy calibration and were measured simultaneously with the 66Ga. A source of 24Na was not used as its 2754 keV line could not be resolved from the 2752 keV line of 66Ga. A 30 cm 3 closed-end cylindrical coaxial Ge(Li) detector made by Nuclear Diodes, Inc., was used. The detector was drifted to a depth of 12.5 mm and was used with a bias of 2000 V. The system resolution ( F W H M ) of the 1.33 MeV peak of 6°Co was about 3 keV. Spectral measurements were made with A R M S P A N 7) (ARgonne Multichannel Stored Program ANalyser) in conjunction with our high-resolution pulse processing system s). An amplifier with a 2 # sec integrating and differentiating time constant was used. The spectrometer gain and zero-intercept were servo-stabilized
198
M. G. STRAUSS AND F. R. LENKSZUS
using our stable double pulser 9 ) a s reference source. The pulser signals were injected into the preamplifier via a 1 pF air capacitor housed in a temperature controlled oven t. The drift of the stabilized system was no more than about _+0.1 channel of 4000 over the course of the experiment. The effect of this small residual drift was further reduced by measuring the 7-rays from 66Ga and from the calibration sources simultaneously rather than sequentially. The effects of counting rates on the system response were carefully examined. Two spectra were measured (0.8 keV/channel) using several sources in each which ranged between 0.5 to 2.75 MeV. One spectrum was measured at 1000 pulses/sec and the other at 13 000 pulses/sec. Comparison of the two spectra showed that the peak positions changed less than _ 0.1 keV, part of which was undoubtedly due to errors in peak centroid determinations. The differential response was therefore measured without the background of the detector signals. This was realized by replacing the detector with an equivalent capacitor while the response was measured. Despite the fact that the system proved to be insensitive to counting rates, in the measurements reported here the rates were below 3000 pulses/sec. The relationship between the peak centroid and the position of the source relative to the detector was also investigated. Two spectra were measured (0.8 keV/channel) with the same input rate using the four sources 22Na, 137Cs, 88y and ThC". The first spectrum was measured with the four sources oriented along the detector axis. In the second measurement, the position of SSy and T h C " was changed by 90 °, while 22Na and 13VCs remained the same. The changes observed in the positions of the peaks of SSy and T h C " were virtually the same as those observed with 22Na and 13 VCs" Observed changes of less than _ 40 eV were attributed to errors in peak centroid determinations. While this report was being prepared, it was noted that Gunnink et al. 11) have observed that the pulse-height from a planar Ge(Li) detector is a function of the incident direction of the y-rays relative to the detector electric field. Following the 66Ga measurements, the differential response of the system was measured with the sliding pulser. Unfortunately the technique of stabilizing the system while the differential response is measured 2) was not conceived at that time. The differential response was measured over a weekend (65 h) without stabilization. During this time, the gain and zero undoubtedly fluctuated slightly. However, we believe that over this lengthy period, the fluctuations largely cancelled, thus, on the average, the gain and zero did not vary appreciably.
4. Results
One of the three measured spectra of 66Ga is shown in fig. 2. Only the energies of the most prominent peaks have been studied. There are three peaks for each of the high-energy y-rays, e.g. the full-energy peak (F), the single-escape peak (S) and the t A new ultra stable 1 pF capacitor, which does not require an oven, has since been developed t o).
~-RAYS
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double-escape peak ( D ) . In several cases, are superposed. Thus, the 4806 S overlaps overlap the 4806 D peak, and the 3791 S ( F W H M ) o f the system was 3.9 k e V at 1
199
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two or three peaks of different transitions the 4295 F peak, the 4295 S and the 3791 F overlaps the 4295 D peak. The resolution MeV and 5.7 keV at 4.8 M e V as indicated
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Fig. 2. Spectrum of 7-rays present in the decay of 9.5 b 6~Oa. The measured energies (in keV) of the 7-rays are indicated. The adopted value (table 2) of the weak 1232 keV line was modified slightly in accordance with its position in the decay scheme. Double-escape peaks are denoted by D, singleescape peaks by S and full-energy peaks by F.
