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Drift field limitations to the energy resolution in Time Projection Chambers for 136Xe neutrino-less double beta decay search
Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Drift field limitations to the energy resolution in Time Projection Chambers for 136Xe neutrino-less double beta decay search P.N.B. Neves a,n, C.A.N. Conde a, L.M.N. Ta´vora a,b a b
Centro de Instrumentac- a~ o, Unidade 217/94, Departamento de Fı´sica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal ESTG, Instituto Polite´cnico de Leiria, Morro do Lena—Alto Vieiro, P-2411-901 Leiria, Portugal
a r t i c l e i n f o
abstract
Article history: Received 26 November 2010 Received in revised form 11 March 2011 Accepted 11 March 2011 Available online 3 April 2011
The effect of drift electric field in the degradation of the energy resolution of gaseous xenon Time Projection Chambers for the search of neutrino-less double beta decay of 136Xe is calculated with the PENELOPE code. Calculations are presented first for single electron emission with energies from 0.2 to 3 MeV and reduced electric fields in the 0.1–2 V cm 1 Torr 1 range, showing energy resolution degradations by as much as 12% (FWHM). Calculations are also presented for neutrino-less double beta decay of 136Xe assuming two decay mechanisms, the mass mechanism (MM) and the right-handed current due to the l parameter (RHCl) mechanism, for reduced drift electric fields in the 0.03–0.8 V cm 1 Torr 1 range. It is shown that the drift field degrades the energy resolution of the two electrons sum peak (2457.8 keV) by an amount that is significant even for reduced fields as low as 0.1 V cm 1 Torr 1. It is concluded that to reach the experimental target of 1% (FWHM) for the energy resolution of TPCs set-ups (like the NEXT collaboration set-up) the drift electric field should be weaker than about 0.1 V cm 1 Torr 1. & 2011 Elsevier B.V. All rights reserved.
Keywords: Neutrino-less double beta decay 136 Xe decay Time projection chamber Drift electric field effects Xenon gaseous detectors
1. Introduction Double beta decay is a very slow nuclear process that can occur in two modes: (i) with two anti-neutrino emission and (ii) with no neutrino emission. While the first mode has already been observed for a few cases, there is insufficient experimental evidence regarding the observation of the second mode [1]. The observation of the neutrino-less double beta decay mode would mean violation of the lepton number conservation and that the neutrino is a Majorana particle, i.e. the neutrinos and anti-neutrinos are identical particles. While the first mode is characterized by a continuous beta ray energy spectrum of the two electrons emitted in the decay with total energies from zero up to the Q-value of the decay, the neutrino-less decay mode is characterized by a two electrons sum spectrum with a peak at an energy almost equal to the Q-value. Both processes can be simultaneously present. Therefore, the search for neutrino-less double beta decay should be based on large size and internal counting electron detectors with very good energy resolution ( E1% or better) in an extremely low background environment. About 10 different nuclides are candidates for such a search and various research groups are carrying out experiments with different set-ups [2]. One of the most interesting candidates is
n
Corresponding author. Tel.: þ351 239410663; fax: þ351 239 829 158. E-mail address: pneves@gian.fis.uc.pt (P.N.B. Neves).
