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Table of Contents
Abstract
1. Introduction
2. Experimental Setup
3. Simulation Setup
4. Energy Calibration
5. Experimental Results
4, 304.5, 0, 151, 202, 224, 243, 244, 247, 253, 263, 269, 283, 289, 303,
5.1. Error Estimation
6. Model For Parameterization Of BGO And BSO Quenching
6.1. Implications For The Birks Constant, KB
7. Discussion And Conclusions
8. Summary
Acknowledgments
Abstract
Scintillator non-linearity is an important parameter in calibration of scintillators, especially when measuring ions. Here we investigate the response of two scintillators, namely BGO (Bi4Ge3O12) and BSO (Bi4Si3O12), to different ions from helium to iron. We compare the scintillator output with the energy loss according to GEANT4 simulations and determine the quenching parameters for each ion species. BGO and BSO share the same crystalline structure but differ in one single component, therefore we also analyse differences in light output and non-linearity between the two scintillators caused by this similarity and present a model predicting these effects for heavy ions. 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier .com/locate /n imb Quenching comparison of BGO and BSO for heavy ions http://dx.doi.org/10.1016/j.nimb.2015.07.127 0168-583X/ 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ⇑ Corresponding author. E-mail address: tammen@physik.uni-kiel.de (J. Tammen). J. Tammen ⇑, R. Elftmann, S.R. Kulkarni, S.I. Böttcher, R.F. Wimmer-Schweingruber Institut für Experimentelle und Angewandte Physik, Universität Kiel, 24105 Kiel, Germany a r t i c l e i n f o Article history: Received 3 June 2015 Received in revised form 24 July 2015 Accepted 27 July 2015 Available online 2 September 2015 Keywords: BGO BSO Scintillator non-linearity Quenching a b s t r a c t Scintillator non-linearity is an important parameter in calibration of scintillators, especially when measuring ions. Here we investigate the response of two scintillators, namely BGO (Bi4Ge3O12) and BSO (Bi4Si3O12), to different ions from helium to iron. We compare the scintillator output with the energy loss according to GEANT4 simulations and determine the quenching parameters for each ion species. BGO and BSO share the same crystalline structure but differ in one single component, therefore we also analyse differences in light output and non-linearity between the two scintillators caused by this similarity and present a model predicting these effects for heavy ions. 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Scintillators are commonly used to detect radiation. Quenching [1] introduces a non-linearity in the light output of scintillators which has to be considered during calibration of an instrument or detector. In the literature this phenomenon has often been investigated. There are measurements with electrons, X-rays and/or c-rays [2–4] but only few publications for ions, and these focus on light ions [5] or lower energy ranges [6,7]. Nevertheless there is some data available for BGOs response to heavy ions [8]. All of those previously mentioned publications focus on stopping heavy ions while we also include penetrating ions in our study to extend the validity range of our model. There are only few applications in which heavy ions are routinely measured. Consequently, there are only few measurements of the quenching of the light output of heavy ions. Nevertheless, in these applications, the knowledge of scintillation performance parameters is vital to achieve an accurate energy measurement with good resolution. With their high density scintillators provide high stopping power within a small volume, which can be further reduced when using a photodiode readout instead of photomultipliers. Small volume and the ensuring low packaging mass make scintillators very attractive for radiation measurements in space. For instance the Radiation Assessment Detector (RAD) [9] on NASA’s Curiosity rover [10] uses a CsI scintillator. In this paper we measure the response of Bismuth Germanate (BGO, Bi4Ge3O12) and Bismuth Silicate (BSO, Bi4Si3O12) to ions from helium to iron and compare those results with GEANT4 simulations of the expected energy deposition. BGO and BSO have the same crystal structure and differ only in one atom type which is Germanium for BGO and Silicon for BSO. This similarity becomes visible in the physical properties of both crystals where many parameters such as radiation length and peak emission/excitation are almost the same while the density differs by only 5% due to different atomic masses [11,12]. Considering this similarity we evaluate the effects it has on the scintillation parameters. We describe the experimental setup in Section 2, the simulations performed to estimate the quenching in Section 3 and the energy calibration in Section 4. Section 5 gives the experimental results which are discussed and interpreted in Section 7.