200
M . G . STRAUSS AND F. R. LENKSZUS
on the spectrum. The stray capacitance of the oven containing the 1 pF charge injection capacitor resulted in some line broadening. The centroids of the peaks were generally computed by using that portion of the peak that exceeded ~ 20 ~ of the peak height. However, in the cases of contaminated peaks, only the peak area above the ~ 50 ~ level was used. The energy difference between the full-energy peak and the double-escape peak for each of eight ?-rays was calculated. The mean of these differences was assumed to be equal to 2mo cz (1022.012 _+0.003 keV) and was used for computing the calibration constant in counts/keV (fig. 1). The ?-ray energies corresponding to the full-energy peaks of TABLE 1 Comparison
of the energy sum of v-ray cascades with the energy of crossover v-rays from 66Ga
v-ray cascade (keV) (a) 1039.09-4-0.25+2751.98±0.25 = 3791.074-0.35 1039.09±0.25+2189.60±0.25 = 3228.69-4-0.35 3228.93 ±0.25 + 1232.41 ±0.35 = 4461.34±0.43 1039.09 ±0.25 +2189.604-0.25 q- 1232.41 ~0.35 = 4461.10-t0.50
Crossover v-ray Differenceof (keV) (b)-(a) (b) (c) 3791.29±0.25 3228.93±0.25 4461.594-0.25 4461.59±0.25
0.22±0.43 0.24±0.43 0.25±0.50 0.49±0.56
88y and T h C " were used as calibration references. The energies of all but three ?-rays were derived from the arithmetic mean of the values obtained for the full-energy and double-escape peaks. The single-escape peak was not used as it is considerably weaker than the other two peaks. The energy of the 3791 keV y-ray was based solely on its double-escape peak, and the energies of the 1232 and 1039 keV lines were based on their respective full-energy peaks. The arithmetic mean of the values obtained in the three runs is indicated for each ?-ray on the spectrum shown in fig. 2. The average difference between the mean of the three runs and any given run was 0.032 keV. The uncertainty assigned to the energies shown is estimated at ___0.25 keV except for the 1232 keV line which is ___0.35 keV (see sect. 5). The decay scheme of 66Ga reported by Freedman et al. 4) shows several ?-ray cascades. A comparison between four 7-ray cascades and their corresponding crossover ?-rays is shown in table 1. Column (a) lists the constituent ?-ray energies and the sum of the cascade. Column (b) shows the corresponding energies of the crossover ?-rays and column (c) the difference between the energies of the crossover ?-rays and the sum of the cascade. Ideally this difference should be zero. However in practice, statistical uncertainties are expected to be reflected in differences which are smaller than the measurement uncertainty. Using the energy values from fig. 2, we noticed that this was the case for the two cascades listed at the top of table 1, but for the two cascades listed at the bottom this was not so. However, the determination of the energy of the 1232 keV line is not held to be as precise as those of other transitions since its value was based on the measurement of only a single weak peak [(peak height/back-
y-RAYS FROM 66Ga
231
g r o u n d level) ~ 0.6], whereas the energy of most other y-rays was based on the average o f the two peaks F and D. Thus, in light o f these small discrepancies between the cascade energy sum and the crossover energy, we have re-assigned this ?-ray an energy of 1232.41 keV, which is 0.2 keV higher than that shown on the spectrum o f fig. 2. The uncertainty was also increased to _ 0.35 keV, which is 0.1 keV higher than TABLE 2 Measured energies of~'-rays from 66Ga and comparison with published values Measured energy (keV) (a) 1039.09 ~0.25 1232.41,0.35 2189.60:]:0.25 2751.98 ~:0.25 3228.93,0.25 3381.02~0.25 3791.29~0.25 4086.18,0.25 4295.61 --0.25 4461.59 ~:0.25 4806.58 ~0.25
Freedman et al. 4) energy difference of (keV) (b)-(a) (b) (c) 1039.3±1.5 1231.6,1.5 2190.0J:: 1.5 2752.4±1.5 3229.4±1.5 3381.24-1.5 3791.5±1.5 4086.2 :k:1.5 4295.0± 1.5 4461.64-1.5 4805.9±1.5
0.21 --0.81 0.40 0.42 0.47 0.18 0.21 0.02 --0.61 0.01 --0.68
energy (keV) (d)
Camp s) difference of (d)-(a) (e)
1039.0~:0.1 1232.6i0.6 2190.5~0.6 2752.3~:0.6 3229.5=1::0.7 3381.1=]=0.7 3791.3~0.6 4088.0~1.0 4296.0i0.9 4462.1i l . 0 4805.0±1.0
--0.09 0.19 0.90 0.32 0.57 0.08 0.01 1.82 0.39 0.51 --1.58
Cot6 et al. 9) energy difference of (keV) (f)-(a) (f) (g)
4087.1±1.5 4296.9±1.5 4462.3±1.5 4808.2~1.5
0.92 1.29 0.71 1.62
that of all other lines. The corrected value is in g o o d agreement with a recent low-energy measurement by Bolotin 12) at A r g o n n e in which the gain was only 0.6 keV/channel. While the differences listed in column (c) of table 1 are all smaller than the measurement uncertainty, we note (but offer no explanation) that they are all positive, whereas one would expect some to be also negative. The energy values adopted are listed in table 2 with values obtained in other recent measurements. The agreement a m o n g the four measurements is generally good. The comparison with the results obtained by Freedman, Porter and Wagner is particularly noteworthy as the largest difference [column (c)] is only 0.8 keV. Our values and those measured by Cot6 e t al. overlap within the combined uncertainties.