0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.03.021
136
Xe, which has the two possible decay modes
136
136
Xe-136 Baþ 2e þ 2n
Xe-136 Ba þ 2e
with a Q-value of 2457.83(37) keV [3] but neither of these modes has yet been observed. A few groups are working on experimental set-ups aimed at detecting these 136Xe processes [1], either with liquid Xe or else with high-pressure xenon gas (HPXe) Time Projection Chamber (TPC) detectors [4]. The advantages of HPXe TPC detectors over liquid phase detectors have been discussed by Nygren [5] and lie in their superior potential as far as energy resolution is concerned, one of the most important issues for neutrino-less decay studies. TPCs, as well as most other gaseous detectors, use an electric field to drift the primary electrons, produced in the gaseous medium by the ionizing beta rays, towards a region (a MWPC, a Micromegas or a secondary scintillation region) where a signal is expected to be produced with an amplitude proportional to the energy T0 of the absorbed beta ray. However, since beta rays have energies that can reach values over 2 MeV, their tracks are lengthy (up to about 30 cm in Xe at 10 atm) and so the beta rays can gain or lose a significant amount of energy, from the drift electric field, along their tracks. For example (Fig. 1) a beta ray with energy T0, starting at the z coordinate z1 and stopping at z2 will dissipate in the gas an energy of T0 ¼T0 þqE(z1–z2), where q is the modulus of the electron charge, which is less than T0 (if the
88
P.N.B. Neves et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
reduced electric drift fields considered in the calculations are in the range 0.1–2 V cm 1 Torr 1. We note that in the absence of an electric field the deposited energy is equal to the energy T0 of the initial electron. Secondly we studied this same effect on the total energy deposited by the 2 electrons emitted in a 136Xe 0n2b decay for reduced electric fields in the range 0.03–0.8 V cm 1 Torr 1 (Fig. 2). As in Ref. [11] two decay mechanisms were taken into account, the mass mechanism (MM) and the right-handed current due to the l parameter (RHCl). The angle between the two emitted electrons (y12) and their kinetic energies (T1 and T2) were extracted from the respective probability distributions. Mathematical expressions for the probability distributions are given in Ref. [11] (using units such as the mass of the electron, m0 ¼1 and the speed of light c ¼1) by
rMM ðT1 ,T2 ,cos y12 Þ ¼ c1 ðT1 þ 1Þp1 ðT2 þ1Þp2 FðT1 ,ZÞFðT2 ,ZÞdðQ T1 T2 Þð1b1 b2 cos y12 Þ
rRHC ðT1 ,T2 ,cos y12 Þ ¼ c2 ðT1 þ 1Þp1 ðT2 þ1Þp2 FðT1 ,ZÞFðT2 ,ZÞðT1 T2 Þ2 dðQ T1 T2 Þð1 þ b1 b2 cos y12 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi here the electron momenta are pi ¼ Ti ðTi þ2Þ, velocities are bi ¼Pi/(Ti þ1), and the mass difference is Q between the mother and daughter nucleus, which in this case is Q ¼2457.83(37) keV; c1 and c2 are normalization constants. The Fermi function F is given by 2
Fig. 1. Schematic representation of the track of a single electron with an initial energy T0 in a gaseous Xe medium at 10 atm under the influence of a uniform electric field E.
FðT,ZÞ ¼ c3 p2s2 epu 9Gðsþ iuÞ9 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where s ¼ 1ðaZÞ2 , u ¼ aZðT þ 1Þ=p, a ¼ 1=137:036, G is the Gamma function and c3 is a normalization constant. Z is the atomic number of the daughter nucleus, which in this case is Z¼56 (136Ba). These curves were normalized to unit area before being used to simulate 0n2b decays. 105 events were generated
beta ray moved in the opposite direction T0 would be larger than T0). This energy gain, or loss, can be large; for example for a 20 cm electron track in Xe at 10 atm under an electric field below the threshold for secondary scintillation (1 V cm 1 Torr 1) it can reach values as high as 150 keV. This effect will introduce fluctuations in the energy dissipated in the gas and so in the number of primary electrons produced [6], degrading the energy resolution. In previous works [7–9], we have carried out the study of the degradation of the energy resolution with the magnitude of the drift electric field but for electron energies up to 200 keV and found the effect to be small. However, as discussed above, for 2–3 MeV electrons it might not be so. The purpose of the present work is to study the effect of the drift electric field on the total energy deposited by the two electrons emitted in a 136Xe 0n2b decay. For that we use the PENELOPE code which simulates the electrons’ tracks in Xe, during slow-down.
2. Simulation method The PENELOPE software package [10] is a Monte Carlo algorithm based computer code used for the simulation of coupled electron–photon transport from energies of a few hundred eV up to 1 GeV, including the effect of the applied electromagnetic fields. In this type of applications the user defines the detector geometry and absorbing medium and PENELOPE routines keep track of several quantities, including the energy deposited during the absorption and energy degradation process. This work has been divided into 2 parts. Firstly we assessed the effect of the drift electric field on the energy deposited by single monoenergetic electrons with energies from 0.2 to 3 MeV, isotropically emitted in a gaseous medium of Xe at 10 atm (Fig. 1). The
Fig. 2. Schematic representation of the tracks of the two electrons emitted in a 136 Xe 0n2b decay under the influence of a uniform drift electric field E. T1 and T2 are the electrons’ initial kinetic energies and y12 is the emission angle.
