We have designed a multi-ring detector (MRD) based on Bismuth Germanate (BGO) crystals, coupled to Silicon PhotoMultipliers (SiPM) for measuring the Ps time of flight (TOF). The set-up geometry was optimized by Monte Carlo simulations to take into account at different Ps velocities: (i) the background noise due to backscattered positrons, (ii) the crosstalk between adjacent detectors, (iii) the lifetime of Ps decay. Three parameters were defined to evaluate the different configurations and a figure of merit was obtained. This allows the choice of the best set up configuration for measuring Ps emitted with a particular energy range, optimizing the signal to noise ratio and keeping the acquisition time acceptable

G-F Dalla Betta

L Di Noto

M Benetti

R S Brusa

S Mariazzi

Undetermined

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This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 176.9.35.147This content was downloaded on 24/06/2016 at 23:49Please note that terms and conditions apply.Optimization of a multi-ring detector for Ps time of flight measurementsView the table of contents for this issue, or go to the journal homepage for more2013 J. Phys.: Conf. Ser. 443 012074(http://iopscience.iop.org/1742-6596/443/1/012074)Home Search Collections Journals About Contact us My IOPscience  Optimization of a multi-ring detector for Ps time of flight measurements  L Di Noto1,3, M Benetti2, S Mariazzi1, G-F Dalla Betta2 and R S Brusa1  1Dipartimento di Fisica,  Università di Trento and INFN, Gruppo collegato di Trento, Via Sommarive 14,  I-38123 Povo, Trento, Italy 2Dipartimento di Ingegneria e Scienza dell’Informazione, Università di Trento and INFN, Gruppo collegato di Trento, Via Sommarive 14, I-38123 Povo, Trento, Italy  E-mail: di.noto@science.unitn.it  Abstract. We have designed a multi-ring detector (MRD) based on Bismuth Germanate  (BGO) crystals, coupled to Silicon PhotoMultipliers (SiPM) for measuring the Ps time of flight (TOF). The set-up geometry was optimized by Monte Carlo simulations to take into account at different Ps velocities: (i) the background noise due to backscattered positrons, (ii) the cross-talk between adjacent detectors, (iii) the lifetime of Ps decay. Three parameters were defined to evaluate the different configurations and a figure of merit was obtained. This allows the choice of the best set up configuration for measuring Ps emitted with a particular energy range, optimizing the signal to noise ratio and  keeping the acquisition time acceptable.  1. Introduction A TOF apparatus to investigate Ps cooling by measuring the energy distribution of Ps emitted from porous materials was developed in Trento [1] and it is being set up at the NEutron induced POsitron Source MUnich (NEPOMUC) [2]. The system was realized to work with continuous e+ beams. The secondary electrons ejected by the e+ entering the sample are used as start signal as recorded by two channeltrons. The stop signal is given by the Ps annihilation  rays observed by detectors placed at a known distance z from the sample surface. In order to improve the efficiency of this apparatus we designed a 4-ring detector where each ring is separated from another ring by tungsten shields. A multi-ring detector MRD allows the acquisition of simultaneously TOF spectra at different distances. Since the MRD requires small size detectors, BGO crystals, with 4x4x10 mm3 dimensions, coupled with SiPMs were considered [3].  2. Monte Carlo Simulations and results  To take into account the increasing of the noise caused by background signal from the backscattered positrons and by false counts of Ps that don't annihilate in front of the ring (cross-talk effect between adjacent detectors), many Monte Carlo simulations have been carried for different configurations obtained varying the thickness (𝑡 ÷1-9 mm) of the shield among the detector’s rings together with the                                                           3  To whom any correspondence should be addressed. 