5. Measurement accuracy
The energy difference between the full-energy and double-escape peak was c o m p u t e d for eight 7-rays shown in fig. 2. The differences between the c o m p u t e d values and the mean value (2m o e 2) were calculated and were found to display an average deviation of 0.067 keV and a standard deviation of 0.080 keV. The distribution of these ~ 1 MeV energy intervals as a function o f 7-ray energy is shown in fig. 3. This figure demonstrates the overall accuracy which was obtained with the sliding pulser call-
202
M. G . STRAUSS A N D F. R. L E N K S Z U S
bration technique at a gain o f 1.4 keY/channel. The largest error in a measured 2roD c2 energy interval is ~ 0.1 keV or less than 0.1 channel and the average error is only 0.05 channel. The results f r o m the other two runs show r a n d o m deviations from those shown in fig. 3 but exhibit a comparable spread a b o u t the mean. The scatter SOURCE; BBGa DETECTOR', 30cm3 COAXIALGe{Li) GAIN: 1,4keVI CHANNEL :>
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Fig. 3. Measured energy intervals of 2moc 2 as a function ofT-ray energy. Note the overall accuracy and linearity (errors less than 0.1 channel) which were obtained at a gain of 1.4 keV/channel when the coaxial Ge(Li) spectrometer was calibrated with the sliding pulser. a b o u t the m e a n is due to measurement errors and system non-linearity. The nonlinearity o f the ramp generator is a function o f its output voltage 1,2). Similarly, one suspects that any detector non-linearity would also be correlated to energy 11). Yet, the scatter in fig. 3 appears r a n d o m rather than systematic. Therefore we concluded that the scatter is largely due to measurement errors, and that the incremental non-linearity of the coaxial Ge(Li) detector in the range of 1 to 5 MeV is less than +0.1 keV. The uncertainties in the measured energies result f r o m three basic limitations e.g. the accuracy to which the calibration standards are known, the precision to which one can determine the location o f a peak and the statistical fluctuations in the n u m b e r o f counts/channel in the sliding pulser differential response *. While some of these errors can be calculated, m o s t o f them must be assessed on the basis o f experimental evidence. The uncertainties can be divided into two major categories; e.g. r a n d o m fluctuations and systematic errors. R a n d o m fluctuations have been minimized by averaging the three runs. Systematic errors have been reduced by making the measurements with different system components. Thus, two different ramp generators and two different mercury relay choppers were used. Fig. 3 shows that with a gain of 1.4 keV/channel, a given energy interval can be measured to an accuracy of about + 0.1 keV. Since the calibration reference energy which must be added to the interval has an uncertainty 1) t For a more detailed discussion of the measurement uncertainties, see ref.