P.N.B. Neves et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
and the resulting T1 and y12 values were displayed in the form of histograms (Figs. 3 and 4, respectively). These results show obvious differences between the two decay mechanisms considered (MM and RHCl) regarding both the average kinetic energy of
89
the emitted electrons and the average emission angle, which will lead to different results.
3. Results and discussion
Fig. 3. Histograms of the kinetic energy, T1, of one of the electrons emitted in a 136Xe 0n2b decay, either through mechanism MM or RHCl.
Fig. 4. Histograms of the angle between electrons emitted in a either through mechanism MM or RHCl.
136
Xe 0n2b decay,
Histograms describing the total energy deposited by 0.5 and 1 MeV single electrons under 0.4 and 0.8 V cm 1 Torr 1 reduced electric fields are shown in Fig. 5. Similarly, Fig. 6 shows the energy deposited by 2 and 3 MeV electrons under 0.6 and 1 V cm 1 Torr 1 reduced electric fields. The spread of the deposited energy peak increases with the energy of the initial electron because faster electrons have longer tracks in the gas and the energy exchanges with the field will, accordingly, increase [8]. Naturally, the effect becomes more important at higher applied electric fields. Gaussians were fitted to the histograms (Fig. 5) and then the energy resolution (FWHM), R¼2.35s/m , was calculated, using the gaussians centroid (m) and standard deviation (s). Calculations were extended to other energies and reduced electric fields, and the results are shown in Table 1. The data presented make it clear that if energy resolutions below 1% are to be achieved then, for electron energies above 1 MeV, reduced drift electric fields below or about 0.1 V cm 1 Torr 1 are required. In 136Xe 0n2b decays, electrons with energies up to 2.457 MeV are emitted Fig. 7. In the second part of the work we again used the PENELOPE code to follow the trajectories of the electrons, which are emitted in a 0n2b decay. The kinetic energies, T1 and T2, of the two electrons as well as the angle, y12 , between them were sampled from the associated probability distribution functions referred to above (Figs. 3 and 4). The histograms that show the spread in the peak of total energy deposited were fit to Gaussians, from which the energy resolution R (FWHM) was calculated. Histograms for both MM and RHCl mechanisms and reduced electric fields of 0.03 and 0.8 V cm 1 Torr 1 are plotted in Figs. 8 and 9, respectively. The full results obtained for the two decay mechanisms considered (MM and RHCl) are presented in Table 2. In a 136Xe 0n2b decay at least one of the emitted electrons has an energy greater than 1 MeV. If we compare the results from Table 2 with those of Table 1 for energies of 2 MeV, one notices that for the same reduced drift electric fields, the energy resolution is better in Table 2, which simulates the 0n2b decay. For example, for 0.8 V cm 1 Torr 1 Table 1 gives 3.93% while Table 2 gives 3.4% and 3.79%. This is due to the fact that in a 0n2b decay two electrons are emitted in different directions. In some cases it may happen that one electron is emitted downwards while the other electron is emitted upwards. In such cases one electron gains and the other one loses energy from the electric field, which
Fig. 5. Energy deposited in a gaseous Xe medium at 10 atm by 0.5 and 1 MeV single electrons under 0.4 and 0.8 V cm 1 Torr 1 reduced drift electric fields: histograms showing the spread in the total deposited energy peak due to the applied electric fields.
90
P.N.B. Neves et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
Fig. 6. Energy deposited in a gaseous Xe medium at 10 atm by 2 and 3 MeV single electrons under 0.6 and 1 V cm 1 Torr 1 reduced drift electric fields: histograms showing the spread in the total deposited energy peak due to the applied electric fields.