2. Experimental setup
The BSO crystal was bought from Molecular Technology (MolTech) GmbH and has a cubic shape with 2 cm edge length. The BGO crystal was bought from Eckhard Kruse Meechnik and has a hexagonal shape with 2 cm side length and 2 cm thickness. Both crystals were originally polished on all surfaces. Two opposing sides of each crystal were roughened and a Hamamatsu photo diode S3590-19 was glued with Dow Corning DC93-500 space grade glue to each of these two sides. All other faces remained polished. After gluing the diodes both crystals were wrapped in two layers of nitrocellulose filter sheets (Millipore Corporation, 0.45 lm pore size, 140 lm thick) and two layers of PTFE (150 lm in total) to minimize light loss. The experimental setup is illustrated in Fig. 1. For the BGO measurements two circular silicon passivated ion-implanted planar sil- icon detectors (Canberra, Belgium, £ 12 mm, 300 lm thickness) were placed in front of the crystal (shown in blue) at 5 mm and 45 mm distance from the crystal front. They serve as tracking detectors for the ion beam. In Fig. 1(a) they are indicated as green rectangles and labeled ‘‘D’’. One photo diode (Hamamatsu S3204) was placed behind the crystal acting as anticoincidence (labeled F). In the case of BSO (bottom label) two photodiodes (Hamamatsu S3590-19) were used as tracking detectors (D) and anticoincidence (F). In both configurations the scintillators were read out by photodiodes (labeled ‘‘E’’) and the detectors and crystals were put into light tight boxes with an entrance window covered by 50 lm thick aluminum foils (C). Each detector is connected to a charge sensitive preamplifier followed by two shapers (2.2 ls shaping time) with times 1 and times 16 gain, followed by two ADCs with FPGA readout at 3 MHz. From the ADC data the pulse-heights of all channels are reconstructed. A similar data-acquisition system is being developed for the Energetic Particle Detector (EPD) on the Solar Orbiter mission [13,14]. Heavy ion (He, C, O, Ne, Si and Fe) beams were provided by the Heavy Ion Medical Accelerator in Chiba (HIMAC) [15], Japan. We used the ions listed in Table 1 with a rate of 100–1000 ions/s for a duration of 15 minutes per datapoint. The energy of monoenergetic incident particles was reduced using polyethylene (PET) blocks with different thicknesses (Fig. 1B). All absorber thicknesses are listed in Table 1. A scintillator for controlling particle flux was positioned 5 cm behind the beam exit window with varying thicknesses of 50 lm (C, O, Si, Ne, Fe) and 3 mm (He) (Fig. 1A). The distance between beam exit and the instrument entrance window was 80 cm in air.
3. Simulation setup
We performed simulations of all combinations of ions, beam energies and absorber thicknesses listed in Table 1 using GEANT4 toolkit version 10.0.1 [16,17]. BSO and BGO densities were taken as 6.80 g cm 3 and 7.13 g cm 3 respectively [11]. The density of our absorber was set to 0.96 g cm 3 since the measured density of polyethylene in the experiment was 0.959 ± 0.003 g cm 3. For the density of the ceramic backs of the BSO tracking diode we used a simple aluminum oxide based ceramic with a density of 3.9 g cm 3. Consistency between simulations and experiment was checked using the anticoincidence detector signal with barely stopping and barely penetrating ions. Both showed a good agreement of simulations and experiment.
