Efectos presentes en la célula Peltier

First the slow pulses library is qualitatively compared with the low energy spectrum of

241_{Am which is also used to constrain the recombination rate in the n}+ _{electrode model.}

The recombination rate is further tested with a90Sr source spectrum where, however, slow pulse and MSE features overlap. Then the bulk library and the corresponding MSE effects are tested with a228Th source spectrum. After qualitative validation of slow pulse and bulk library, the 90Sr data is compared with the MC on a quantitative level. The application to42K, 2νββ decay and39Ar follows in the next section.

241_{Am Source}

The low energy spectrum of an241Am calibration source is dominated by SSE slow pulses and can be used to tune the n+ electrode model at different depths independent of MSE effects. A given energy degradation of the 59.5 keV γ-ray and a given A/E value corre- spond to a certain distance of the interaction from the FCCD. Hence, the distribution of A/E versus E below the γ-line can be used to infer the most suitable recombination rate as defined inSec. 8.4.1.

(a) data (b) MC model 0.002

Figure 8.20 Comparison of 241Am A/E values between measurement (left) and best recombination model in the MC (black scatter plot on the right).

The measurement was performed with GD91C at LNGS using the Beta2000 collimator pointed at the 0 deg position on the n+ electrode (Fig. 6.17a). Fig. 8.20 shows the A/E versus E plot for data (left) and for data overlaid with MC according to the best fitting recombination rate (right). The model which qualitatively best describes the data has a recombination probability of 0.002 per ns in the RDR. The same plots with the other re- combination rates can be found inFig. D.4in the appendix for comparison. The choice of the best recombination rate is based on the form of the arc below the 59.5 keV peak which is created by events just above the FCCD where the n+ electrode is the most sensitive. A beta going through the whole n+ electrode is seeing the integral effect and will get the largest slow pulse contribution from this region; thus, here the model has to fit best. The region below 30 keV is affected by noise which is not included in the simulation and cannot

(a)241Am (b) 90Sr

Figure 8.21 Comparison of energy spectra between MC and data before and after an A/E cut. The data histograms are subtracted with a background spectrum for illustration. For241_{Am (left) MC and}

data are normalized to the peak counts. The A/E cut is based on 0.9 < A/E < 1.1. For 90_Sr

(right) the spectra are normalized to the energy region 650_{− 1450 keV. The A/E cut is based on} 0.98 < A/E < 1.07.

be used for comparison.

InFig. 8.21bit can be seen that for a given energy below the peak, the A/E distribution in the data is wider than in the MC. This is likely due to local variation of the n+ electrode properties14. Such effects are not modeled in the MC and can create larger variations in the slow pulse behavior at a given depth than expected. This is a point of improvement for further studies.

The energy spectrum of241Am can be seen inFig. 8.21afor data and MC, before and after an A/E cut of 0.9 < A/E < 1.1. The data histograms are subtracted with a background spectrum15. The unsuppressed data and MC spectra are normalized to the 59.5 keV peak before cut. The general shape is well described by the MC with the n+ electrode model. The strong suppression below the peak can be reproduced. Discrepancies arise below 30 keV due to noise. The slow pulse component is slightly underrepresented in the MC. However, the spectrum after cut which is less affected by noise is well reproduced until below 10 keV. A mismatch around 50 keV is likely due to Compton scattering on material that is not implemented in the MC (see Sec. D.1in the appendix for a similar phenomenon). It should be stressed that it would not be possible to reproduce the low energy 241Am spectrum without an n+ model.

90_{Sr Source}

The A/E versus E spectrum of a90Sr source is shown in Fig. 8.22. The data was taken with the same collimator on the same n+ electrode section as the 241Am measurement. The MC spectrum on the right is based on the same best recombination model as found with241Am. Only 90Y decays of the90Sr₋ 90Y decay chain are simulated which is only valid for comparison above the90Sr beta endpoint of 545.9 keV. The decays were sampled

14

These can be e.g. local impurities variations which influence the creation of recombination centers.

15

Source and background histograms are scaled with the live-time and quality cut efficiency (pile-up and baseline spread) and subtracted which can results in negative bin contents and is only performed for illustration.

8.5 Comparison with Data 153

(a) data (b) MC model 0.002

Figure 8.22 Comparison of90_{Sr A/E values between measurement (left) and best recombination model}

in the MC (right).

with Decay016. The 90Sr spectra for other recombination rates are shown inFig. D.4 in the appendix. The qualitative comparison is based on the position of the slow pulse band below the SSE band and the lowest A/E values.

The same recombination probability is found to be optimal for the high energy region of

90_{Sr as well as for the low energy region of} 241_{Am. This is remarkable given the fact that}

the features of241_{Am are created by single site interaction whereas the features of}90_{Sr are}

created by the integral effect of the beta trajectory. This is a strong indication that the n+ electrode model with the inferred recombination rate can qualitatively describe very different event topologies and can hence be extrapolated to event types which are not eas- ily accessible for data i.e.42K and 2νββ decay.