Table 1 Contribution of drift electric field to the degradation of the energy resolution (%) (FWHM) for different single electron energies under various reduced drift electric fields (E/p) in Xe at 10 atm. E/p (V cm 1 Torr 1)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2
Energy (MeV) 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2
3
0.26 0.51 0.77 1.02 1.30 1.54 1.79 2.04 2.29 2.55 5.09
0.32 0.63 0.92 1.27 1.56 1.88 2.21 2.56 2.83 3.22 6.38
0.36 0.70 1.07 1.43 1.78 2.14 2.48 2.96 3.24 3.56 7.19
0.40 0.79 1.18 1.58 1.96 2.34 2.75 3.18 3.49 3.95 7.56
0.42 0.82 1.28 1.66 2.11 2.50 2.96 3.37 3.76 4.28 8.50
0.45 0.87 1.32 1.80 2.19 2.69 3.11 3.63 4.09 4.47 9.01
0.47 0.91 1.40 1.88 2.32 2.72 3.21 3.75 4.14 4.64 9.21
0.48 0.95 1.42 1.90 2.41 2.87 3.30 3.82 4.32 4.81 9.58
0.49 0.96 1.46 1.95 2.44 2.90 3.42 3.93 4.47 4.98 9.84
0.58 1.17 1.72 2.35 2.85 3.41 4.00 4.63 5.24 5.74 11.50
0.61 1.24 1.89 2.46 3.09 3.72 4.33 4.90 5.63 6.18 12.34
Fig. 7. Histogram showing the total energy deposited by 0.7 MeV single electrons under a 0.7 V cm 1 Torr 1 reduced drift electric field. A Gaussian curve was fitted to the results and the energy resolution R was calculated.
Fig. 8. Histogram showing the total energy deposited by two electrons emitted in a 136Xe 0n2b decay under a 0.03 V cm 1 Torr 1 reduced drift electric field, for the two decay modes considered in this work.
in someway balances the energy transfer. Fig. 4 shows that the average angle between the two emitted electrons is different in the two decay mechanisms considered. This angle is typically wider in the MM decay mechanism, which means that a situation where the two electrons are emitted in opposite hemispheres is more likely for such decay mechanism. This explains why the energy resolution is lower in the MM decay. In the RHCl decay it is more likely for the electrons to either both gain or lose energy
from the drift electric field, which broadens the total deposited energy peak.
4. Conclusions We have shown that the drift electric field applied to Xe filled Time Projection Chambers used for the search of neutrino-less
P.N.B. Neves et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
91
avalanche multiplication limitations effects. It must be taken into consideration for both TPCs with electroluminescent (secondary scintillation) and electron avalanche (micromegas) energy readout, like the TPCs envisaged for the NEXT (Neutrino Experiment with a Xenon TPC) set-up [4]. It is concluded that to reach the experimental target of 1% (FWHM) for the energy resolution of 136 Xe TPCs set-ups, the drift electric field should be weaker than about 0.1 V cm 1 Torr 1.
Acknowledgements This work was carried out at Physics Department, University of Coimbra, Portugal, and was supported by the FEDER/QREN/POFC program through FCT (Fundac- a~ o para a Ciˆencia e Tecnologia, Portugal) Project PTDC/FIS/112272/2009. References Fig. 9. Histogram showing the total energy deposited by two electrons emitted in a 136Xe 0n2b decay under a 0.8 V cm 1 Torr 1 reduced drift electric field, for the two decay modes considered in this work.
Table 2 Contribution of the drift electric field to the degradation of the energy resolution (%) (FWHM) for the total energy deposited by the two electrons (2457.83(37) keV) emitted in a 136Xe 0n2b decay, under various reduced drift electric fields. E/p (V cm 1 Torr 1)
MM
RHCk
0.03 0.05 0.1 0.2 0.4 0.8
0.12 0.21 0.41 0.82 1.7 3.4
0.15 0.24 0.49 0.95 1.9 3.79
double beta decay of 136Xe may play an important role in limiting the experimentally achievable energy resolution, by degrading it. This effect is in addition to Fano factor limitations and to electron
