Astroparticle Physics

4.8 Problems 61board of a satellite, in a balloon, or at ground level, or even inan underground laboratory. The quality of the measurementdepends on the energy and position resolution of the detector.In most cases the ionization energy loss is the relevantdetection mechanism.In gaseous detectors an average of typically 30 eV is requiredto produce an electron–ion pair. The liberated chargesare collected in an external electric field and produce anelectric signal which can be further processed. In contrast,in solid-state detectors, the average energy for the creationof an electron–hole pair is only ≈ 3 eV, resulting in an improvedenergy resolution. If, instead, excitation photons producedby the process of scintillation in a crystal detectorare recorded, e.g., by photomultipliers, energy deposits ofabout 25 eV are necessary to yield a scintillation photon ininorganic materials (like NaI(Tl)), while in organic crystals≈ 100 eV are required to create a scintillation photon. Incryogenic detectors much less energy is needed to producecharge carriers. This substantial advantage which gives riseto excellent energy resolutions is only obtained at the expenseof operating the detectors at cryogenic temperatures,mostly in the milli-Kelvin range.energy andposition resolutionsolid-state detectorsscintillatorscryogenic devices4.8 Problems1. Show that (4.1) is dimensionally correct.2. The average energy required for the production ofa) a photon in a plastic scintillator is 100 eV,b) an electron–ion pair in air is 30 eV,c) an electron–hole pair in silicon is 3.65 eV,d) a quasiparticle (break-up of a Cooper pair in a superconductor)is 1 meV.What is the relative energy resolution in these countersfor a stopping 10 keV particle assuming Poisson statistics(neglecting the Fano effect 3 )?3 For any specific value of a particle energy the fluctuationsof secondary particle production (like electron–ion pairs) aresmaller than might be expected according to a Poissonian distribution.This is a simple consequence of the fact that the totalenergy loss is constrained by the fixed energy of the incidentparticle. This leads to a standard error of σ = √ FN,whereNis the number of produced secondaries and F , the Fano factor,is smaller than 1.