8.6 Application of the n + Model in Phase II
8.6.1 Application to 42 K Background
The slow pulse influence on the spectral shape of42K and the survival probability of 42K events after A/E cut in the ROI of Qββ±200 keV are determined with MC simulations.
Preliminary results of this study have been already used in the construction of the BEGe background model in Phase I [115]. The simulation of the42K A/E values and its strong potential for the rejection of surface events has been included in the pulse shape discrimi- nation for the Phase I 0νββ decay analysis [97].
21
This model was used inChap. 7to determined the FCCD with peak rations. The charge collection efficiency changes step-like from 0 in the dead layer to 1 in the active volume. This model does not predict any A/E information for surface events.
In a first scenario42K decays are sampled with Decay0 in a LAr volume 6 cm thick around the single detector GD91C. This sampling volume is sufficiently large so that no emitted beta from outside that volume can contribute to the spectrum. The n+ electrode and p+ electrode are equally exposed according to a homogeneous distribution of 42K in the detector vicinity. Another scenario is simulated where42K events are sampled directly on the detector surface describing a situation in which charged42K ions are attracted towards
and stick onto the electrical contacts. The results of the homogeneous scenario in the 6 cm thick volume are presented in the main text and the pure surface scenario is shown in the appendix for comparison (Sec. D.2).
The MC simulations are post processed with the new and the old model. Fig. 8.27bshows the energy spectra of the new n+ electrode model in red, the old model in black as well as the new model after A/E cut in green. The energy and A/E values of the simulation are convolved with the resolution determined for the setup of GD91C at LNGS. Note that the A/E resolution in Gerda might be different which can affect the qualitative statements below22.
(a) A/E versus E (b) energy spectrum
Figure 8.27 Comparison of n+models with simulated42K decays in a 6 cm wide LAr volume around the
detector. Left: A/E versus E spectrum of simulated42K decays with the new model. Right: Energy
spectrum with the new model (red), the old model (black) and the new model after A/E cut (green). The residual refers to the unsuppressed new and old model.
The new model shows a substantial increase of the event rate in the whole spectrum compared to the old model since the surface layers are now semi-active. More events are detected for the same activity of42K. This effect is especially significant above the 1524 keV peak where the energy spectrum is dominated by betas. In Qββ±200 keV, the expected
number of events increases by 35 %. The plot also illustrates the strong suppression after A/E cut which could previously not be understood in detail. The suppression will be quantified below.
The A/E versus E plot according to the new model is shown in 8.27a. Below the peak the spectrum is dominated by SSE populating the SSB being created by the Compton scattered γ-rays. Above the peak the spectrum is dominated by slow pulses which almost exclusively populate the SPB. The A/E spectrum in Qββ±200 keV is shown in Fig. 8.28 22Typically a better energy and A/E resolution is achieved for BEGe detectors in a vacuum cryostat
8.6 Application of the n+ Model in Phase II 161
separated into two plots showing the whole range and a zoom onto the SSB and SPB. The majority bulk and majority n+ events are distinguished in red and green respectively. It becomes evident that almost all events in this energy range are majority bulk events which have been shifted towards lower A/E by a small slow pulse contribution while passing through the n+ electrode. In fact the SPB is almost peak-like suggesting a single domi- nant event topology for those events. Note however, that the comparison with 90Sr and 241Am suggested that the MC code is underestimating the variety of slow pulses and that
the peak-like structure is likely to be washed out in the data.
(a) wide (b) zoom
Figure 8.28 A/E spectra of42K decays in a 6 cm wide volume around the detector in the energy range
of Qββ±200 keV as predicted by the new model (red). The events are separated into majority bulk
events (blue) and majority n+ events (green).
The same plots for the scenario of42K events on the detector surface is shown inFig. D.5 andD.6in the appendix. The energy spectrum is more dominated by the beta components and a larger fraction of events extend to higher energies23. In the A/E spectra almost no events are present in the SSB. This can be explained by less dead volume between the ori- gin of the decay and the sensitive detector volume in which Bremsstrahlung can be created that can jump the n+ electrode.
A quantitative prediction is performed as for90Sr with a low and a high A/E cut of 0.98 and 1.07, respectively. These cut values clearly separate the SSB and SPB and are illus- trated as vertical dashed lines inFig. 8.28. The dominant event type are low A/E events with a fraction of 89.0± 0.9 %. The rest of the total fraction is shared by high A/E events with 8.8± 0.3 % and SSB events with 2.2 ± 0.2 %.
The SSB event fraction of 2.2± 0.2 % is the survival fraction of 42K events close to the detector surface after A/E cut. For 42K directly on the surface the survival fraction is even lower with 0.69± 0.02 %. This was the dominant background component for the BEGe detectors in Phase I and will also be the dominant background in Phase II. This background component can be suppressed by a factor of 45 in the homogeneous scenario
23A simulation artifact can be seen at the endpoint of the spectrum where less events are present in
the new model compared to the old model. Events around the endpoint are created by betas entering the detector via the p+ electrode or the groove. The artificial energy loss for interactions around the groove in the ADL simulations shifts those events towards lower energy. However, only very few events are affected and the effect is only visible at the endpoint.
and by a factor of 145 in the pure surface scenario for GD91C.