[1] F.T. Avignone, Steven R. Elliott, Jonathan Engel, Reviews of Modern Physics 80 (2008) 481. [2] Serge Jullian, Cemptes Rendus Physique 6 (2005) 778. [3] M. Redshaw, E. Wingfield, J. McDaniel, E.G. Myers, Physical Review Letters 98 (2007) 053003. [4] Nadia Yahlali, M. Ball, S. Ca´rcel, J. Dı´az, A. Gil, J.J. Go´mez Cadenas, J. Martı´n-Albo, F. Monrabal, L. Serra, M. Sorel, Nuclear Instruments and Methods in Physics Research A 617 (2010) 520. [5] D. Nygren, Nuclear Instruments and Methods in Physics Research A 603 (2009) 337. [6] P.J.B.M. Rachinhas, T.H.V.T. Dias, F.P. Santos, C.A.N. Conde, A.D. Stauffer, IEEE Transactions on Nuclear Science NS-46 (1999) 1898. [7] L.M.N. Tavora, C.A.N. Conde, F.P. Santos, T.H.V.T. Dias, P.J.B.M. Rachinhas, Radiation Physics and Chemistry 71 (2004) 723. [8] L.M.N. Tavora, T.H.V.T. Dias, C.A.N. Conde, Nuclear Instruments and Methods in Physics Research A 562 (2006) 306. [9] P.N.B. Neves, L.M.N. Tavora, C.A.N. Conde, IEEE Transactions on Nuclear Science NS-53 (2006) 1371. [10] F. Salvat, J.M. Fernandez-Varea, J. Sempau, PENELOPE-2008—A Code System for Monte Carlo Simulation of Electron and Photon Transport, OECD ISBN 978-92-64-99066-1. [11] R. Arnold et al., Probing new physics models of neutrinoless double beta decay with SuperNEMO, arXiv:1005.1241v1.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Drift field limitations to the energy resolution in Time Projection Chambers for 136Xe neutrino-less double beta decay search P.N.B. Neves a,n, C.A.N. Conde a, L.M.N. Ta´vora a,b a b
Centro de Instrumentac- a~ o, Unidade 217/94, Departamento de Fı´sica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal ESTG, Instituto Polite´cnico de Leiria, Morro do Lena—Alto Vieiro, P-2411-901 Leiria, Portugal
a r t i c l e i n f o
abstract
Article history: Received 26 November 2010 Received in revised form 11 March 2011 Accepted 11 March 2011 Available online 3 April 2011
The effect of drift electric field in the degradation of the energy resolution of gaseous xenon Time Projection Chambers for the search of neutrino-less double beta decay of 136Xe is calculated with the PENELOPE code. Calculations are presented first for single electron emission with energies from 0.2 to 3 MeV and reduced electric fields in the 0.1–2 V cm 1 Torr 1 range, showing energy resolution degradations by as much as 12% (FWHM). Calculations are also presented for neutrino-less double beta decay of 136Xe assuming two decay mechanisms, the mass mechanism (MM) and the right-handed current due to the l parameter (RHCl) mechanism, for reduced drift electric fields in the 0.03–0.8 V cm 1 Torr 1 range. It is shown that the drift field degrades the energy resolution of the two electrons sum peak (2457.8 keV) by an amount that is significant even for reduced fields as low as 0.1 V cm 1 Torr 1. It is concluded that to reach the experimental target of 1% (FWHM) for the energy resolution of TPCs set-ups (like the NEXT collaboration set-up) the drift electric field should be weaker than about 0.1 V cm 1 Torr 1. & 2011 Elsevier B.V. All rights reserved.
Keywords: Neutrino-less double beta decay 136 Xe decay Time projection chamber Drift electric field effects Xenon gaseous detectors
1. Introduction Double beta decay is a very slow nuclear process that can occur in two modes: (i) with two anti-neutrino emission and (ii) with no neutrino emission. While the first mode has already been observed for a few cases, there is insufficient experimental evidence regarding the observation of the second mode [1]. The observation of the neutrino-less double beta decay mode would mean violation of the lepton number conservation and that the neutrino is a Majorana particle, i.e. the neutrinos and anti-neutrinos are identical particles. While the first mode is characterized by a continuous beta ray energy spectrum of the two electrons emitted in the decay with total energies from zero up to the Q-value of the decay, the neutrino-less decay mode is characterized by a two electrons sum spectrum with a peak at an energy almost equal to the Q-value. Both processes can be simultaneously present. Therefore, the search for neutrino-less double beta decay should be based on large size and internal counting electron detectors with very good energy resolution ( E1% or better) in an extremely low background environment. About 10 different nuclides are candidates for such a search and various research groups are carrying out experiments with different set-ups [2]. One of the most interesting candidates is
n
Corresponding author. Tel.: þ351 239410663; fax: þ351 239 829 158. E-mail address: pneves@gian.fis.uc.pt (P.N.B. Neves).