4. Energy calibration
Energy calibration was performed in an iterative way. In a first step we simulated the energy deposit of cosmic muons in the scintillators and assumed that quenching is negligible for these. This seems reasonable to us since electrons [18] and protons [5,19] are commonly used as references when calculating quenching parameters. Subsequently we verified that penetrating secondary protons from fragmentation inside the polyethylene absorber were in good agreement with this calibration after which they were added as additional calibration points. This procedure was repeated with penetrating helium ions without any absorber. As one can see in Fig. 2 this method leads to good calibration curves for both crystals confirming the assumption of negligible quenching for penetrating protons and helium. The silicon detectors were calibrated using the same procedure and the same datapoints.
5. Experimental results
Fig. 4 shows selected data points of simulated (left) and calibrated experimental data (right) for carbon ions in the BGO crystal. ESi and ECrystal denote the calibrated energy deposit in the first tracking detector (Si) and in the Crystal. The simulated energy deposit in the tracking detector agrees very well with the experimental values while the energy measured in the scintillators is reduced by the quenching effect when compared to the simulated values. As the ion energy approaches the Bragg peak, the measured energy is approximately 45% lower than the simulated energy deposit. We fitted the position of each peak individually using a
4, 304.5, 0, 151, 202, 224, 243, 244, 247, 253, 263, 269, 283, 289, 303,
rotated two-dimensional Gaussian function with two independent values for rSilicon and rCrystal. We compare the resulting peak positions for measurement and simulation in Fig. 5. These peak positions correspond to the measured (simulated) energy deposits in the two crystals, BGO and BSO. The measured energy deposits (in MeV/nuc) are plotted vs. simulated energy deposit in red symbols for BGO and blue for BSO. Ions having enough energy to penetrate through the crystals and trigger the anticoincidence are plotted as triangles while particles stopping in the crystals are plotted as squares. A simple approximation for the curves of stopping particles can be derived assuming Birks-like quenching [1]. In this case the light output, dL, per unit length, dx, can be described as dL dx ¼ S dEdx 1þ KB dEdx ð1Þ where S describes the efficiency for converting the energy deposited per unit length into scintillation photons, B dEdx describes the probability to create defects along the particle’s path and K is the trapping probability inside a defect compared to ‘‘normal’’ radiative rystal and carbon ions. Counts are not normalized and experimental data includes etectors. recombination. For energies well below the minimally ionizing values, the energy loss dEdx, is often approximated as [20] dE dx C AZ 2 E ; ð2Þ which allows one to determine an analytical expression for the integral: LðE;A; ZÞ ¼ Z dL ¼ Z xmax 0 dx S dEdx 1þ KB dEdx ¼ f 1 E f 2 AZ 2 log Eþ f 2 AZ 2 f 2 AZ 2 ! ! ð3Þ For ions stopping inside the scintillator [5] xmax is the range inside the crystal. f 1 ¼ S ð4Þ is a measure of the energy to light conversion efficiency for a specific ion while f 2 ¼ C KB ð5Þ describes the probability for quenching of charge carriers. Fitting Eq. (3) to the datapoints of stopping ions (squares in Fig. 5) leads to the dashed lines in Fig. 5. These lines are thus the calibration curves for BGO and BSO for the various ions indicated beneath. Although Eq. (2) is a commonly used approximation which leads to an analytically solvable equation, we found that the energy loss in the particular energy range covered in this paper is better described by (see also Fig. 3): Ion Crystal Numerical solution, added penetrating ions dE dX / E 1 dE dX / E 0:7 f1/a.u. f2/MeV f1/a.u f2/MeV He BGO 1:002 0:013 1:052 0:144 1:043 0:014 0:372 0:039 BSO 1:007 0:010 0:347 0:083 1:024 0:011 0:137 0:026 C BGO 0:868 0:023 0:902 0:103 0:995 0:031 0:185 