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Energy and efficiency calibration of an array of six Euroball Cluster detectors used for beta-decay studies
Nuclear Instruments and Methods in Physics Research A 419 (1998) 121—131
Energy and efficiency calibration of an array of six Euroball Cluster detectors used for beta-decay studies Z. Hu, R. Collatz, H. Grawe, E. Roeckl* Gesellschaft fu( r Schwerionenforschung, Planckstr. 1, D-64291 Darmstadt, Germany Received 20 July 1998
Abstract The use of an array of six Euroball Cluster detectors, i.e. 42 large-volume germanium detectors, for beta-decay studies is described. The solid angle with respect to a source placed in the center of the array amounts to 65% of 4p sr. The total photo-peak efficiency for 1.33 MeV c-rays is 10.2(5)%, without “adding back” the Compton-scattered events. For this c-ray energy, the energy resolution of the entire setup is 2.8 keV. The performance of the array up to c-ray energies of 8 MeV is discussed, and alternative ways of determining the photo-peak efficiency are presented. 1998 Elsevier Science B.V. All rights reserved. PACS: 23.40; 29.30.K; 07.85.N Keywords: b-decay; Euroball Cluster; Photo-peak efficiency; c-intensity
1. Introduction Motivated by the need of high-energy resolution and high efficiency for the measurement of c-rays in high-spin studies, the technique of manufacturing germanium (Ge) detectors has experienced a continuous progress, e.g. within the framework of the Euroball project [1]. At present, one of the most advanced Ge detectors is the Euroball Cluster detector [2]. Each cluster consists of seven hexagonal tapered Ge crystals which are individually encapsulated and mounted closely packed in a common cryostat. By adding the pulse heights of Compton-scattered events registered by the seven Ge detectors (“add-back” mode), the system behaves similar to a single Ge detector with a volume of 2000 cm [3]. The excellent performance of this kind of Ge detectors is also interesting for b-decay studies. Especially in recent years the problem of missing strength in Gamow—Teller b-decay has attracted considerable experimental and theoretical interest. Progress in this research field strongly depends upon the increase of the (singles and coincidence) efficiency of the detection system compared to standard Ge detectors.
* Corresponding author. Tel.: 06159 71 2433; fax: 06159 71 2785; e-mail: [email protected]. 0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 1 1 3 7 - 1
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We were able to make use of a cube-like array of six Euroball Cluster detectors (Cluster Cube) for b-decay studies at the mass separator [4] online to the heavy-ion accelerator UNILAC of GSI Darmstadt. In comparison with in-beam c-spectroscopy, the measurement of b-delayed c-rays emitted from exotic nuclei requires an accurate energy and photo-peak efficiency calibration which covers the c-ray energy range from tens of keV up to 5 MeV or even higher. In this paper, we discuss some features of the Cluster Cube concerning energy resolution, add-back factor, c photo-peak efficiency, and intensity of single and double escape peaks. Moreover, we present methods of determining the relative and absolute photo-peak efficiency for c-ray detection. The term “relative” refers to the case in which dead-time losses occur in the data acquisition system, while the term “absolute” identifies the ideal case without dead-time losses. This report focuses on the methods used for the evaluation of data on the b-decays of Ag and Ag [5], whereas the corresponding details concerning the decays of other nuclei near Sn and Gd [6] will be published elsewhere.
2. Mechanical set-up The measurements were performed at the online mass separator of GSI Darmstadt. The mass-separated beam of radioactive atoms, which were produced by using fusion-evaporation reactions and extracted from a FEBIAD-B2 source [7] as singly charged ions, was implanted into a tape. After a pre-selected collection period, the resulting radioactive source was moved out of the vacuum of the mass separator to the center of the Cluster Cube (see Fig. 1), where it came to rest for a counting period. The solid angle for a radioactive source in the center of the Cluster Cube amounted to 65% of 4p sr. The cycle time of the moving tape collector was adjusted to the half-life of the isotopes to be studied. In order to reduce temperature instabilities, the Cluster Cube including the high-voltage supplies for the capsules were located in an air-conditioned plastic tent.
Fig. 1. View on five of the six Euroball Cluster detectors, the sixth one being removed to make the transport tape visible.
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3. Electronics and data acquisition system Due to space limitations, the electronics and data acquisition system was separated by about 30 m from the detectors. This aggravated the problem of electronic noise and thus influenced the overall energy resolution of the Cluster Cube. For the acquisition of c-singles and c—c coincidence data, four kinds of triggers were provided based on the timing signals from all capsules. A logic OR of all timing signals formed the first trigger type. The other three types of triggers consisted of events corresponding to the detection of a single c-ray (“hit”) in one of the capsules, multiple hits in the neighboring capsules, and real c—c coincidences (hits in non-neighboring capsules), respectively. Any of these four types of triggers delivered the “master trigger” for the acquisition of list-mode data. The energy signals were converted by ADCs which unfortunately revealed a sizable non-linearity. This problem will be discussed in Section 4. Subsequently, they were read by the corresponding VME cards, with the data being stored on magnet tape in list-mode. Two VME processor boards (Eurocom-7) were used for the data acquisition. In the offline analysis, both singles spectra and coincidence matrices were retrieved from the list-mode data by requiring a “master trigger” which consisted of a logic OR of the other three types of triggers mentioned above. For determining the c-intensities, the add-back mode was not used due to the complexity caused by the summing effect which will be discussed in Section 4. In addition, we chose 4 capsules from the Cluster Cube, connected the pulses through an OR condition into ADCs working independently of the data acquisition system for the list mode data, and stored the data in the so-called MR2000 modules. We refer to these spectra as MR2000 spectra. As the dead-time involved in this additional data acquisition system amounted to only a few microseconds, the corresponding dead-time losses are negligible. Therefore, the obtained MR2000 spectra can be used to determine the half-lives of c-transitions without caring about the dead-time correction.