0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.03.021
136
Xe, which has the two possible decay modes
136
136
Xe-136 Baþ 2e þ 2n
Xe-136 Ba þ 2e
with a Q-value of 2457.83(37) keV [3] but neither of these modes has yet been observed. A few groups are working on experimental set-ups aimed at detecting these 136Xe processes [1], either with liquid Xe or else with high-pressure xenon gas (HPXe) Time Projection Chamber (TPC) detectors [4]. The advantages of HPXe TPC detectors over liquid phase detectors have been discussed by Nygren [5] and lie in their superior potential as far as energy resolution is concerned, one of the most important issues for neutrino-less decay studies. TPCs, as well as most other gaseous detectors, use an electric field to drift the primary electrons, produced in the gaseous medium by the ionizing beta rays, towards a region (a MWPC, a Micromegas or a secondary scintillation region) where a signal is expected to be produced with an amplitude proportional to the energy T0 of the absorbed beta ray. However, since beta rays have energies that can reach values over 2 MeV, their tracks are lengthy (up to about 30 cm in Xe at 10 atm) and so the beta rays can gain or lose a significant amount of energy, from the drift electric field, along their tracks. For example (Fig. 1) a beta ray with energy T0, starting at the z coordinate z1 and stopping at z2 will dissipate in the gas an energy of T0 ¼T0 þqE(z1–z2), where q is the modulus of the electron charge, which is less than T0 (if the
88
P.N.B. Neves et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
reduced electric drift fields considered in the calculations are in the range 0.1–2 V cm 1 Torr 1. We note that in the absence of an electric field the deposited energy is equal to the energy T0 of the initial electron. Secondly we studied this same effect on the total energy deposited by the 2 electrons emitted in a 136Xe 0n2b decay for reduced electric fields in the range 0.03–0.8 V cm 1 Torr 1 (Fig. 2). As in Ref. [11] two decay mechanisms were taken into account, the mass mechanism (MM) and the right-handed current due to the l parameter (RHCl). The angle between the two emitted electrons (y12) and their kinetic energies (T1 and T2) were extracted from the respective probability distributions. Mathematical expressions for the probability distributions are given in Ref. [11] (using units such as the mass of the electron, m0 ¼1 and the speed of light c ¼1) by
rMM ðT1 ,T2 ,cos y12 Þ ¼ c1 ðT1 þ 1Þp1 ðT2 þ1Þp2 FðT1 ,ZÞFðT2 ,ZÞdðQ T1 T2 Þð1b1 b2 cos y12 Þ
rRHC ðT1 ,T2 ,cos y12 Þ ¼ c2 ðT1 þ 1Þp1 ðT2 þ1Þp2 FðT1 ,ZÞFðT2 ,ZÞðT1 T2 Þ2 dðQ T1 T2 Þð1 þ b1 b2 cos y12 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi here the electron momenta are pi ¼ Ti ðTi þ2Þ, velocities are bi ¼Pi/(Ti þ1), and the mass difference is Q between the mother and daughter nucleus, which in this case is Q ¼2457.83(37) keV; c1 and c2 are normalization constants. The Fermi function F is given by 2
Fig. 1. Schematic representation of the track of a single electron with an initial energy T0 in a gaseous Xe medium at 10 atm under the influence of a uniform electric field E.
FðT,ZÞ ¼ c3 p2s2 epu 9Gðsþ iuÞ9 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where s ¼ 1ðaZÞ2 , u ¼ aZðT þ 1Þ=p, a ¼ 1=137:036, G is the Gamma function and c3 is a normalization constant. Z is the atomic number of the daughter nucleus, which in this case is Z¼56 (136Ba). These curves were normalized to unit area before being used to simulate 0n2b decays. 105 events were generated
beta ray moved in the opposite direction T0 would be larger than T0). This energy gain, or loss, can be large; for example for a 20 cm electron track in Xe at 10 atm under an electric field below the threshold for secondary scintillation (1 V cm 1 Torr 1) it can reach values as high as 150 keV. This effect will introduce fluctuations in the energy dissipated in the gas and so in the number of primary electrons produced [6], degrading the energy resolution. In previous works [7–9], we have carried out the study of the degradation of the energy resolution with the magnitude of the drift electric field but for electron energies up to 200 keV and found the effect to be small. However, as discussed above, for 2–3 MeV electrons it might not be so. The purpose of the present work is to study the effect of the drift electric field on the total energy deposited by the two electrons emitted in a 136Xe 0n2b decay. For that we use the PENELOPE code which simulates the electrons’ tracks in Xe, during slow-down.