0:018 BSO 0:912 0:016 0:555 0:054 0:996 0:017 0:113 0:008 O BGO 0:793 0:015 0:600 0:053 0:902 0:021 0:104 0:008 BSO 0:833 0:031 0:379 0:099 0:914 0:042 0:066 0:014 Ne BGO 0:699 0:010 0:337 0:022 0:774 0:009 0:053 0:002 BSO 0:761 0:018 0:225 0:026 0:841 0:019 0:041 0:003 Si BGO 0:626 0:012 0:164 0:018 0:679 0:015 0:022 0:002 BSO 0:691 0:025 0:107 0:029 0:733 0:029 0:015 0:003 Fe BGO 0:442 0:020 0:009 0:006 0:452 0:027 0:001 0:001 BSO 0:507 0:013 0:000 0:001 0:514 0:032 0:000 0:001 dE dx C AZ 2 E0:7 : ð6Þ Using this expression for dEdx in Eq. (1) leads to an integral (3) which cannot be solved analytically. Therefore, we solved (3) numerically. To check the validity of this treatment, we also numerically integrated (3) for dEdx given by Eq. (2). We then fitted the constants f 1 and f 2 to the data for the analytical and both numerical solutions. Tables 2 and 3 list the resulting fitting parameters which are also plotted in Figs. 6 and 7. Figs. 6(a) and 7(a) show the results listed in Table 2. There we compare our analytical solution (Eq. (3)) with the numerically integrated Eq. (2). The two should ideally be the same. One can see that both fits agree very well within their errorbars. This assures us that our numerical solution is accurate enough for our purposes. For this comparison we limited our dataset to stopping ions. Stopping means that the ion does not have enough energy to penetrate through the scintillating crystal and does not trigger the anticoincidence. The limitation to stopping ions has the advantage that we can set one limits of the integration (Eq. (3)) to zero. Otherwise we would need to use the calculated stopping energy as integration limit which would possibly decrease the accuracy of our result. The results in Table 3 correspond to the curves in Figs. 6(b) and 7(b). These results are obtained by using all datapoints of stopping and penetrating particles and numerically integrating Eqs. (2) and (6). In the following Section 5.1 we describe in detail how our errors were estimated and thereafter we discuss our results in Section 7.
5.1. Error estimation
The two dominant sources of uncertainties are the energy calibration and the thickness and density of the PET energy absorbers. The first error can be directly calculated from the confidence interval of our calibration. The second uncertainty was estimated by varying the absorber thickness in the simulation and comparing the values of the energy depositions in the tracking detectors. The absorber thickness, d, in our simulations was varied around the measured value of the absorber, d0, until the simulated and experimental energy deposits in the tracking detectors were equal ESi;simðdÞ ¼ ESi;expðd0Þ: ð7Þ The resulting simulated crystal energy at modified thickness ECrystal;simðdÞ was then compared to the simulated energy at measured thickness ECrystal;simðd0Þ. The difference between those two values should then be a measure for the uncertainty due to possible variations in effective material thickness. For the uppermost peak in Fig. 4 (at ECrystal;exp ¼ 500 MeV and ESi;exp ¼ 16 MeV) this leads to an error of 2%. This procedure also covers alignment errors for the absorber since a possible small tilt angle would result in a slightly thicker effective absorber. The absorber thickness error yields greater uncertainties the lower the energy of the incident particle is because the high non-linearity of the energy loss near the Bragg-peak results in large differences due to small variations in the absorber thickness. This leads to larger error bars for stopping ions with low energies. The effect can especially been seen in Fig. 5(a) where the four data points of helium with the lowest energy for both crystal types differ a lot from the calculated light yield curve and they partly lie above f ðEÞ ¼ E which is unphysical. The estimated energy error for these points is 60%, assuming 2% uncertainty for the absorber thickness. Nevertheless this error non-linearity only affects very low energy stopping particles and is included in the error bars plotted in Fig. 5.