The n+ electrode properties are influencing the suppression of 42K of each detector indi- vidually. The full construction of the slow pulse and bulk library is repeated for a selection of Phase II detectors based on the individual BEGe dimensions, impurity concentrations and FCCD values. The selection includes GD35B, GD02C and GD79C as detectors with a small, medium and large FCCD, respectively.
(a) energy (b) A/E
Figure 8.29 Comparison of42K decays in a 6 cm thick volume around selected Phase II detectors. The energy spectrum is shown left and the A/E spectrum in Qββ±200 keV is shown right. The residuals in
the energy spectra are defined with respect to the energy spectrum of GD91C.
The energy spectra are shown inFig. 8.29a. The same number of42K decays are simulated for each detector. The residual plots show the difference with respect to GD91C. The largest difference can seen above the peak. The count difference before cut in the energy range of Qββ±200 keV is shown in the third row inTab. 8.3and is up to 60 % between the
two extreme cases of GD35B and GD79C.
Table 8.3 Suppression of42
K decays in a 6 cm wide volume around selected Phase II BEGe detectors. The first two rows show the FCCD and the relative counts in Qββ±200 keV compared to GD91C. The
next three rows show the fraction of events after A/E cut separated in low A/E, SSB, and high A/E events. The last row shows the relative number of42K counts after A/E cut for the same number of
simulated decays normalized to GD91C.
detector GD35B GD91C GD02C GD79C
FCCD [mm] 0.55 0.68 0.75 0.85
relative42K counts before cut [%] 131.1 100 90.0 71.2
A/E > 1.1 [%] 6.1± 0.2 8.8± 0.3 8.4± 0.3 10.2± 0.4
0.98 < A/E < 1.07 [%] 1.7± 0.1 2.2± 0.2 2.0± 0.2 2.4± 0.2 A/E < 0.98 [%] 92.2± 0.8 89.0± 0.9 89.6± 1.0 87.4± 1.1
relative42K counts after cut [%] 101.3 100 81.8 77.6
Fig. 8.29bshows the A/E spectra in the energy range of Qββ±200 keV. The event fraction
in each region is shown inTab. 8.3for the selected BEGe detectors. With increasing FCCD, the relative fraction of events in the SPB is decreasing whereas the fraction of p+ electrode
8.6 Application of the n+ Model in Phase II 163
events is increasing. This can be explained by the additional attenuation of betas with larger FCCD whereas the number of p+ electrode events is not influenced. These fractions are, however, also dependent on the individual BEGe size and n+ electrode surface area (see Tab. B.3in the appendix).
The SSB fraction and hence the survival probability of 42K events is slightly increasing with increasing FCCD. This is explained by a similar amount of SSB events but a fewer amount of slow pulse events: The SSB events are created by Bremsstrahlung photons and low probability γ-rays which are not as much attenuated with a larger FCCD as betas which create the slow pulses. The number of surviving42K counts after attenuation in the
n+ electrode and after the A/E cut is shown in the last row ofTab. 8.3relatively compared to GD91C. The expected 42K background is decreasing with larger FCCD and can vary up to 30 % between detectors
This large difference in 42K background can be expected for the various Phase II BEGe detectors and is a combination of beta attenuation and PSD suppression. In case of a worse A/E resolution in Gerda it might be necessary to loosen the A/E cut to retain a large survival fraction for 0νββ events in the SSB. This would significantly change the conclusion. A lower A/E cut would not as well separate the SSB and SPB especially for small FCCD detectors (see Fig. 8.29b). This would strongly affect the PSD suppression which, however, cannot be reliably described by the current n+ model since the MC seems to overestimate the band gap. It might be worthwhile to consider different A/E cuts for each detector to optimize the 42K background reduction against the 0νββ survival effi- ciency for each detector individually.
The scenario of 42K decays directly on the detector surface is shown in Fig. D.7 and Tab. D.1 in the appendix. The survival fraction of 42K events decreased by roughly a factor of 3 to 4 compared to the homogeneous scenario. The difference of42K counts after cuts can differ up to 50 %.
This investigation shows that42K events can be suppressed with PSD by a factor of 45 in the 6 cm wide homogeneous scenario and by a factor of 145 in the pure surface scenario. The PSD suppression is complementary to the LAr veto (Chap. 9). Betas which create Bremsstrahlung in the LAr that jumps the n+ electrode in the homogeneous scenario will deposit energy in the LAr and can be vetoed to some degree. On the other hand, 42K decays on the surface practically cannot be vetoed since the beta enters directly the de- tector. Hence the combined PSD and LAr veto suppression for pure surface events is the suppression of PSD alone. The combined suppression of close to surface events requires the combined simulation of PSD and LAr veto and is larger than the PSD suppression alone.
So far these conclusion are drawn from detailed measurements of GD91C and extrapolated to the other detectors. However,90Sr measurements of other Phase II detectors would sig- nificantly strengthen the presented arguments and open the possibility for cut optimization based on direct measurements24.
24The in-situ optimization for individual detectors is not feasible with the low count rate around Q ββin