2. Simulation method The PENELOPE software package [10] is a Monte Carlo algorithm based computer code used for the simulation of coupled electron–photon transport from energies of a few hundred eV up to 1 GeV, including the effect of the applied electromagnetic fields. In this type of applications the user defines the detector geometry and absorbing medium and PENELOPE routines keep track of several quantities, including the energy deposited during the absorption and energy degradation process. This work has been divided into 2 parts. Firstly we assessed the effect of the drift electric field on the energy deposited by single monoenergetic electrons with energies from 0.2 to 3 MeV, isotropically emitted in a gaseous medium of Xe at 10 atm (Fig. 1). The
Fig. 2. Schematic representation of the tracks of the two electrons emitted in a 136 Xe 0n2b decay under the influence of a uniform drift electric field E. T1 and T2 are the electrons’ initial kinetic energies and y12 is the emission angle.
P.N.B. Neves et al. / Nuclear Instruments and Methods in Physics Research A 641 (2011) 87–91
and the resulting T1 and y12 values were displayed in the form of histograms (Figs. 3 and 4, respectively). These results show obvious differences between the two decay mechanisms considered (MM and RHCl) regarding both the average kinetic energy of
89
the emitted electrons and the average emission angle, which will lead to different results.
3. Results and discussion
Fig. 3. Histograms of the kinetic energy, T1, of one of the electrons emitted in a 136Xe 0n2b decay, either through mechanism MM or RHCl.
Fig. 4. Histograms of the angle between electrons emitted in a either through mechanism MM or RHCl.
136
Xe 0n2b decay,
Histograms describing the total energy deposited by 0.5 and 1 MeV single electrons under 0.4 and 0.8 V cm 1 Torr 1 reduced electric fields are shown in Fig. 5. Similarly, Fig. 6 shows the energy deposited by 2 and 3 MeV electrons under 0.6 and 1 V cm 1 Torr 1 reduced electric fields. The spread of the deposited energy peak increases with the energy of the initial electron because faster electrons have longer tracks in the gas and the energy exchanges with the field will, accordingly, increase [8]. Naturally, the effect becomes more important at higher applied electric fields. Gaussians were fitted to the histograms (Fig. 5) and then the energy resolution (FWHM), R¼2.35s/m , was calculated, using the gaussians centroid (m) and standard deviation (s). Calculations were extended to other energies and reduced electric fields, and the results are shown in Table 1. The data presented make it clear that if energy resolutions below 1% are to be achieved then, for electron energies above 1 MeV, reduced drift electric fields below or about 0.1 V cm 1 Torr 1 are required. In 136Xe 0n2b decays, electrons with energies up to 2.457 MeV are emitted Fig. 7. In the second part of the work we again used the PENELOPE code to follow the trajectories of the electrons, which are emitted in a 0n2b decay. The kinetic energies, T1 and T2, of the two electrons as well as the angle, y12 , between them were sampled from the associated probability distribution functions referred to above (Figs. 3 and 4). The histograms that show the spread in the peak of total energy deposited were fit to Gaussians, from which the energy resolution R (FWHM) was calculated. Histograms for both MM and RHCl mechanisms and reduced electric fields of 0.03 and 0.8 V cm 1 Torr 1 are plotted in Figs. 8 and 9, respectively. The full results obtained for the two decay mechanisms considered (MM and RHCl) are presented in Table 2. In a 136Xe 0n2b decay at least one of the emitted electrons has an energy greater than 1 MeV. If we compare the results from Table 2 with those of Table 1 for energies of 2 MeV, one notices that for the same reduced drift electric fields, the energy resolution is better in Table 2, which simulates the 0n2b decay. For example, for 0.8 V cm 1 Torr 1 Table 1 gives 3.93% while Table 2 gives 3.4% and 3.79%. This is due to the fact that in a 0n2b decay two electrons are emitted in different directions. In some cases it may happen that one electron is emitted downwards while the other electron is emitted upwards. In such cases one electron gains and the other one loses energy from the electric field, which
Fig. 5. Energy deposited in a gaseous Xe medium at 10 atm by 0.5 and 1 MeV single electrons under 0.4 and 0.8 V cm 1 Torr 1 reduced drift electric fields: histograms showing the spread in the total deposited energy peak due to the applied electric fields.