4. Energy resolution and add-back factor By means of standard c-ray sources, the c-energy calibration was performed up to 6.13 MeV. The highest-energy calibration point was achieved by using the C(a, nc)O reaction occurring in a composite source of Pu and C. Due to the non-linearity of the ADCs (see Fig. 2), separate energy calibrations were performed for each capsule by carrying out least-squares fits for two consecutive energy intervals. Careful matching of all the spectra from all 42 capsules, obtained from a 4 days measurement of the b-decay of Ag [5], leads to an overall resolution of 2.8 keV FWHM for the Cluster Cube at a c-ray energy of 1.33 MeV, while the overall energy resolution for individual capsules is 2.36 keV [2]. We consider this result to be satisfactory in view of the large length of the cables between Cluster Cube and electronics, mentioned in Section 3. To demonstrate the reliability of the matching procedure, we inspect a doublet around 7.6 MeV. This energy lies 1.5 MeV above the highest energy reached by calibration sources. As can be seen from Fig. 3, the individual components of the doublet are well resolved in the photo-peaks as well as in the single and double escape peaks. This doublet was assigned to transitions in Fe from Fe(n, c)Fe reactions induced by neutrons that were produced in the UNILAC beam dumps of this or other UNILAC experiments. The energies for this doublet from our calibration are 7647.3(2) keV and 7633.1(2) keV, in good agreement with the literature values of 7646.7(7) and 7631.7(20) [8], respectively. The add-back factor is defined [3] as the total number of photo-peak events, including all single and all multiple-fold photo events recorded in all Ge capsules of a Cluster detector, divided by the number of single photo-peak events for a given energy. We obtained a value of 1.4(1) for a c-ray energy of 1.33 MeV, which is consistent with the result given in Ref. [3]. In principle, this factor is an important feature in designing Ge balls for in-beam experiments. In b-decay studies, however, the b-feeding is determined from the intensity balance, with small uncertainties in the feeding translating to large uncertainties in the reduced b-strength
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Fig. 2. Non-linearity of the energy calibration for one capsule of the Cluster Cube.
due to the influence of the phase-space factors. Therefore, besides efficiency, granularity is required. The summing effects with 511 keV quanta and cascade c-rays make the efficiency calibration too difficult to meet the high accuracy requirement if one used the add-back mode. Furthermore, the consideration of the add-back operation corresponds to a complex trade-off between gain in c-singles and loss in c—c coincidences, which depends upon the c-ray multiplicity of the decay under investigation. Therefore, we only used the add-back mode as a help for establishing level schemes, but not in determining the c-intensities. 5. Relative photo-peak efficiency Radioactive sources of Ba, Co, Eu, and a so-called mixed source were used for the calibration of relative photo-peak efficiencies. In this way, a calibration up to c-ray energies of 3.5 MeV was achieved. For higher energies, a GEANT simulation [9] was used. As the absolute activities of all the sources except the mixed source were unknown, the results obtained from different sources had to be normalized as described in the following. We assume that there exist m#1 data sets S , each of which has N energy-efficiency pairs (e , e ) and I I G G corresponding efficiency uncertainties p , with k"0, 1, 2,2, m and i"0, 1, 2,2, N . We then choose the G I data set N as the reference, and bring other sets of data to this standard by scaling the efficiencies e with G some constants. If the scaling constant for the data set S is a , there is a series of constants I I a , a , a ,2, a ,2, a , with a "1 since data set N was chosen as the reference. I K The efficiency curve between 200 keV and 2000 keV can be approximated to be linear in a log—log plot [10], i.e. log e (e)"a log e#b,
(1)
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Fig. 3. Full absorption, single escape and double escape lines for the 7633—7647 keV doublet detected in the Cluster Cube.
with e, e denoting the energy and relative photo-peak efficiency of c-rays, respectively, and a, b being characteristic constants of the detection system. To find reasonable values for a , one has to minimize the function I K ,I f (a, b, a ,2, a ,2, a )" u (log e (e )!log(a e )), (2) I K G G IG I G with 200 keV(e (2000 keV, the u "e /p denoting the weights. To solve £f (a, b, a ,2, a ,2, a )" G G G G I K 0, one calculates *f 1 ,I "!2 u (log e (e )!log(a e )) G G IG *a a I I G 1 ,I ,I ,I ,I "!2 a u log e #b u !log a u ! u log e k"1, 2,2, m G G G I G G G a I G G G G *f K ,I "2 u (log e(e )!log(a e )) G G IG *b I G K ,I K ,I K ,I K ,I "2a u log e #2b u !2 u log a !2 u log e G G G G I G G I G I G I G I G
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Z. Hu et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 121—131
*f K ,I "2 u (log e (e )!log(a e ))log e G G IG G *a I G K ,I K ,I K ,I "2a u (log e )#2b u log e !2 u log e log a G G G G G G I I G I G I G K ,I !2 u log e log e G G G I G This leads to the matrix equation
, u G G
0
2
0
$
, u G G
\
\
0
\
\
0
0
2
, u G G
, u G G
, , u log e u log e G G G G G G
,K u G G ,K u G G
, ! u log e G G G , ! u log e G G G
log a $
b a
\
$
,
$
"
log a K
, u log e G G G , u log e G G G
,K ,K u u log e G G G G G K ,I K ,I 2 u u log e G G G I G I G ,K K ,I K ,I 2 u log e u log e u (log e ) G G G G G G G I G I G 0
log a
, u G G , u G G
,K ! u log e G G G K ,I u log e G G I G K ,I u log e log e G G G I G
.