The energy spectra of data and the MC with the best recombination model are shown in Fig. 8.21b. The background is subtracted from the data histograms. The unsuppressed data and MC spectra, are normalized to the energy region of 650− 1450 keV. The full spectrum and the spectrum after an A/E cut of 0.98 < A/E < 1.07 is distinguished. The shape of the unsuppressed spectrum is well reproduced above 600 keV by the MC. At lower energies the data has additional contributions from 90Sr decays. However, the MC strongly overestimates the events at those energies. This is likely due to noise and the trigger threshold in the data since a large fraction of events has A/E values below 0.2 (see Fig. 8.22). Some of those very slow events might not pass the hardware trigger or quality cuts in the data. This is likely to be improved by adding experimental noise to the simulated pulses and processing them in the same framework as the data pulses. The strong suppression after A/E cut can be reproduced at higher energies but seems to be slightly underestimated in the MC. This will be further discussed in the quantitative comparison below.

16

The decay generation with Geant4 based on the RadioactiveDecay3.3 database includes a 1760.7 keV γ-ray with 0.0115 % emission probability. However, the latest nuclear data [138] does not include a valid emission probability. The MC with Geant4 suggest that this γ-line would be a dominant feature at this energy before and after A/E cut; however, there is no evidence in the data. Hence, the 90_{Y decays are}

228_{Th Source}

The validation of the ADL code and the bulk library is performed with a 228Th source measurement in the GD91C setup at LNGS. The A/E values of the 2614.5 keV γ-line, the DEP and the SEP are compared with simulated 208_{Tl decays in Fig. 8.23. The spectra}

are normalized to all events in the±6 keV energy range of the A/E spectrum for data and MC individually. The228Th calibration source is dominant in the peak regions so that no background subtraction is needed.

(a)208_{Tl FEP (b)} 208_{Tl SEP}

(c) 208_{Tl DEP (d)}208_{Tl DEP zoom}

Figure 8.23 A/E values for data and simulation at the208_{Tl FEP, SEP and DEP. The bottom right}

shows a zoom of the SSE band of the DEP in which the SSE and MSE components are fitted to the data.

The general shape of the simulated A/E distributions fit well with the data for all spectra. Small discrepancies can be observed on the far end of the high A/E side which may be due to the ADL artifacts around the groove or strongly decreasing statistics in the histograms. Those artifacts are irrelevant for this work since those events can be clearly separated from other event types. However, for the DEP spectrum a slightly larger high A/E tail on the SSB is visible in the MC compared to the data which can potentially introduce a bias in the p+ electrode event separation. At the low A/E side the agreement between MC and data is good which validates the bulk library to be used for estimation of the MSE components. A zoom into the DEP region is shown inFig. 8.23d. Here the A/E distribution of the data is fitted with a Gaussian for the SSE component (green) and an exponential tail for the

8.5 Comparison with Data 155

MSE component (red). The fit function is defined as in [97]17:

f (x = A/E) = n σA/E· √ 2π· e −(x−µA/E) 2 2σ2 A/E _{+ m·}e g·(x−l)_{+ d} e1t(x−l)+ 1 , (8.14)

with n and m being the strength of the Gaussian and tail term respectively and g, l, d and t being empirical parameters of the tail. The width of the Gaussian σA/E is directly used

for the smearing of A/E values in the MC; however, the simulated distributions shows a broader width than the σA/E. The difference is due to a binning artifact arising from the

A/E reconstruction in the bulk library creating an additional resolution of simulated A/E values. Certain positions inside the bulk have periodically slightly different A/E values in the order of 1 % as illustrated with a control plot in Fig. D.3 in the appendix. However, the MSE tail region is well described by the MC below A/E< 0.985 which can be taken as the tightest A/E cut value which is valid for this investigation.

Figure 8.24 Comparison of228Th energy spectra between MC and data before and after an A/E cut of 0.98 < A/E < 1.07. The data spectrum was taken with a trigger threshold of _{≈ 500 keV and is} subtracted with a background spectrum for illustration. The MC spectra consist only of208Tl and212Bi events. The full spectral range is shown on the left and a zoom on the 1620.5 keV 212Bi γ-line and the208Tl DEP is shown on the right. The unsuppressed spectra are normalized to the 2614.5 keV peak counts.

The energy spectrum before and after A/E cut of 0.98 < A/E < 1.07 is shown inFig. 8.24 for background corrected data and MC. The unsuppressed spectra are normalized to the 2614.5 keV peak. The spectral shape can be well reproduced before and after cut. The energy range of the208Tl DEP and the 1620.5 keV 212Bi γ-line is shown on the right. The small suppression of the DEP as well as the larger suppression of the γ-line can also be reproduced. This validates the bulk library for estimations of MSE.