16th International Conference on Positron Annihilation (ICPA-16) IOP PublishingJournal of Physics: Conference Series 443 (2013) 012074 doi:10.1088/1742-6596/443/1/012074Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd 1  distance (d÷20-90 mm) between the detectors and the chamber axis (see figure 1). Each ring covers an angle of 180° in the xy plane and the slit dimension was chosen to be ∆=4 mm to fit with the BGO- SiPMs dimensions. The distance h between the target and the middle of the first ring was fixed to 1 cm, while D=10 mm was the radius of the chamber [3]. To extract a figure of merit, three parameters  𝑀1𝑗  , 𝑀2𝑗 ,  𝑀3𝑗   were defined for each ring j, and studied at different velocities v of the emitted Ps:  𝑀1𝑗  is the fraction of Ps detected by each ring j and  𝑀1 =  𝑀1𝑗4𝑗=1 ;     𝑀2𝑗  takes into account the rate of the noise events due to the background  rays coming from e+ annihilation on the chamber walls and detected in each ring j;   𝑀3𝑗  takes into account the rate of the false events due to the cross-talk recorded in each ring j.   Figure 1. Geometry of the set up used in the Monte Carlo simulations  By considering Ps annihilating in flight along the z axis (stars in figure 1), the 𝑀1𝑗  parameters can be calculated as the product of the solid angle  𝛼𝑗 (𝑑) = 𝜋∆𝑑+𝐷  and the probability that Ps decays in front of each detector j. Defining the lower z-coordinate of each ring 𝑠𝑖 = ℎ +𝛥2+ 𝑖  𝑡 + 𝛥  with i=0,..,3, we obtain  𝑀1  𝑡,𝑑, 𝑣 =  𝑀1𝑗  (𝑡,𝑑, 𝑣)3𝑖=0 =  𝛼𝑗  3𝑖=0  𝑒−𝑠𝑖𝑣𝜏 − 𝑒−𝑠𝑖+𝛥𝑣𝜏  , with 𝜏 = 142 𝑛𝑠  the oPs lifetime. The parameter 𝑀1 as a function of v (figure 2) increases at low v until it reaches a maximum, then it decreases. Given the MRD geometry, this behavior is due to the balance of two factors: on one side 𝑀1 decreases if v increases because the time spent by Ps in front of the slits decreases; on the other side, as v increases, Ps annihilations are also recorded by the more distant rings. In fact only when the TOF required for Ps to reach the higher ring is comparable with 𝜏, the counting rate of the higher scintillator becomes significant. In figure 3 𝑀1 as a function of t and d is reported, where 𝑀1 is bigger for smaller shield dimensions. The obscured zone below the resolution line corresponds to geometries that are not usable because the  annihilations are directly seen by two different rings. The importance of 𝑀1𝑗  is the fact that it can be related to the measurement time. Considering that in a TOF measurement with a continuous e+ beam 106 e+/s maximum can be used to avoid false start-stop coincidence events [3] and that at least 105 events must be collected for each spectrum, we can estimate the acquisition time as 𝑇𝑗 = 10−1  𝑀1𝑗 ∙  𝛽  [𝑠] where 𝛽(𝑣) is the fraction of the implanted e+ emitted as Ps with the desired energy [1,4].  To estimate the background noise, the distributed e+ annihilations on the chamber walls were simulated with four  beam sources [5] in front of each detector (numbered crosses in figure 1). For each shield configuration, the deposited energies 𝐸𝑖  from each source i (i=0-4) in the ring j was evaluated considering the beam sources i pointing towards the ring j, in order to calculate: 16th International Conference on Positron Annihilation (ICPA-16) IOP PublishingJournal of Physics: Conference Series 443 (2013) 012074 doi:10.1088/1742-6596/443/1/0120742    𝑀2𝑗 = 𝐸𝑖3𝑖≠𝑗 ,𝑖=0𝐸  where 𝐸  is the deposited energy from the source placed in front of the ring j.      Figure 2. M1 calculated with d=20 mm and t=8 mm and t=1 mm as a function of the Ps velocity   Figure 3. M1 as a function of t and d calculated for Ps velocity of  𝑣 = 6 ∙ 104 m/s  Similarly, the noise due to cross-talk was simulated with   beam sources placed on the chamber axis z (numbered stars in figure 1) and pointing towards the considered ring j: 𝑀3𝑗 = 𝐸𝑖𝑐3𝑖≠𝑗 ,𝑖=0𝐸 , where 𝐸𝑖𝑐  are the deposited energies in the ring j for each source i. 𝑀2𝑗  and 𝑀3𝑗  express the two effects that increase the noise of a MRD with respect to a single detector. In order to sum the two effects their relative weights have to be determined. Because the Ps emission yield depends on the sample properties and the Ps energy, while the intensity of the backscattered e+ is connected to the e+ beam, to the sample surface and to the set up characteristics, we can look at an experimental TOF spectrum (figure 3) carried out at Trento by using a single ring detector placed at h= 1 cm (figure 3). From this plot, for each Ps velocity we can extract a signal to background ratio 𝛿  𝑣  in order to obtain a new parameter  𝑀𝑗 = 𝑀3𝑗 + 𝑀2𝑗  𝛿  𝑣   for each ring j. Thus 𝑀𝑗  takes into account both the background and the cross-talk noise.   