(3)
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To solve this equation, a computer program was made and applied to the data obtained from the Ba, Co, Eu sources and the mixed source. In addition, results obtained from the GEANT simulation [9] for selected c-energies were taken into account, with the mixed source as a reference. As can be seen from Fig. 4, the data from various sources including simulation data yield a consistent picture. On the basis of these data, an overall fit from 60 keV up to 8 MeV was performed with the following polynomial function: y"p #p x#p x#p x#p x#p x, (4) where x"log e, y"log e , e and e are energy and relative photo-peak efficiency, respectively, and p , p ,2, p are free parameters. The results obtained from this fit are shown in Fig. 4. According to this fit, the relative photo-peak efficiency for 1.33 MeV c-rays is 6.5%. The relative deviations between the fitted efficiencies and the values from experiment or simulation are less than 5% on the average.
6. Absolute photo-peak efficiency As already mentioned, the accurate determination of c-ray intensities is an important requirement in b-decay measurements. There are two ways to reach this goal. The first one is to fit the c peaks in the c-singles spectrum, and then use the following formula for the c-intensities: N N I" A " A , A e f e A A
(5)
Fig. 4. Relative photo-peak efficiencies of the Cluster Cube, obtained by using various c-sources together with results from a simulation [9]. All data points are matched to those from the mixed source. The solid curve represents the result obtained by a polynomial fit mentioned in the text, the dotted curves showing 95% confidence bands.
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where N, e (e ), f denote the fitted c peak area in the c-singles spectrum, the absolute (relative) A A A c photo-peak efficiency (e "f e ) and the dead-time correction factor of the data acquisition system, A A respectively. The second way to deduce c-intensities is to use the c—c coincidence matrix. One can fit peaks in the c-gated projection, and then apply the following formula for obtaining the c-intensities: N Nf A " A , I" A e e f e e A A
(6)
where N is the fitted c-peak area in the gated spectrum, e (e ) the absolute (relative) photo-peak A A A efficiency for this c-ray energy, e (e ) the absolute (relative) photo-peak efficiency for the energy of the c-gate, and f the dead-time correction factor of the data acquisition system. If the determination of c-intensities is based on either c-singles or c—c coincidence data, one can use the relative photo-peak efficiencies to deduce relative intensities. However, c-intensities of weak transitions and multiplets can only be deduced from the c—c coincidences, while intensities of c-rays without any coincidence relationship can only be determined from the c-singles. Therefore, it is desirable to apply both methods for deducing all c-intensities. If only using the relative photo-peak efficiencies, one has to normalize the relative c-intensities obtained from both methods. For the normalization, one can use the dead-time correction factor or choose a c-line for which both methods can be applied. Alternatively, by using the absolute photo-peak efficiencies, one does not need this normalization. In practice, the absolute photo-peak efficiencies can be deduced from the relative ones, if the former are known for at least one c-energy point. One can get the absolute photo-peak efficiencies for the whole energy range by multiplying the values of relative photo-peak efficiencies with a factor determined from this single reference point. The two methods used for this purpose are discussed in the following. (a) Use of summing peaks in the c-singles spectrum Summing corrections for accurate intensity measurements have been extensively discussed in the literature [11]. For a large array of Ge detectors such as the Cluster Cube, the summing peaks are clearly visible in the spectra, even though the efficiency for an individual capsule is as small as for a conventional Ge detector. The summing of two c-rays c and c in c-singles leads to the following relations: N "I e e n f (7) N "I e n f (1!e ), (8) N "I e n f (1!e ), (9) where I and I are the intensities of the c-rays c and c , I the coincident intensity of the c —c cascade, N and N the peak area for c and c , e and e the absolute photo-peak efficiency of one capsule for c and c , f the dead-time correction factor of the data acquisition system, n the number of capsules (42 in case of the Cluster Cube), and e and e the total detection efficiencies of one capsule for c and c , respectively. The total detection efficiency is defined as the ratio of the number of pulses recorded in the spectrum and the number of photons emitted from the source. By dividing Eq. (7) by Eqs. (8) and (9), respectively, one gets N I e " , N I N I e " , N I
(10)
(11)
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where the last terms in Eqs. (8) and (9) are neglected, since the total detection efficiency of one capsule is very small (The GEANT simulation yields a value of 1.5% at 1.3 MeV [9]). Eqs. (10) and (11) can be used to obtain the absolute photo-peak efficiencies of two c-lines under the condition that their intensities are known and their summing peak is visible in the c-singles. However, one has to consider the summing losses due to the detection of other coincident transitions and, in case of b>-decay, of positrons or 511 keV quanta. This leads to correction factors (1! e ) for Eqs. (7)—(9), AY AY respectively, where c denotes all coincident transitions, e being the corresponding total detection AY efficiencies of one capsule. If one chooses two c-lines without other coincident transitions, the summing losses in case of b>-decay arise only from positrons or 511 keV quanta. The latter effect can be neglected since the correction factors on N , N and N in Eqs. (7)—(9) are approximately identical. We verified this method by using two c-lines of Co, namely 846.8 keV (100%) and 3253.4 keV (7.62%) [12], which are in coincidence but have no other coincident transitions. The absolute photo-peak efficiency of the Cluster Cube