6. Model for parameterization of BGO and BSO quenching
We developed a simple model to describe the scintillation properties of BGO and BSO for heavy ions. It predicts the values for f 1 and f 2 for different heavy ion species using a limited number of parameters. We plan to verify this model by testing BGO with other heavy ion species in the future. The model uses the following two functions f 1ðZÞ ¼minðI1;A1 expð k1 Z þ O1ÞÞ ð8Þ and f 2ðZÞ ¼ I2 expð k2 ZÞ ð9Þ to describe the dependence of f 1 and f 2 on Z. Both functions are fitted to the individual results of f 1 and f 2 as determined in the previous sections for the numerical solution with dEdx / E 0:7 (data with blue and red diamonds in Figs. 6(b) and 7(b)). The helium data was omitted for the f 2 parameter because the helium datapoints which determine the f 2 parameter have large uncertainties (see Fig. 5(a) in the low energy region below 30 MeV/nuc). The resulting parameter values for both crystal types (BGO, BSO) are listed in Table 4 and the corresponding functions are plotted in Fig. 8 as solid lines. The quality of this remarkably simple model can be seen in Fig. 9 which shows the same data as in Fig. 5 but now with the addition of dashed curves which show the quenching curves predicted by our model using the values in Table 4. In contrast, the solid lines describe the best individual fit for each ion/crystal combination of the numerically solved Eq. (1) with the approximation of Eq. (6) using all datapoints (stopping and penetrating ions). The energy-to-light curve described by our model follows those of the individual fits with almost no deviation for oxygen and heavier ions. Small deviations can be seen for carbon but the model still describes the measured data very well within the errors of the individual datapoints and might also be taken as good approximation for this ion species. For helium the larger deviations are caused by the fact that the helium data was excluded from our model for the f 2 parameter. Overall the model describes the energy-to-light conversion ratio for both BGO and BSO crystals in this particular energy range from a few MeV/nucto approximately 100 MeV/nuc very well within the errors of the experimental results.
6.1. Implications for the Birks constant, KB
Using our model for parameter f 2 from Eq. (9) and combining it with Eq. (5) leads to an expression for the Birks constant: KB ¼ f 2ðZÞ CðZÞ ð10Þ where C originates from Eq. (6) and can be estimated from Fig. 3 for BGO and in the same way for BSO which is not shown here. Fig. 10 shows the quotient of the modeling function (9) and the C Fig. 8. Fit results for the model functions (8) and (9) to the individual parameters f 1 and figure legend, the reader is referred to the web version of this article.) parameter as a function of particle Z value. This is the value for the Birks constant for different types of ions. Helium data is again excluded before fitting the exponential decay KBðZÞ ¼ A expð B ZÞ ð11Þ to the data points since the it was shown in the previous section that the model fails in describing the helium behavior. Nevertheless the calculated data points for helium are plotted and the fit results are shown in Table 5. It can be seen that all data points except the ones of helium are well described by an exponential law, the helium data points follow the same trend, but differ from their expected values when compared to the other ion species.