1),
y-RAYS FROM 66Ga
203
of + 0.11 keV, the uncertainty assigned to the measured energies is + 0.25 keV except for the 1232 keV line which is +0.35 keV. These uncertainties correspond to a confidence level of about 90 %. It is a pleasure to acknowledge the support and encouragement received from H. H. Bolotin and L. M. Bollinger. The assistance of M. S. Freedman and M. C. Oselka in preparing the 66Ga source is greatly appreciated. References 1) M. G. Strauss, F. R. Lenkszus and J. J. Eichholz, to be published 2) J. J. Eichholz, M. G. Strauss and R. W. Bannon, to be published 3) R. E. Cot6, R. Guso, S. Raboy, R. A. Carrigan Jr., A. Gaigalas, R. B. Sutton and C. C. Trail, Nucl. Phys. 77 (1966) 239 and private communication 4) M. S. Freedman, F. T. Porter and F. Wagner, Phys. Rev. 151 (1966) 899 5) D. C. Camp, Lawrence Radiation Laboratory report UCRL-50156 (1967) 6) H. H. Bolotin and D. A. McClure, Phys. Rev,, in press 7) F. R. Lenkszus and M. G. Strauss, Nucl. Instr., in press 8) M. G. Strauss, I. S. Sherman, R. Brenner, S. J. Rudnick, R. N. Larsen and H. M. Mann, Roy. Sci. Instr. 38 (1967) 725 9) M. G. Strauss, L. L. Sifter, F. R. Lenkszus and R. Brenner, IEEE Trans. Nucl. Sci. 15 (1968) 518 10) R. Brenner, Rev. Sci. Instr., in press 11) R. Gunnink, R. A. Meyer, J. B. Niday and R. P. Anderson, Nucl. Instr. 65 (1968) 26 12) H. H. Bolotin, Argonne National Laboratory, private communication
l
Nuclear Physics A132 (1969) 195--203; ~ ) North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprint or microfilmwithout written permission from the publisher
PRECISE ENERGY D E T E R M I N A T I O N S OF ?-RAYS F R O M 66Ga M. G. STRAUSS and F. R. LENKSZUS Argonne National Laboratory, Argonne, Illinois 60439 USA * Received 24 March 1969
Abstract: A simple and precise technique for energy calibration of Ge(Li) 7-ray spectrometers has been developed. The technique, which is particularly useful in studies of decay schemes, was used in measuring the energies of the 7-rays present in the decay of 9.5 h 66Ga. The highenergy lines were measured to a precision of 0.25 keV which is a significant improvement over previous measurements in which the uncertainties are 0.9-1.5 keV. The accuracy is demonstrated in a measurement of equal energy intervals of 2moc 2 as a function of 7-ray energy. The standard deviation of the eight measured 2moc 2 intervals was only 0.08 keV. The largest deviation from the mean was about 0.1 keV or less than 0.1 channel. The four high-energy 7-rays are particularly useful as calibration lines. Their energies in keV are 4086.18:L0.25, 4295.6l :L0.25, 4461.59±0.25 and 4806.58±0.25. E I
RADIOACTIVITY 66Ga [fr°m 64Zn(c~' I N2n)]; target. ameasured t E7" u 66Zn r deduced a l levels"
1. Introduction A precise c a l i b r a t i o n technique for m e a s u r i n g 7-ray energies a n d G e ( L i ) d e t e c t o r linearity has been recently d e v e l o p e d 1). A m p l i f i e r - a n a l y s e r non-linearity is c o r r e c t e d for by the system differential response o b t a i n e d with a sliding pulse g e n e r a t o r 1,z) whose i n c r e m e n t a l n o n - l i n e a r i t y is 0.005-0.01%. The technique is simple, fast a n d virtually a u t o m a t i c . The m e t h o d was evaluated b y m e a s u r i n g y-ray energies (0.272.75 M e V ) from the following sources: Z°3Hg, 51Cr, 137Cs, 54Mn, 2°7Bi, 22Na, 6OCo ' SSy, T h C " a n d / 4 N a . T h e results are in a g r e e m e n t with previously r e p o r t e d a n d generally accepted values to within 40-110 eV. The y-rays p r e s e n t in the decay o f 66Ga were initially used to study the linearity o f a coaxial G e ( L i ) d e t e c t o r a). Since there are n o t m a n y y-ray s t a n d a r d s a b o v e 3 M e V p a r t i c u l a r l y in source form, 66Ga could serve as a high-energy (up to 4.8 M e V ) y-ray c a l i b r a t i o n source. W i d e s p r e a d interest in m o r e precise d e t e r m i n a t i o n s o f the energies o f 7-rays f r o m the decay o f this nucleide p r o m p t e d further m e a s u r e m e n t s . The 7-ray energies f r o m 66Ga have been recently m e a s u r e d with a G e ( L i ) s p e c t r o m eter by Cot6 et al. 3), F r e e d m a n el al. 4) a n d C a m p 5). Their values for the h i g h - e n e r g y lines have an assigned u n c e r t a i n t y o f 0.9-1.5 keV. Based on our linearity m e a s u r e ments 1) a n d the results o b t a i n e d at energies b e l o w 3 MeV, we felt t h a t with the use o f the sliding p u l s e r c a l i b r a t i o n technique these uncertainties could be r e d u c e d a p p r e ciably. * Work performed under the auspices of the U.S. Atomic Energy Commission. 195