for the 846.8 keV c-line was determined to be 15.3(25)%. With the relative photo-peak efficiency calibration described in Section 5, we deduced the absolute photo-peak efficiency of the Cluster Cube for 1.33 MeV c-rays to be 11.0(18)%. (b) Use of c—c coincidence data It is well known [13] that absolute intensities can be determined from coincidence data, if compared to singles data. This provides an alternative method to determine absolute photo-peak efficiencies. Photo-peak intensities from the c-gated projection and the c-singles data are interconnected by the following equations, N "I e e f , (12) A A N "I e f , (13) A AA where I is the c-intensity, I the intensity relevant for coincidences between this c-ray and that used as the A gate, N the peak area in the gated projection, and N the peak area in the singles spectrum. A A From Eqs. (12) and (13), we have N I e " A A . (14) NI A If we choose two c-rays that are interconnected by a direct cascade and use the lower-lying transition as the gate, Eq. (14) can be simplified to yield N (15) e " A. N A This means that, in order to get the absolute photo-peak efficiency for a given c-line, one only has to use it as a gate, inspect another c-transition from a directly connected cascade, and then calculate the ratio between the peak area in the gated projection and that in the singles. However, it is worth noting that this method may suffer from systematic deviation depending on how one sets the gates. In reality, this kind of uncertainty can be minimized by choosing a large gate width (about 4 FWHM) for the c-lines under consideration. Applying Eq. (15) to the two c-lines of Co, used in method (a), we got a value of 14.1(3)% for the absolute photo-peak efficiency at 846.8 keV. Using the known relative photo-peak efficiency, we obtained 10.1(5)% for the absolute photo-peak efficiency at 1.33 MeV. By determining the weighted average of the values obtained by the two methods, the photo-peak efficiencies of the Cluster Cube for 1.33 MeV c-rays was found to be 10.2(5)%. The main advantage of these methods is that they do not depend on the dead-time of the data acquisition system, which can dramatically
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Fig. 5. Ratio between the summed intensities of the single and double escape peaks and the intensity of corresponding full-energy absorption lines. The curve is used to guide the eye.
vary with time. For example, electronic noise or microphonics may affect one of the 42 detectors for a short time interval, which makes the dead-time correction difficult. However, if one compares the absolute photo-peak efficiency obtained in this way and the relative photo-peak efficiency deduced without dead-time correction, the dead-time effect can be deduced. Using the relative photo-peak efficiency of 6.5% deduced in Section 5 and the absolute one of 10.2% for 1.33 MeV c-rays, we estimated the average dead-time correction to be 63.7% during the measurement of the mixed source, which corresponds to an average counting rate of approximately 6 kHz (such high rates were not reached during the online measurements).
7. Single and double escape effects In the determination of c intensities, the single and double escape effect of high-energy c-rays has to be considered. As can be seen from Fig. 5, this effect is comparatively large for arrays like the Cluster Cube which is efficient even at high c-ray energies. The intensity ratio between the single and the double escape peak is roughly constant, namely 2.5$0.5. From Fig. 5, one can clearly see that the escape effect is negligible below 1.5 MeV.
8. Summary In this paper, we investigated the performance of the Cluster Cube, and described, in particular, methods for determining the photo-peak efficiency. Its absolute value for 1.33 MeV c-rays without add-back was
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found to be 10.2(5)%, the energy resolution at this energy being 2.8 keV. In spite of a considerable non-linearity of the ADCs, it was possible to maintain the good energy resolution up to c-ray energies of 8 MeV. This feature was verified by means of the 7633—7647 keV doublet occurring in Fe(n, c)Fe reactions. We note that the accurate knowledge of the energy calibration up to large c-ray energies and of the corresponding photo-peak efficiency is indeed an important prerequisite of modern b-decay work. To our knowledge, the Cluster Cube offers the highest photo-peak efficiency of all high-resolution detectors that have ever been used for b-decay studies. The excellent performance has already yielded excellent results on the Gamow—Teller decay of neutron-deficient isotopes near Sn and Gd [5,6]. It is easy to predict that this kind of large arrays of Ge detectors will be used more often in the future. We hope that this work contributes to the success of such studies.
Acknowledgements The authors would like to thank the German Euroball collaboration for making the Euroball Cluster detectors available for experiment at GSI. These detectors were supported by the German BMBF, the KFA Ju¨lich, GSI Darmstadt, and MPI-K Heidelberg.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
J. Eberth, Prog. Part. Nucl. Phys. 28 (1992) 495. J. Eberth et al., Prog. Part. Nucl. Phys. 38 (1997) 29. M. Wilhelm et al., Nucl. Instr. and Meth. A 381 (1996) 462. K. Burkard et al., Nucl. Instr. and Meth. B 126 (1997) 12. Z. Hu et al., GSI Annual Report 1997, in: Proc. Int. Conf. Exotic Nuclei and Atomic Masses, Bellaire, Michigan, USA, 1998, in print. J. Agramunt et al., GSI Annual Report 1997, in: Proc. Int. Conf. Exotic Nuclei and Atomic Masses, Bellaire, Michigan, USA, 1998, in print. R. Kirchner et al., Nucl. Instr. and Meth. A 234 (1985) 224. R. Vennink et al., Nucl. Phys. A 344 (1980) 421. J.L. Tain, private communication. K. Debertin, R.G. Helmer, c- and X-Ray Spectrometry with Semiconductor Detectors, Elsevier, Amsterdam, 1988, p. 220. K. Debertin, R.G. Helmer, c- and X-Ray Spectrometry with Semiconductor Detectors, Elsevier, Amsterdam, 1988, p. 258. Report IAEA-TECDOC-619, 1991. K. Debertin, R.G. Helmer, c-and X-Ray Spectrometry with Semiconductor Detectors, Elsevier, Amsterdam, 1988, p. 115.