7. Discussion and conclusions
Scintillators are used in many applications and an accurate knowledge of their light output is required for any quantitative analysis. In principle, one would need to calibrate every detector with all expected ion species, which is unrealistic. Here we presented a model which predicts the quenching properties of BGO and BSO which has been fitted to calibration data for He, C, O, Ne, Si, and Fe. It does not predict the absolute light yield of BGO and BSO which differs by approximately a factor of 5 [11], but the relative behavior of the two scintillators and various heavy ions. It is required to pass through zero light output for vanishing incident energy, and shows an asymptotically linear behavior which is superimposed by a non-linear one at low energies for stopping ions. The light output shows the opposite behavior for penetrating ions. We investigate the non-linear nature of the light output and have ‘‘calibrated out’’ this overall factor 5 by using muons, protons, and one high-energy He data point for which a linear behavior and no quenching is expected. Thus, this factor 5 is not reflected in our f 1 parameter which describes the energy to light conversion efficiency. With the use of calibrated data we also exclude any influence of the crystal geometry to affect our analysis. Therefore the observed difference in the linear regime (f 1), between BGO and BSO is real. f 2 for BGO (red) and BSO (blue). (For interpretation of the references to color in this A key finding is that the energy loss suffered by heavy ions in this energy range is better described by E 0:7 than by the conventionally used E 1:0. Using this expression for the energy loss, we find that both crystals qualitatively show the same behavior for f 1 and f 2. For f 1 it looks like a step function with a plateau up to carbon (Z ¼ 6) which is followed by an exponential decrease towards heavier ions (Z J 14). The f 2 parameter also shows an exponential behavior for BGO as well as BSO, but requires a separate treatment of He. The decay constant k2 is very similar for the two scintillators. The f 2 parameter is mainly responsible for the curvature of the light yield in the lower energy range, so its value may also be affected by the small number of data points and by larger uncertainties in this region which is particularly true for the helium datapoints (see Section 5.1) making it hard to derive the exact shape in this region. The large uncertainties for helium might also be a reason why our model describes the performance of other ions very precisely with one set of parameters while the helium data needs to be treated separately. Other (doped) scintillators [21] may be described with a single set of parameters, including helium, using also a Birks like approach. However, this might still be a scintillator specific property of BGO and BSO. The f 1 parameter is comparable to the slope of the models used to describe the BGO behavior in other publications [8,7]. There the slope is found to be linear with logðAZ2Þ for similar ions and energies. In the particular Z-range investigated here our curve for the f 1 parameter may also be described by a linear dependence with logðAZ2Þ within the estimated errors, excluding our helium datapoints. On the other hand, our f 2 parameter is not comparable to the intercept used in those models [8]. Especially in the low-energy range the intercept implies a cut-off energy below which the light output reaches zero. Low energy data [7] shows a steady decrease without a cut-off. Our model provides such a steady decrease and light output converges to zero when particle energy is diminished. It is for this reason that we believe that our model to describes the scintillator response better than others. One can see that the fit parameters change slightly when adding additional data points from penetrating ions, but those changes can still be explained within their uncertainties. In contrast to that the choice of E 1 or E 0:7 is affects the absolute values of f 2 considerably, as can be seen in Fig. 7(b). It is noticeable that f 1 of BGO lies systematically below the one of BSO and vice versa for the f 2 parameter. This causes the linear portion of the BGO light curves (see Fig. 5) to be flatter than those of BSO. A perfect scintillator with linear energy-to-light conversion would follow the black dashed line in Fig. 5. BSO therefore, despite his lower absolute light output, is closer to the optimal linear light-to-energy relation than BGO.
8. Summary
We measured the response of BGO and BSO to He, C, O, Ne, Si and Fe ions in the energy range of several tens to hundreds MeV/nuc with a dual photodiode readout system designed for space applications and compared those measurements with GEANT4 simulations. We showed that the very simple Birks-like approach which describes quenching inside an inorganic crystal can be used as a first approximation to describe light yields of heavy ions in both scintillators. We also showed that the choice how to approximate the energy loss dEdx / E 1 or dEdx / E 0:7 has a strong impact on the calculated light yield parameters. We found that the latter choice (E 0:7) better describes our data. The two different crystal types, BGO and BSO, behaved qualitatively in a very similar way as one would expect based on their identical crystalline structure. Nevertheless the nonlinearity in their light output differs quantitatively by a few percent up to a few ten percent depending on the incident ions. We presented a simple model which predicts the quenching properties of these scintillators with remarkable accuracy for heavy ions (Z56). Future tests with additional ions species will allow us to verify and possibly refine the model.
Acknowledgments
We would thank the NIRS-HIMAC team, especially Yukio Uchihori and Hisashi Kitamura, for the opportunity to perform research with their accelerator, and their Accelerator Engineering Corporation (AEC) for smooth beam times. This work was supported by Grant 50 OT 1202 from the German Space Agency (DLR).
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