Figure 4. TOF measurement of escaping Ps in continuous line, background in dot.  The vertical bars show the velocities considered as examples for calculations.  Because 𝑀𝑗  and 𝑇𝑗 ∝ 1 𝑀1𝑗  depend on v, also the choice of the best geometry depends on the v value that is going to be measured. As examples, we have considered four most significant values of v (corresponding to values indicated by vertical lines in figure 4): 1)  𝑣 = 2 ∙ 105  m/s where the background dominates over the Ps signal, 2) 𝑣 = 1 ∙ 105 m/s where 𝑀1  reaches its maximum 3) 𝑣 = 6 ∙ 104 m/s where the background and signal are comparable, 4) 𝑣 = 4 ∙ 104 m/s where the background is lower than the signal. From geometric considerations it can be observed that the ring called 1 or 2 in figure 1 are more exposed to the background and cross-talk noise. For this reason, in order to size the MRD, we have considered only the second ring, where the worst conditions in term of signal to noise ratio occur. Thus the MRD geometry must be chosen looking at the signal to noise ratio 16th International Conference on Positron Annihilation (ICPA-16) IOP PublishingJournal of Physics: Conference Series 443 (2013) 012074 doi:10.1088/1742-6596/443/1/0120743  𝑀12/𝑀2, the measuring time 𝑇2 =10−1𝑀12 ∙ 𝛽[𝑠], and the spatial resolution ∆𝑧 =𝛥𝑑 𝑑2+ 𝐷  (see figure 1) which is related to the  resolution on the kinetic energy value E extracted by a TOF measurement by the relation: ∆𝐸𝐸=2∆𝑧𝑧.      Figure 5. Colours express the value of the ratio  𝑀12/𝑀2 , in log scale, as a function of t and d, for four different Ps velocities (the same indicated with bars in figure 3). The limitations imposed by the resolution (in the bottom) are shown. The resolution ∆𝑧  on the Ps annihilation position is marked by red vertical lines and the measurement time is indicated by black lines. The squares indicate the best configuration set up as explained in the text.  The behavior of 𝑀12/𝑀2 with the time 𝑇2 and the ∆𝑧 values (expressed in the continuous black and red lines respectively) is shown in figure 5 for the selected four Ps velocities. To calculate 𝑇2 the parameter 𝛽 was estimated by multiplying the yield (25%) of emitted Ps as reported in [4] to the fraction (0.08, 0.06, 0.02, 0.016) calculated considering the Ps signal in figure 4. From figure 5 we can observe that the signal to noise ratio 𝑀12/𝑀2  increases going towards the zone in which the shield dimensions increase, because the effect of the decreasing of noise (i.e of 𝑀2) is more relevant with respect to the decrease of 𝑀12. Thus, by imposing a limitation on the energy resolution and on the measurement time (if necessary), and optimizing the signal to noise ratio, for each velocity the best configuration can be chosen. For instance, for larger velocity, for which Ps is emitted more abundant and the measurement time is always less than 3 hours, the best set up is with higher values of t and d (see figure 5.a,b). On the contrary, when the measurement time increases, the best configuration can be chosen by imposing for instance T<3 h and  ∆𝑧 <2.7 mm as indicated in figure 5c. Finally, when Ps with low velocity is of interest, the measurement time increases and configurations with smaller shield are necessary (figure 5 d). 3. References [1] Di Noto L, Mariazzi S, Bettonte M, Nebbia G and Brusa R S 2012 Eur. Phys. J. D 66 118  [2] Hugenschmidt C 2010 Physics with many positrons ed R S Brusa, A Dupasquier and A P Mills  Jr (Amsterdam: IOS; Bologna: SIF)  p 399 [3] Mazzuca E, Benetti M, Mariazzi S, Brusa R S, Dalla Betta G-F and Piemonte C 2012 J. Instr 7 P05006  [4] Mariazzi S, Bettotti P and Brusa R S 2010 Phys. Rev. Lett. 104 243401 [5] Gentit F-X 2002 Nucl. Instr. Meth. Phys. Res. A 486 35 16th International Conference on Positron Annihilation (ICPA-16) IOP PublishingJournal of Physics: Conference Series 443 (2013) 012074 doi:10.1088/1742-6596/443/1/0120744

Optimization of a multi-ring detector for Ps time of flight measurements

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Optimization of a multi-ring detector for Ps time of flight measurements

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