Energy and efficiency calibration of an array of six Euroball Cluster detectors used for beta-decay studies Z. Hu, R. Collatz, H. Grawe, E. Roeckl* Gesellschaft fu( r Schwerionenforschung, Planckstr. 1, D-64291 Darmstadt, Germany Received 20 July 1998
Abstract The use of an array of six Euroball Cluster detectors, i.e. 42 large-volume germanium detectors, for beta-decay studies is described. The solid angle with respect to a source placed in the center of the array amounts to 65% of 4p sr. The total photo-peak efficiency for 1.33 MeV c-rays is 10.2(5)%, without “adding back” the Compton-scattered events. For this c-ray energy, the energy resolution of the entire setup is 2.8 keV. The performance of the array up to c-ray energies of 8 MeV is discussed, and alternative ways of determining the photo-peak efficiency are presented. 1998 Elsevier Science B.V. All rights reserved. PACS: 23.40; 29.30.K; 07.85.N Keywords: b-decay; Euroball Cluster; Photo-peak efficiency; c-intensity
1. Introduction Motivated by the need of high-energy resolution and high efficiency for the measurement of c-rays in high-spin studies, the technique of manufacturing germanium (Ge) detectors has experienced a continuous progress, e.g. within the framework of the Euroball project [1]. At present, one of the most advanced Ge detectors is the Euroball Cluster detector [2]. Each cluster consists of seven hexagonal tapered Ge crystals which are individually encapsulated and mounted closely packed in a common cryostat. By adding the pulse heights of Compton-scattered events registered by the seven Ge detectors (“add-back” mode), the system behaves similar to a single Ge detector with a volume of 2000 cm [3]. The excellent performance of this kind of Ge detectors is also interesting for b-decay studies. Especially in recent years the problem of missing strength in Gamow—Teller b-decay has attracted considerable experimental and theoretical interest. Progress in this research field strongly depends upon the increase of the (singles and coincidence) efficiency of the detection system compared to standard Ge detectors.
* Corresponding author. Tel.: 06159 71 2433; fax: 06159 71 2785; e-mail: [email protected]. 0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 1 1 3 7 - 1
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We were able to make use of a cube-like array of six Euroball Cluster detectors (Cluster Cube) for b-decay studies at the mass separator [4] online to the heavy-ion accelerator UNILAC of GSI Darmstadt. In comparison with in-beam c-spectroscopy, the measurement of b-delayed c-rays emitted from exotic nuclei requires an accurate energy and photo-peak efficiency calibration which covers the c-ray energy range from tens of keV up to 5 MeV or even higher. In this paper, we discuss some features of the Cluster Cube concerning energy resolution, add-back factor, c photo-peak efficiency, and intensity of single and double escape peaks. Moreover, we present methods of determining the relative and absolute photo-peak efficiency for c-ray detection. The term “relative” refers to the case in which dead-time losses occur in the data acquisition system, while the term “absolute” identifies the ideal case without dead-time losses. This report focuses on the methods used for the evaluation of data on the b-decays of Ag and Ag [5], whereas the corresponding details concerning the decays of other nuclei near Sn and Gd [6] will be published elsewhere.
2. Mechanical set-up The measurements were performed at the online mass separator of GSI Darmstadt. The mass-separated beam of radioactive atoms, which were produced by using fusion-evaporation reactions and extracted from a FEBIAD-B2 source [7] as singly charged ions, was implanted into a tape. After a pre-selected collection period, the resulting radioactive source was moved out of the vacuum of the mass separator to the center of the Cluster Cube (see Fig. 1), where it came to rest for a counting period. The solid angle for a radioactive source in the center of the Cluster Cube amounted to 65% of 4p sr. The cycle time of the moving tape collector was adjusted to the half-life of the isotopes to be studied. In order to reduce temperature instabilities, the Cluster Cube including the high-voltage supplies for the capsules were located in an air-conditioned plastic tent.
Fig. 1. View on five of the six Euroball Cluster detectors, the sixth one being removed to make the transport tape visible.
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3. Electronics and data acquisition system Due to space limitations, the electronics and data acquisition system was separated by about 30 m from the detectors. This aggravated the problem of electronic noise and thus influenced the overall energy resolution of the Cluster Cube. For the acquisition of c-singles and c—c coincidence data, four kinds of triggers were provided based on the timing signals from all capsules. A logic OR of all timing signals formed the first trigger type. The other three types of triggers consisted of events corresponding to the detection of a single c-ray (“hit”) in one of the capsules, multiple hits in the neighboring capsules, and real c—c coincidences (hits in non-neighboring capsules), respectively. Any of these four types of triggers delivered the “master trigger” for the acquisition of list-mode data. The energy signals were converted by ADCs which unfortunately revealed a sizable non-linearity. This problem will be discussed in Section 4. Subsequently, they were read by the corresponding VME cards, with the data being stored on magnet tape in list-mode. Two VME processor boards (Eurocom-7) were used for the data acquisition. In the offline analysis, both singles spectra and coincidence matrices were retrieved from the list-mode data by requiring a “master trigger” which consisted of a logic OR of the other three types of triggers mentioned above. For determining the c-intensities, the add-back mode was not used due to the complexity caused by the summing effect which will be discussed in Section 4. In addition, we chose 4 capsules from the Cluster Cube, connected the pulses through an OR condition into ADCs working independently of the data acquisition system for the list mode data, and stored the data in the so-called MR2000 modules. We refer to these spectra as MR2000 spectra. As the dead-time involved in this additional data acquisition system amounted to only a few microseconds, the corresponding dead-time losses are negligible. Therefore, the obtained MR2000 spectra can be used to determine the half-lives of c-transitions without caring about the dead-time correction.