196
M. G. STRAUSSAND F. R. LENKSZUS
2. Principle of energy calibration technique l'he differential response of an amplifier-multi-channel analyser system is measured by applying signals to the input of the preamplifier from a sliding pulse generator ~' 2) whose output amplitude increases linearly with time. A hypothetical response with an exaggerated non-linearity is shown in fig. l(b). The counts in each channel are proportional to the channel width and therefore also to the energy/channel. The (a) ENERGY SPECTRUM El
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integral of the differential response with respect to counts is an absolutely linear function of energy provided the sliding pulser is perfectly linear. To use this linear function for energy calibration, the relationship between the number of counts and the channels of interest must be established. Suppose that in the spectrum shown in fig. 1(a), it is desired to determine the energy Ex on the basis of the known calibration energies E1 and E2. Since peaks E1 and Ex lie in the non-linear regions of the analyser, the observed centroids must be corrected. The correct energy is determined
7-RAYS FROM 66Ga
197
from the differential response shown in fig. l(b). The counts between the channel numbers [in fig. 1 (b)] corresponding to the peaks E1 and E2 [in fig. l(a)] are integrated. The integral N12 divided by the energy difference AEI2 is the calibration constant (counts/keV) which is independent of channel number. The unknown energy interval AE2x is then equal to the integral N2x divided by the calibration constant. The differential response [fig. l(b)] serves the same purpose as a gain correction curve obtained with a conventional pulse generator or with radioactive sources, namely, to correct the experimental data for the non-linearity of the amplifier-analyser system. However, the differential response is obtained from a direct measurement carried out by using a simple and rather effortless process, whereas the gain correction curve is obtained indirectly from a tedious point-by-point (usually not contiguous) measurement. This calibration method is particularly useful in studies of decay schemes, as it essentially consists of determining relative energies rather than absolute energies. The accuracy of this technique depends only on the linearity of the sliding pulser and the Ge(Li) detector. In comparisons with standard 7-ray energies, our results routinely show agreements within 40 eV at a gain of 0.4 keV/channel and 110 eV at 0.8 keV/channel, thus attesting to the linearity of both components. In fact, even if high precision is not required, the simplicity and speed with which the differential response can be measured merit the use of the sliding pulser technique for energy calibration. 3. Energy measurements The nucleide 66Ga is a relatively convenient high-energy source with a half-life of 9.5 h and y-rays extending to 4.8 MeV. It can be produced by bombarding natural zinc with protons 3, 5), deuterons 4) or a-particles 6). Subsequent chemical separation is not necessary. We have utilized the last two methods, but, herein report the results of the last one only. Zinc foil of ~ 0.06 mm thickness was bombarded with 35 MeV a-particles from the Argonne 1.5 m cyclotron for about 1 h at a rate of 30 I~A/h. Short half-life activities were allowed to decay for about 5 h before the measurement began. Prior to taking data, a 4 h background run was taken to insure that the 66Ga spectrum would be free of contamination. Gamma rays fi'om SSy and ThC" were used for energy calibration and were measured simultaneously with the 66Ga. A source of 24Na was not used as its 2754 keV line could not be resolved from the 2752 keV line of 66Ga. A 30 cm 3 closed-end cylindrical coaxial Ge(Li) detector made by Nuclear Diodes, Inc., was used. The detector was drifted to a depth of 12.5 mm and was used with a bias of 2000 V. The system resolution ( F W H M ) of the 1.33 MeV peak of 6°Co was about 3 keV. Spectral measurements were made with A R M S P A N 7) (ARgonne Multichannel Stored Program ANalyser) in conjunction with our high-resolution pulse processing system s). An amplifier with a 2 # sec integrating and differentiating time constant was used. The spectrometer gain and zero-intercept were servo-stabilized
198
M. G. STRAUSS AND F. R. LENKSZUS
