Características de las prácticas no capitalistas

The event topology with additional de-excitation γ-rays permits different experimental strategies. The three major approaches are illustrated in Fig. 3.11. Standard gamma spectroscopy with a HPGe detector (a) can be used to investigate a DBD sample. This approach is independent of the target isotope and the technology is well established for decades. In fact, gamma spectroscopy has been used for the only two observations of ex- cited state transitions in100Mo and150Nd. The principle is the equivalent of an off-source experiment where only the γ-rays can be detected. Information on the 0νββ or 2νββ regime is lost with the electrons remaining in the source material. Quoted half-life limits are valid for both regimes. Gamma spectroscopy is used to investigate DBD excited state transitions in102Pd and110Pd in Chap. 11of this work.

6

The physics case for excited state transitions in 2νββ decays does not create sufficient interest to construct larger dedicated experiments. The other two approaches (b) and (c) are using the target mass, detector system and infrastructure of larger scale 0νββ decay experiments. Those are often constructed with detector segmentation as e.g. in the case of Gerda and CUORE (b) or with large scale homogeneous detectors as in the case of e.g. EXO and NEXT (c). In case of (b) the segmentation can be used to tag real coincidences between detectors. This is e.g. done in CUORICINO [64] and in Gerda (Chap. 10in this work). In combination with good energy resolution this allows for larger background discrimination. For homogeneous experiments (c) the multi-site topology has to be selected with pulse shape information which adds complexity to the analysis and typically does not allow for strong background discrimination. On the other hand, the target mass and detection efficiency is typically larger in homogeneous experiments. An analysis is performed for instance with EXO-200 data [65].

Figure 3.11 Three approaches for investigating excited state transitions. (a) Gamma spectroscopy of a DBD sample with a HPGe detector. Only the de-excitation γ-rays are detected and 2νββ and 0νββ modes cannot be distinguished. (b) Utilization of the detector segmentation of a large scale DBD experiment as e.g. Gerda. The electron and gamma components are measured in separate detectors and 2νββ and 0νββ modes can be distinguished. (c) Utilization of a large single volume DBD experiment as e.g. EXO-200. The separation between electron and gamma interaction is fuzzy and has to be done via pulse shapes.

Chapter 4

Particle Detection

The detection and precise energy measurement of elementary particles is essential for DBD experiments. Equally important is an ultra low background environment avoiding various sources of natural and anthropogenic radioactivity. Such an environment can only be re- alized in underground laboratories using a natural overburden for shielding against cosmic radiation.

This chapter is organized as follows: The fundamentally different interactions of α, β and γ radiation with matter are described in Sec. 4.1. The energy deposition of the particles can be measured with different detector technologies. The relevant detector systems for this work are germanium semiconductors and liquid argon (LAr) which are introduced in Sec. 4.2 and Sec. 4.3, respectively. The different forms of radioactive background are described inSec. 4.4and the relevant underground facilities in Sec. 4.5.

4.1

Interactions with Matter

Particle interactions with matter are important to understand for radiation detection and radiation shielding. The main interaction mechanism for γ-ray, electron, positron and alpha particles is the electromagnetic force acting on these particles. A measurable signal is created by charge separation in the case of HPGe detectors or the creation of optical scintillation photons in LAr.

Gamma interactions: γ-rays interact with matter by three main processes: (1) pho- toelectric effect, (2) incoherent scattering (Compton scattering) and (3) pair production. These processes have different energy dependencies and dominate the γ-ray interaction at different energies. This is illustrated inFig. 4.1for germanium. Fig. 4.1ashows the energy dependent mass attenuation coefficient µ for the three interaction processes. Fig. 4.1b shows the attenuation length d0 for each process, which is defined as the distance after

which the γ-ray interacted with a probability p = 1₋ 1_e. This is e.g. 1 mm for 60 keV, 38 mm for 1333 keV and 51 mm for 2614 keV in germanium. The intensity loss of a γ-ray flux after a certain distance d can be calculated with the mass attenuation coefficient µ and the density of the material ρ:

I I0

= e−µ·ρ·d (4.1)

µ is mainly dependent on the atomic shell structure for low energies. The attenuation length is additionally dependent on the density of the material. Both quantities are shown

inFig. 4.2for various materials relevant in this work.

In all cases the initial γ-ray is transferring its energy to a fast electron which is then creating the measurable effect i.e. charge separation or scintillation. Thus, the γ-ray is a secondary ionizing particle. The individual interaction process are described in the following:

(a) mass attenuation versus energy (b) attenuation length versus energy Figure 4.1 Left: Energy dependent γ-ray mass attenuation in germanium for different interaction pro- cesses. Right: Attenuation length in germanium and the contribution of different interaction processes. Plots created with data from [87].

(a) mass attenuation versus energy (b) attenuation length versus energy Figure 4.2 Left: Energy dependent total mass attenuation for γ-rays in different materials. Right: Attenuation length of the same materials in standard densities (natural elemental abundance; LAr at boiling point). Plots created with data from [87].