4. Energy resolution and add-back factor By means of standard c-ray sources, the c-energy calibration was performed up to 6.13 MeV. The highest-energy calibration point was achieved by using the C(a, nc)O reaction occurring in a composite source of Pu and C. Due to the non-linearity of the ADCs (see Fig. 2), separate energy calibrations were performed for each capsule by carrying out least-squares fits for two consecutive energy intervals. Careful matching of all the spectra from all 42 capsules, obtained from a 4 days measurement of the b-decay of Ag [5], leads to an overall resolution of 2.8 keV FWHM for the Cluster Cube at a c-ray energy of 1.33 MeV, while the overall energy resolution for individual capsules is 2.36 keV [2]. We consider this result to be satisfactory in view of the large length of the cables between Cluster Cube and electronics, mentioned in Section 3. To demonstrate the reliability of the matching procedure, we inspect a doublet around 7.6 MeV. This energy lies 1.5 MeV above the highest energy reached by calibration sources. As can be seen from Fig. 3, the individual components of the doublet are well resolved in the photo-peaks as well as in the single and double escape peaks. This doublet was assigned to transitions in Fe from Fe(n, c)Fe reactions induced by neutrons that were produced in the UNILAC beam dumps of this or other UNILAC experiments. The energies for this doublet from our calibration are 7647.3(2) keV and 7633.1(2) keV, in good agreement with the literature values of 7646.7(7) and 7631.7(20) [8], respectively. The add-back factor is defined [3] as the total number of photo-peak events, including all single and all multiple-fold photo events recorded in all Ge capsules of a Cluster detector, divided by the number of single photo-peak events for a given energy. We obtained a value of 1.4(1) for a c-ray energy of 1.33 MeV, which is consistent with the result given in Ref. [3]. In principle, this factor is an important feature in designing Ge balls for in-beam experiments. In b-decay studies, however, the b-feeding is determined from the intensity balance, with small uncertainties in the feeding translating to large uncertainties in the reduced b-strength
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Fig. 2. Non-linearity of the energy calibration for one capsule of the Cluster Cube.
due to the influence of the phase-space factors. Therefore, besides efficiency, granularity is required. The summing effects with 511 keV quanta and cascade c-rays make the efficiency calibration too difficult to meet the high accuracy requirement if one used the add-back mode. Furthermore, the consideration of the add-back operation corresponds to a complex trade-off between gain in c-singles and loss in c—c coincidences, which depends upon the c-ray multiplicity of the decay under investigation. Therefore, we only used the add-back mode as a help for establishing level schemes, but not in determining the c-intensities. 5. Relative photo-peak efficiency Radioactive sources of Ba, Co, Eu, and a so-called mixed source were used for the calibration of relative photo-peak efficiencies. In this way, a calibration up to c-ray energies of 3.5 MeV was achieved. For higher energies, a GEANT simulation [9] was used. As the absolute activities of all the sources except the mixed source were unknown, the results obtained from different sources had to be normalized as described in the following. We assume that there exist m#1 data sets S , each of which has N energy-efficiency pairs (e , e ) and I I G G corresponding efficiency uncertainties p , with k"0, 1, 2,2, m and i"0, 1, 2,2, N . We then choose the G I data set N as the reference, and bring other sets of data to this standard by scaling the efficiencies e with G some constants. If the scaling constant for the data set S is a , there is a series of constants I I a , a , a ,2, a ,2, a , with a "1 since data set N was chosen as the reference. I K The efficiency curve between 200 keV and 2000 keV can be approximated to be linear in a log—log plot [10], i.e. log e (e)"a log e#b,
(1)
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Fig. 3. Full absorption, single escape and double escape lines for the 7633—7647 keV doublet detected in the Cluster Cube.
with e, e denoting the energy and relative photo-peak efficiency of c-rays, respectively, and a, b being characteristic constants of the detection system. To find reasonable values for a , one has to minimize the function I K ,I f (a, b, a ,2, a ,2, a )" u (log e (e )!log(a e )), (2) I K G G IG I G with 200 keV(e (2000 keV, the u "e /p denoting the weights. To solve £f (a, b, a ,2, a ,2, a )" G G G G I K 0, one calculates *f 1 ,I "!2 u (log e (e )!log(a e )) G G IG *a a I I G 1 ,I ,I ,I ,I "!2 a u log e #b u !log a u ! u log e k"1, 2,2, m G G G I G G G a I G G G G *f K ,I "2 u (log e(e )!log(a e )) G G IG *b I G K ,I K ,I K ,I K ,I "2a u log e #2b u !2 u log a !2 u log e G G G G I G G I G I G I G I G
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*f K ,I "2 u (log e (e )!log(a e ))log e G G IG G *a I G K ,I K ,I K ,I "2a u (log e )#2b u log e !2 u log e log a G G G G G G I I G I G I G K ,I !2 u log e log e G G G I G This leads to the matrix equation
, u G G
0
2
0
$
, u G G
\
\
0
\
\
0
0
2
, u G G
, u G G
, , u log e u log e G G G G G G
,K u G G ,K u G G
, ! u log e G G G , ! u log e G G G
log a $
b a
\
$
,
$
"
log a K
, u log e G G G , u log e G G G
,K ,K u u log e G G G G G K ,I K ,I 2 u u log e G G G I G I G ,K K ,I K ,I 2 u log e u log e u (log e ) G G G G G G G I G I G 0
log a
, u G G , u G G
,K ! u log e G G G K ,I u log e G G I G K ,I u log e log e G G G I G
.