using our stable double pulser 9 ) a s reference source. The pulser signals were injected into the preamplifier via a 1 pF air capacitor housed in a temperature controlled oven t. The drift of the stabilized system was no more than about _+0.1 channel of 4000 over the course of the experiment. The effect of this small residual drift was further reduced by measuring the 7-rays from 66Ga and from the calibration sources simultaneously rather than sequentially. The effects of counting rates on the system response were carefully examined. Two spectra were measured (0.8 keV/channel) using several sources in each which ranged between 0.5 to 2.75 MeV. One spectrum was measured at 1000 pulses/sec and the other at 13 000 pulses/sec. Comparison of the two spectra showed that the peak positions changed less than _ 0.1 keV, part of which was undoubtedly due to errors in peak centroid determinations. The differential response was therefore measured without the background of the detector signals. This was realized by replacing the detector with an equivalent capacitor while the response was measured. Despite the fact that the system proved to be insensitive to counting rates, in the measurements reported here the rates were below 3000 pulses/sec. The relationship between the peak centroid and the position of the source relative to the detector was also investigated. Two spectra were measured (0.8 keV/channel) with the same input rate using the four sources 22Na, 137Cs, 88y and ThC". The first spectrum was measured with the four sources oriented along the detector axis. In the second measurement, the position of SSy and T h C " was changed by 90 °, while 22Na and 13VCs remained the same. The changes observed in the positions of the peaks of SSy and T h C " were virtually the same as those observed with 22Na and 13 VCs" Observed changes of less than _ 40 eV were attributed to errors in peak centroid determinations. While this report was being prepared, it was noted that Gunnink et al. 11) have observed that the pulse-height from a planar Ge(Li) detector is a function of the incident direction of the y-rays relative to the detector electric field. Following the 66Ga measurements, the differential response of the system was measured with the sliding pulser. Unfortunately the technique of stabilizing the system while the differential response is measured 2) was not conceived at that time. The differential response was measured over a weekend (65 h) without stabilization. During this time, the gain and zero undoubtedly fluctuated slightly. However, we believe that over this lengthy period, the fluctuations largely cancelled, thus, on the average, the gain and zero did not vary appreciably.
4. Results
One of the three measured spectra of 66Ga is shown in fig. 2. Only the energies of the most prominent peaks have been studied. There are three peaks for each of the high-energy y-rays, e.g. the full-energy peak (F), the single-escape peak (S) and the t A new ultra stable 1 pF capacitor, which does not require an oven, has since been developed t o).
~-RAYS
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double-escape peak ( D ) . In several cases, are superposed. Thus, the 4806 S overlaps overlap the 4806 D peak, and the 3791 S ( F W H M ) o f the system was 3.9 k e V at 1
199
66Ga
two or three peaks of different transitions the 4295 F peak, the 4295 S and the 3791 F overlaps the 4295 D peak. The resolution MeV and 5.7 keV at 4.8 M e V as indicated
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Fig. 2. Spectrum of 7-rays present in the decay of 9.5 b 6~Oa. The measured energies (in keV) of the 7-rays are indicated. The adopted value (table 2) of the weak 1232 keV line was modified slightly in accordance with its position in the decay scheme. Double-escape peaks are denoted by D, singleescape peaks by S and full-energy peaks by F.
200
M . G . STRAUSS AND F. R. LENKSZUS
on the spectrum. The stray capacitance of the oven containing the 1 pF charge injection capacitor resulted in some line broadening. The centroids of the peaks were generally computed by using that portion of the peak that exceeded ~ 20 ~ of the peak height. However, in the cases of contaminated peaks, only the peak area above the ~ 50 ~ level was used. The energy difference between the full-energy peak and the double-escape peak for each of eight ?-rays was calculated. The mean of these differences was assumed to be equal to 2mo cz (1022.012 _+0.003 keV) and was used for computing the calibration constant in counts/keV (fig. 1). The ?-ray energies corresponding to the full-energy peaks of TABLE 1 Comparison
