Progress in Particle and Nuclear Physics 57 (2006) 263–265
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Review
Towards pulse shape analysis for the GERDA experiment
Kevin Kr¨oninger
∗Max-Planck-Institut f¨ur Physik (Werner-Heisenberg-Institut), Munich, Germany
Abstract
The analysis of pulse shapes in neutrinoless double beta decay experiments is crucial for the suppression of photon induced background events. The development of pulses versus time reveal multiple depositions of energy pointing at multiple scattering of photons. An approach to discriminate between such background and signal events is presented.
c 2005 Elsevier B.V. All rights reserved.
Keywords: Neutrinoless double beta decay; Low background experiments
1. Introduction
The GERDA experiment [1] aims at the observation of neutrinoless double beta decay (NDBD) in 76Ge. High purity germanium crystals, enriched to 86% in 76Ge, are used as source and detector. Considered here is Phase II where a total of 21 crystals are placed in a hexagonal pattern of 7 strings holding 3 crystals each. The proposed crystals are n-type diodes with lithographically defined segmentation. The baseline design has 6 segments in the azimuthal angleφand 3 segments in z.
To reach the required sensitivity for NDBD in GERDA, a background level of
≤10−3 counts/kg/keV/y must be achieved. This requires a careful selection of all materials in the setup. The segmentation of the detectors is used to identify multiple energy depositions through coincidences. To further suppress such events pulse shapes are studied. The main sources
∗Tel.: +49 89 32354 337; fax: +49 89 32354 528.
E-mail address:kroening@mppmu.mpg.de.
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doi:10.1016/j.ppnp.2005.11.009
264 K. Kr¨oninger / Progress in Particle and Nuclear Physics 57 (2006) 263–265
for photons are the cosmogenically produced isotopes68Ge and60Co inside the crystals and the decay products of the natural decay chains of uranium and thorium in all materials. Photons with energies in the region around or above the signal energy of 2039 keV are dangerous. Compton scattering is the dominant mechanism of energy loss and the photons are expected to scatter multiple times in the crystals. Those events are referred to as multi-site events (MSEs). The NDBD process has two electrons in the final state which are expected to deposit their energy locally, i.e. within a volume of the order of mm3. Those events are referred to as single-site events (SSEs). A discrimination between SSE and MSE therefore serves to discriminate against gamma-induced background.
2. Simulation of the signal development
In order to investigate the SSE–MSE-discrimination in GERDA, the electrical signals produced by the germanium detectors were simulated. Incident particles deposit energy within the detector volume and create electron–hole pairs. Due to the applied reverse bias voltage the charge carriers separate and drift towards the electrodes. The drift velocity is on the order of 100 ns/cm. During the drift electrons and holes induce mirror charges on the electrodes which are seen by the pre-amplifiers. Finally, amplified signals are fed into the read-out system.
The electric field inside the detector is calculated using numerical methods. The drift velocity of the charge carriers depends not only on the electric field but also on the angle between the field and the crystal axes [2]. This anisotropy effect was included in the calculations following a phenomenological approach [3].
The induced charges on the electrodes are calculated using Ramo’s Theorem assuming that the clouds of electrons and holes can be treated as point-like charges. The induced charge Q is time dependent and is given by
Qi(t)= −q·Φ(x(t)), (1)
where Qi(t)is the induced charge on electrode i , q is the charge of the point-like source,Φis the so-called weighting potential and x(t)describes the trajectory of the source. The weighting potential can be calculated by setting all space charges within the detector volume to zero and grounding all electrodes except the one under study.
3. Pulse shape analysis
For SSEs it is possible to obtain information on the position of the energy deposition. The risetime of a pulse, defined as the time from 10% to 90% of the amplitude, is correlated with the radial position. For segmented detectors, the asymmetry between the amplitudes of neighboring segments yields further information on the azimuthal angleφand the z-coordinate.
As a technically feasible analysis method, a template library approach was investigated. A library of pulse shapes, well known in energy and position, is calculated. Every data pulse is fitted to the library usingχ2as measure for the average deviation. From all library pulse shapes the one with the lowestχ2is chosen and its coordinates assigned. Spatial resolutions in r of 0.4 cm were achieved for simulated events for unsegmented detectors.
Since the superposition principle holds, pulses from MSEs can be decomposed into single-site pulses. Qualitative differences between SSEs and MSEs are therefore observable that manifest themselves in the previously definedχ2. The distributions of the minimum χ2 already show a separation power between SSEs and MSEs for unsegmented detectors. This results in a
K. Kr¨oninger / Progress in Particle and Nuclear Physics 57 (2006) 263–265 265
background reduction of 50% with a signal efficiency of 88%. An additional factor of 2 in background reduction is expected for segmented detectors.
4. Conclusion and outlook
A simulation of pulse shapes for the GERDA experiment was developed. An analysis approach that makes use of the calculated pulses shows promising results with respect to spatial resolution for SSEs and the discrimination between SSEs and MSEs. Teststands at the MPI in Munich are currently under construction in order to verify the calculations.
References
[1] S. Schonert et al., GERDA Collaboration, Nucl. Phys. Proc. Suppl. 145 (2005) 242.
[2] M.I. Nathan, Phys. Rev. 130 (1963) 2201.
[3] H.G. Reik, H. Risken, Phys. Rev. 126 (1962) 1737.