(3)
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To solve this equation, a computer program was made and applied to the data obtained from the Ba, Co, Eu sources and the mixed source. In addition, results obtained from the GEANT simulation [9] for selected c-energies were taken into account, with the mixed source as a reference. As can be seen from Fig. 4, the data from various sources including simulation data yield a consistent picture. On the basis of these data, an overall fit from 60 keV up to 8 MeV was performed with the following polynomial function: y"p #p x#p x#p x#p x#p x, (4) where x"log e, y"log e , e and e are energy and relative photo-peak efficiency, respectively, and p , p ,2, p are free parameters. The results obtained from this fit are shown in Fig. 4. According to this fit, the relative photo-peak efficiency for 1.33 MeV c-rays is 6.5%. The relative deviations between the fitted efficiencies and the values from experiment or simulation are less than 5% on the average.
6. Absolute photo-peak efficiency As already mentioned, the accurate determination of c-ray intensities is an important requirement in b-decay measurements. There are two ways to reach this goal. The first one is to fit the c peaks in the c-singles spectrum, and then use the following formula for the c-intensities: N N I" A " A , A e f e A A
(5)
Fig. 4. Relative photo-peak efficiencies of the Cluster Cube, obtained by using various c-sources together with results from a simulation [9]. All data points are matched to those from the mixed source. The solid curve represents the result obtained by a polynomial fit mentioned in the text, the dotted curves showing 95% confidence bands.
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where N, e (e ), f denote the fitted c peak area in the c-singles spectrum, the absolute (relative) A A A c photo-peak efficiency (e "f e ) and the dead-time correction factor of the data acquisition system, A A respectively. The second way to deduce c-intensities is to use the c—c coincidence matrix. One can fit peaks in the c-gated projection, and then apply the following formula for obtaining the c-intensities: N Nf A " A , I" A e e f e e A A
(6)
where N is the fitted c-peak area in the gated spectrum, e (e ) the absolute (relative) photo-peak A A A efficiency for this c-ray energy, e (e ) the absolute (relative) photo-peak efficiency for the energy of the c-gate, and f the dead-time correction factor of the data acquisition system. If the determination of c-intensities is based on either c-singles or c—c coincidence data, one can use the relative photo-peak efficiencies to deduce relative intensities. However, c-intensities of weak transitions and multiplets can only be deduced from the c—c coincidences, while intensities of c-rays without any coincidence relationship can only be determined from the c-singles. Therefore, it is desirable to apply both methods for deducing all c-intensities. If only using the relative photo-peak efficiencies, one has to normalize the relative c-intensities obtained from both methods. For the normalization, one can use the dead-time correction factor or choose a c-line for which both methods can be applied. Alternatively, by using the absolute photo-peak efficiencies, one does not need this normalization. In practice, the absolute photo-peak efficiencies can be deduced from the relative ones, if the former are known for at least one c-energy point. One can get the absolute photo-peak efficiencies for the whole energy range by multiplying the values of relative photo-peak efficiencies with a factor determined from this single reference point. The two methods used for this purpose are discussed in the following. (a) Use of summing peaks in the c-singles spectrum Summing corrections for accurate intensity measurements have been extensively discussed in the literature [11]. For a large array of Ge detectors such as the Cluster Cube, the summing peaks are clearly visible in the spectra, even though the efficiency for an individual capsule is as small as for a conventional Ge detector. The summing of two c-rays c and c in c-singles leads to the following relations: N "I e e n f (7) N "I e n f (1!e ), (8) N "I e n f (1!e ), (9) where I and I are the intensities of the c-rays c and c , I the coincident intensity of the c —c cascade, N and N the peak area for c and c , e and e the absolute photo-peak efficiency of one capsule for c and c , f the dead-time correction factor of the data acquisition system, n the number of capsules (42 in case of the Cluster Cube), and e and e the total detection efficiencies of one capsule for c and c , respectively. The total detection efficiency is defined as the ratio of the number of pulses recorded in the spectrum and the number of photons emitted from the source. By dividing Eq. (7) by Eqs. (8) and (9), respectively, one gets N I e " , N I N I e " , N I
(10)
(11)
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where the last terms in Eqs. (8) and (9) are neglected, since the total detection efficiency of one capsule is very small (The GEANT simulation yields a value of 1.5% at 1.3 MeV [9]). Eqs. (10) and (11) can be used to obtain the absolute photo-peak efficiencies of two c-lines under the condition that their intensities are known and their summing peak is visible in the c-singles. However, one has to consider the summing losses due to the detection of other coincident transitions and, in case of b>-decay, of positrons or 511 keV quanta. This leads to correction factors (1! e ) for Eqs. (7)—(9), AY AY respectively, where c denotes all coincident transitions, e being the corresponding total detection AY efficiencies of one capsule. If one chooses two c-lines without other coincident transitions, the summing losses in case of b>-decay arise only from positrons or 511 keV quanta. The latter effect can be neglected since the correction factors on N , N and N in Eqs. (7)—(9) are approximately identical. We verified this method by using two c-lines of Co, namely 846.8 keV (100%) and 3253.4 keV (7.62%) [12], which are in coincidence but have no other coincident transitions. The absolute photo-peak efficiency of the Cluster Cube