of the energy sum of v-ray cascades with the energy of crossover v-rays from 66Ga
v-ray cascade (keV) (a) 1039.09-4-0.25+2751.98±0.25 = 3791.074-0.35 1039.09±0.25+2189.60±0.25 = 3228.69-4-0.35 3228.93 ±0.25 + 1232.41 ±0.35 = 4461.34±0.43 1039.09 ±0.25 +2189.604-0.25 q- 1232.41 ~0.35 = 4461.10-t0.50
Crossover v-ray Differenceof (keV) (b)-(a) (b) (c) 3791.29±0.25 3228.93±0.25 4461.594-0.25 4461.59±0.25
0.22±0.43 0.24±0.43 0.25±0.50 0.49±0.56
88y and T h C " were used as calibration references. The energies of all but three ?-rays were derived from the arithmetic mean of the values obtained for the full-energy and double-escape peaks. The single-escape peak was not used as it is considerably weaker than the other two peaks. The energy of the 3791 keV y-ray was based solely on its double-escape peak, and the energies of the 1232 and 1039 keV lines were based on their respective full-energy peaks. The arithmetic mean of the values obtained in the three runs is indicated for each ?-ray on the spectrum shown in fig. 2. The average difference between the mean of the three runs and any given run was 0.032 keV. The uncertainty assigned to the energies shown is estimated at ___0.25 keV except for the 1232 keV line which is ___0.35 keV (see sect. 5). The decay scheme of 66Ga reported by Freedman et al. 4) shows several ?-ray cascades. A comparison between four 7-ray cascades and their corresponding crossover ?-rays is shown in table 1. Column (a) lists the constituent ?-ray energies and the sum of the cascade. Column (b) shows the corresponding energies of the crossover ?-rays and column (c) the difference between the energies of the crossover ?-rays and the sum of the cascade. Ideally this difference should be zero. However in practice, statistical uncertainties are expected to be reflected in differences which are smaller than the measurement uncertainty. Using the energy values from fig. 2, we noticed that this was the case for the two cascades listed at the top of table 1, but for the two cascades listed at the bottom this was not so. However, the determination of the energy of the 1232 keV line is not held to be as precise as those of other transitions since its value was based on the measurement of only a single weak peak [(peak height/back-
y-RAYS FROM 66Ga
231
g r o u n d level) ~ 0.6], whereas the energy of most other y-rays was based on the average o f the two peaks F and D. Thus, in light o f these small discrepancies between the cascade energy sum and the crossover energy, we have re-assigned this ?-ray an energy of 1232.41 keV, which is 0.2 keV higher than that shown on the spectrum o f fig. 2. The uncertainty was also increased to _ 0.35 keV, which is 0.1 keV higher than TABLE 2 Measured energies of~'-rays from 66Ga and comparison with published values Measured energy (keV) (a) 1039.09 ~0.25 1232.41,0.35 2189.60:]:0.25 2751.98 ~:0.25 3228.93,0.25 3381.02~0.25 3791.29~0.25 4086.18,0.25 4295.61 --0.25 4461.59 ~:0.25 4806.58 ~0.25
Freedman et al. 4) energy difference of (keV) (b)-(a) (b) (c) 1039.3±1.5 1231.6,1.5 2190.0J:: 1.5 2752.4±1.5 3229.4±1.5 3381.24-1.5 3791.5±1.5 4086.2 :k:1.5 4295.0± 1.5 4461.64-1.5 4805.9±1.5
0.21 --0.81 0.40 0.42 0.47 0.18 0.21 0.02 --0.61 0.01 --0.68
energy (keV) (d)
Camp s) difference of (d)-(a) (e)
1039.0~:0.1 1232.6i0.6 2190.5~0.6 2752.3~:0.6 3229.5=1::0.7 3381.1=]=0.7 3791.3~0.6 4088.0~1.0 4296.0i0.9 4462.1i l . 0 4805.0±1.0
--0.09 0.19 0.90 0.32 0.57 0.08 0.01 1.82 0.39 0.51 --1.58
Cot6 et al. 9) energy difference of (keV) (f)-(a) (f) (g)
4087.1±1.5 4296.9±1.5 4462.3±1.5 4808.2~1.5
0.92 1.29 0.71 1.62
that of all other lines. The corrected value is in g o o d agreement with a recent low-energy measurement by Bolotin 12) at A r g o n n e in which the gain was only 0.6 keV/channel. While the differences listed in column (c) of table 1 are all smaller than the measurement uncertainty, we note (but offer no explanation) that they are all positive, whereas one would expect some to be also negative. The energy values adopted are listed in table 2 with values obtained in other recent measurements. The agreement a m o n g the four measurements is generally good. The comparison with the results obtained by Freedman, Porter and Wagner is particularly noteworthy as the largest difference [column (c)] is only 0.8 keV. Our values and those measured by Cot6 e t al. overlap within the combined uncertainties.