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Fig. 6. Energy deposited in a gaseous Xe medium at 10 atm by 2 and 3 MeV single electrons under 0.6 and 1 V cm 1 Torr 1 reduced drift electric fields: histograms showing the spread in the total deposited energy peak due to the applied electric fields.
Table 1 Contribution of drift electric field to the degradation of the energy resolution (%) (FWHM) for different single electron energies under various reduced drift electric fields (E/p) in Xe at 10 atm. E/p (V cm 1 Torr 1)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2
Energy (MeV) 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2
3
0.26 0.51 0.77 1.02 1.30 1.54 1.79 2.04 2.29 2.55 5.09
0.32 0.63 0.92 1.27 1.56 1.88 2.21 2.56 2.83 3.22 6.38
0.36 0.70 1.07 1.43 1.78 2.14 2.48 2.96 3.24 3.56 7.19
0.40 0.79 1.18 1.58 1.96 2.34 2.75 3.18 3.49 3.95 7.56
0.42 0.82 1.28 1.66 2.11 2.50 2.96 3.37 3.76 4.28 8.50
0.45 0.87 1.32 1.80 2.19 2.69 3.11 3.63 4.09 4.47 9.01
0.47 0.91 1.40 1.88 2.32 2.72 3.21 3.75 4.14 4.64 9.21
0.48 0.95 1.42 1.90 2.41 2.87 3.30 3.82 4.32 4.81 9.58
0.49 0.96 1.46 1.95 2.44 2.90 3.42 3.93 4.47 4.98 9.84
0.58 1.17 1.72 2.35 2.85 3.41 4.00 4.63 5.24 5.74 11.50
0.61 1.24 1.89 2.46 3.09 3.72 4.33 4.90 5.63 6.18 12.34
Fig. 7. Histogram showing the total energy deposited by 0.7 MeV single electrons under a 0.7 V cm 1 Torr 1 reduced drift electric field. A Gaussian curve was fitted to the results and the energy resolution R was calculated.
Fig. 8. Histogram showing the total energy deposited by two electrons emitted in a 136Xe 0n2b decay under a 0.03 V cm 1 Torr 1 reduced drift electric field, for the two decay modes considered in this work.
in someway balances the energy transfer. Fig. 4 shows that the average angle between the two emitted electrons is different in the two decay mechanisms considered. This angle is typically wider in the MM decay mechanism, which means that a situation where the two electrons are emitted in opposite hemispheres is more likely for such decay mechanism. This explains why the energy resolution is lower in the MM decay. In the RHCl decay it is more likely for the electrons to either both gain or lose energy
from the drift electric field, which broadens the total deposited energy peak.
4. Conclusions We have shown that the drift electric field applied to Xe filled Time Projection Chambers used for the search of neutrino-less
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avalanche multiplication limitations effects. It must be taken into consideration for both TPCs with electroluminescent (secondary scintillation) and electron avalanche (micromegas) energy readout, like the TPCs envisaged for the NEXT (Neutrino Experiment with a Xenon TPC) set-up [4]. It is concluded that to reach the experimental target of 1% (FWHM) for the energy resolution of 136 Xe TPCs set-ups, the drift electric field should be weaker than about 0.1 V cm 1 Torr 1.
Acknowledgements This work was carried out at Physics Department, University of Coimbra, Portugal, and was supported by the FEDER/QREN/POFC program through FCT (Fundac- a~ o para a Ciˆencia e Tecnologia, Portugal) Project PTDC/FIS/112272/2009. References Fig. 9. Histogram showing the total energy deposited by two electrons emitted in a 136Xe 0n2b decay under a 0.8 V cm 1 Torr 1 reduced drift electric field, for the two decay modes considered in this work.
Table 2 Contribution of the drift electric field to the degradation of the energy resolution (%) (FWHM) for the total energy deposited by the two electrons (2457.83(37) keV) emitted in a 136Xe 0n2b decay, under various reduced drift electric fields. E/p (V cm 1 Torr 1)
MM
RHCk
0.03 0.05 0.1 0.2 0.4 0.8
0.12 0.21 0.41 0.82 1.7 3.4
0.15 0.24 0.49 0.95 1.9 3.79
double beta decay of 136Xe may play an important role in limiting the experimentally achievable energy resolution, by degrading it. This effect is in addition to Fano factor limitations and to electron
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