The photoelectric effect is a process in which the entire γ-ray energy Eγ is transferred

to an electron. The process is dominating for small energies below ≈ 150 keV in germanium with an energy dependence of _{≈ E}−3.5. The dependence on the nuclear charge of different materials is _{≈ Z}4−5. The energy of the emitted electron Ee

depends on the binding energy of the original electron in the atomic shell Eshell with

Ee= Eγ−Eshell. Interactions occur predominantly with the stronger bound K and L-

shell electrons. The energy transfer creates holes at these shells which are rearranged by the emission of X-ray photons or Auger electrons. X-ray photons in germanium have energies of around Eshell= (9.9− 11.0) keV for the K-shell and 1.2 keV for the

4.1 Interactions with Matter 35

L-shell and are subsequently absorbed via the photoelectric effect with lower bound shell electrons.

The incoherent scattering is the inelastic scattering of a γ-ray on an unbound electron. If there are no free electrons in the material, the scattering is mainly occurring on the loosely bound outer shell electrons. The energy dependence is _{≈ E}−2 and Compton scattering is dominating at energies between≈ 150 keV and ≈ 8 MeV in germanium. The dependence on the nuclear charge is proportional to Z. The energy transfer and the interaction probability depend on the scattering angle between the incident and scattered photon. The energy transfer is largest for backscattering at 180 deg and approaches zero for forward scattering at 0 deg. The angular distribution for a given incident γ-ray energy is described by the Klein-Nishina formula [88] and illustrated in Fig. 4.3. This polar plot of the angular distribution illustrates the high probability of forward scattering for larger γ-ray energies. Also visible is the suppression at 90 deg scattering angles. A higher energetic γ-ray typically scatters once or multiple times until it is fully absorbed by the photoelectric effect. Thus, parts of the energy are deposited on multiple sites.

Figure 4.3 Polar plot of the angular distribution of incoherent scattering. The incident γ-ray with the indicated energy enters from the left. The distance from the plot center shows the relative number of scattered photons into a unit solid angle at polar angle Θ. From [89].

Pair production occurs in the Coulomb field of a nucleus if Eγ is larger than the rest

mass of the e+-e−-pair i.e. Epair = 1022 keV. The subsequent e+ and e− share the

remaining energy E_e+ + E_e− = E_γ− E_pair. The positron annihilates within O(1 ns)

into two γ-rays of 511 keV. Pair production becomes dominant for higher energetic γ-rays > 8 MeV in Ge. The energy dependence is _{≈ log E and the dependence on} the nuclear charge is _{≈ Z}2_{. The production of the two annihilation γ-rays creates}

two common event topologies: The singe escape peak (SEP) and the double escape peak (DEP). SEP events occur if one of the γ-rays escapes the detector volume and have an energy of Eγ− 511 keV in the energy spectrum. DEP events occur if the two

γ-rays escape the detector volume and have an energy of Eγ− 1022 keV.

A summary of the atomic charge and γ-ray energy dependence of the interaction probability can be found below. The dependencies often cannot be described analytically and are based on empirical approximations [89].

process atomic charge γ-ray energy

Photoeffect Z4−5 E−3.5

Compton scattering Z E−2

Pair production Z2 log E

Beta interactions: Different to point-like γ-ray interactions, electrons and positrons interact continuously along their trajectory. With respect to particle detection, the inter- action of direct electrons is identical to the one of γ-rays which always produce secondary electrons.

Electrons and positrons have a nearly identical energy loss via (1) ionization or (2) Brems- strahlung. Ionization occurs when the electron scatters with other electrons in the material. The scattering partners have equal mass which enables large deviations from the initial electron path and produces random trajectories. Bremsstrahlung is created by an abrupt change of momentum which predominantly occurs when the electron scatters in the strong Coulomb field of a nucleus. The emitted Bremsstrahlung γ-rays have a continuous energy spectrum reaching up to the initial electron energy. The fraction of energy loss due to Bremsstrahlung is proportional to Z and E. Therefore, Bremsstrahlung dominantly oc- curs for higher energetic electrons in large Z materials. The fraction of energy loss by Bremsstrahlung in germanium (natural isotopic abundance) and liquid argon is plotted inFig. 4.4a. A 2 MeV electron loses on average roughly 4 % of its energy due to Brems- strahlung in germanium whereas only 2 % in LAr.

(a) Bremsstrahlung fraction (b) electron range

Figure 4.4 Left: Average fraction of energy that is lost via Bremsstrahlung for electron interactions in germanium (natural isotopic abundance density) and liquid argon. Right: Range of electrons as defined with the continuous-slowing-down approximation. Plots created with data from [90].

The electron range is difficult to describe due to the randomness of the electron path. The range definition for the continuous-slowing-down approximation (CSDA) is roughly equivalent to the average path length. The CSDA range in dependence of the electron energy is plotted for germanium and liquid argon in Fig. 4.4b. The CSDA range for a 2 MeV electron is roughly 2 mm in germanium and 10 mm in LAr. Other examples are the range of a 3.5 MeV electron (e.g.42K) of up to 20 mm in LAr and 5 mm in germanium or the range of a 500 keV electron (e.g. 39Ar) with up to 2 mm in LAr and 0.5 mm in germanium. However, the typical penetration depth into a material may be considerably shorter than the average path length. The CSDA ranges can be considered as a maximal