for the 846.8 keV c-line was determined to be 15.3(25)%. With the relative photo-peak efficiency calibration described in Section 5, we deduced the absolute photo-peak efficiency of the Cluster Cube for 1.33 MeV c-rays to be 11.0(18)%. (b) Use of c—c coincidence data It is well known [13] that absolute intensities can be determined from coincidence data, if compared to singles data. This provides an alternative method to determine absolute photo-peak efficiencies. Photo-peak intensities from the c-gated projection and the c-singles data are interconnected by the following equations, N "I e e f , (12) A A N "I e f , (13) A AA where I is the c-intensity, I the intensity relevant for coincidences between this c-ray and that used as the A gate, N the peak area in the gated projection, and N the peak area in the singles spectrum. A A From Eqs. (12) and (13), we have N I e " A A . (14) NI A If we choose two c-rays that are interconnected by a direct cascade and use the lower-lying transition as the gate, Eq. (14) can be simplified to yield N (15) e " A. N A This means that, in order to get the absolute photo-peak efficiency for a given c-line, one only has to use it as a gate, inspect another c-transition from a directly connected cascade, and then calculate the ratio between the peak area in the gated projection and that in the singles. However, it is worth noting that this method may suffer from systematic deviation depending on how one sets the gates. In reality, this kind of uncertainty can be minimized by choosing a large gate width (about 4 FWHM) for the c-lines under consideration. Applying Eq. (15) to the two c-lines of Co, used in method (a), we got a value of 14.1(3)% for the absolute photo-peak efficiency at 846.8 keV. Using the known relative photo-peak efficiency, we obtained 10.1(5)% for the absolute photo-peak efficiency at 1.33 MeV. By determining the weighted average of the values obtained by the two methods, the photo-peak efficiencies of the Cluster Cube for 1.33 MeV c-rays was found to be 10.2(5)%. The main advantage of these methods is that they do not depend on the dead-time of the data acquisition system, which can dramatically
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Fig. 5. Ratio between the summed intensities of the single and double escape peaks and the intensity of corresponding full-energy absorption lines. The curve is used to guide the eye.
vary with time. For example, electronic noise or microphonics may affect one of the 42 detectors for a short time interval, which makes the dead-time correction difficult. However, if one compares the absolute photo-peak efficiency obtained in this way and the relative photo-peak efficiency deduced without dead-time correction, the dead-time effect can be deduced. Using the relative photo-peak efficiency of 6.5% deduced in Section 5 and the absolute one of 10.2% for 1.33 MeV c-rays, we estimated the average dead-time correction to be 63.7% during the measurement of the mixed source, which corresponds to an average counting rate of approximately 6 kHz (such high rates were not reached during the online measurements).
7. Single and double escape effects In the determination of c intensities, the single and double escape effect of high-energy c-rays has to be considered. As can be seen from Fig. 5, this effect is comparatively large for arrays like the Cluster Cube which is efficient even at high c-ray energies. The intensity ratio between the single and the double escape peak is roughly constant, namely 2.5$0.5. From Fig. 5, one can clearly see that the escape effect is negligible below 1.5 MeV.
8. Summary In this paper, we investigated the performance of the Cluster Cube, and described, in particular, methods for determining the photo-peak efficiency. Its absolute value for 1.33 MeV c-rays without add-back was
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found to be 10.2(5)%, the energy resolution at this energy being 2.8 keV. In spite of a considerable non-linearity of the ADCs, it was possible to maintain the good energy resolution up to c-ray energies of 8 MeV. This feature was verified by means of the 7633—7647 keV doublet occurring in Fe(n, c)Fe reactions. We note that the accurate knowledge of the energy calibration up to large c-ray energies and of the corresponding photo-peak efficiency is indeed an important prerequisite of modern b-decay work. To our knowledge, the Cluster Cube offers the highest photo-peak efficiency of all high-resolution detectors that have ever been used for b-decay studies. The excellent performance has already yielded excellent results on the Gamow—Teller decay of neutron-deficient isotopes near Sn and Gd [5,6]. It is easy to predict that this kind of large arrays of Ge detectors will be used more often in the future. We hope that this work contributes to the success of such studies.
Acknowledgements The authors would like to thank the German Euroball collaboration for making the Euroball Cluster detectors available for experiment at GSI. These detectors were supported by the German BMBF, the KFA Ju¨lich, GSI Darmstadt, and MPI-K Heidelberg.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
J. Eberth, Prog. Part. Nucl. Phys. 28 (1992) 495. J. Eberth et al., Prog. Part. Nucl. Phys. 38 (1997) 29. M. Wilhelm et al., Nucl. Instr. and Meth. A 381 (1996) 462. K. Burkard et al., Nucl. Instr. and Meth. B 126 (1997) 12. Z. Hu et al., GSI Annual Report 1997, in: Proc. Int. Conf. Exotic Nuclei and Atomic Masses, Bellaire, Michigan, USA, 1998, in print. J. Agramunt et al., GSI Annual Report 1997, in: Proc. Int. Conf. Exotic Nuclei and Atomic Masses, Bellaire, Michigan, USA, 1998, in print. R. Kirchner et al., Nucl. Instr. and Meth. A 234 (1985) 224. R. Vennink et al., Nucl. Phys. A 344 (1980) 421. J.L. Tain, private communication. K. Debertin, R.G. Helmer, c- and X-Ray Spectrometry with Semiconductor Detectors, Elsevier, Amsterdam, 1988, p. 220. K. Debertin, R.G. Helmer, c- and X-Ray Spectrometry with Semiconductor Detectors, Elsevier, Amsterdam, 1988, p. 258. Report IAEA-TECDOC-619, 1991. K. Debertin, R.G. Helmer, c-and X-Ray Spectrometry with Semiconductor Detectors, Elsevier, Amsterdam, 1988, p. 115.