5. Measurement accuracy
The energy difference between the full-energy and double-escape peak was c o m p u t e d for eight 7-rays shown in fig. 2. The differences between the c o m p u t e d values and the mean value (2m o e 2) were calculated and were found to display an average deviation of 0.067 keV and a standard deviation of 0.080 keV. The distribution of these ~ 1 MeV energy intervals as a function o f 7-ray energy is shown in fig. 3. This figure demonstrates the overall accuracy which was obtained with the sliding pulser call-
202
M. G . STRAUSS A N D F. R. L E N K S Z U S
bration technique at a gain o f 1.4 keY/channel. The largest error in a measured 2roD c2 energy interval is ~ 0.1 keV or less than 0.1 channel and the average error is only 0.05 channel. The results f r o m the other two runs show r a n d o m deviations from those shown in fig. 3 but exhibit a comparable spread a b o u t the mean. The scatter SOURCE; BBGa DETECTOR', 30cm3 COAXIALGe{Li) GAIN: 1,4keVI CHANNEL :>
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Fig. 3. Measured energy intervals of 2moc 2 as a function ofT-ray energy. Note the overall accuracy and linearity (errors less than 0.1 channel) which were obtained at a gain of 1.4 keV/channel when the coaxial Ge(Li) spectrometer was calibrated with the sliding pulser. a b o u t the m e a n is due to measurement errors and system non-linearity. The nonlinearity o f the ramp generator is a function o f its output voltage 1,2). Similarly, one suspects that any detector non-linearity would also be correlated to energy 11). Yet, the scatter in fig. 3 appears r a n d o m rather than systematic. Therefore we concluded that the scatter is largely due to measurement errors, and that the incremental non-linearity of the coaxial Ge(Li) detector in the range of 1 to 5 MeV is less than +0.1 keV. The uncertainties in the measured energies result f r o m three basic limitations e.g. the accuracy to which the calibration standards are known, the precision to which one can determine the location o f a peak and the statistical fluctuations in the n u m b e r o f counts/channel in the sliding pulser differential response *. While some of these errors can be calculated, m o s t o f them must be assessed on the basis o f experimental evidence. The uncertainties can be divided into two major categories; e.g. r a n d o m fluctuations and systematic errors. R a n d o m fluctuations have been minimized by averaging the three runs. Systematic errors have been reduced by making the measurements with different system components. Thus, two different ramp generators and two different mercury relay choppers were used. Fig. 3 shows that with a gain of 1.4 keV/channel, a given energy interval can be measured to an accuracy of about + 0.1 keV. Since the calibration reference energy which must be added to the interval has an uncertainty 1) t For a more detailed discussion of the measurement uncertainties, see ref.
1),
y-RAYS FROM 66Ga
203
of + 0.11 keV, the uncertainty assigned to the measured energies is + 0.25 keV except for the 1232 keV line which is +0.35 keV. These uncertainties correspond to a confidence level of about 90 %. It is a pleasure to acknowledge the support and encouragement received from H. H. Bolotin and L. M. Bollinger. The assistance of M. S. Freedman and M. C. Oselka in preparing the 66Ga source is greatly appreciated. References 1) M. G. Strauss, F. R. Lenkszus and J. J. Eichholz, to be published 2) J. J. Eichholz, M. G. Strauss and R. W. Bannon, to be published 3) R. E. Cot6, R. Guso, S. Raboy, R. A. Carrigan Jr., A. Gaigalas, R. B. Sutton and C. C. Trail, Nucl. Phys. 77 (1966) 239 and private communication 4) M. S. Freedman, F. T. Porter and F. Wagner, Phys. Rev. 151 (1966) 899 5) D. C. Camp, Lawrence Radiation Laboratory report UCRL-50156 (1967) 6) H. H. Bolotin and D. A. McClure, Phys. Rev,, in press 7) F. R. Lenkszus and M. G. Strauss, Nucl. Instr., in press 8) M. G. Strauss, I. S. Sherman, R. Brenner, S. J. Rudnick, R. N. Larsen and H. M. Mann, Roy. Sci. Instr. 38 (1967) 725 9) M. G. Strauss, L. L. Sifter, F. R. Lenkszus and R. Brenner, IEEE Trans. Nucl. Sci. 15 (1968) 518 10) R. Brenner, Rev. Sci. Instr., in press 11) R. Gunnink, R. A. Meyer, J. B. Niday and R. P. Anderson, Nucl. Instr. 65 (1968) 26 12) H. H. Bolotin, Argonne National Laboratory, private communication