Particle and Radiation Detectors: Advances & Applications Lectures: Hans-Jürgen Wollersheim e-mail: h.j.wollersheim@gsi.de

Particle Interaction with Matter Aurora Borealis Ionization

Particle Interaction with Matter Characteristic glow from a reactor Cherenkov Light Cherenkov radiation is an effect similar to sonic booms when the plane exceeds the velocity of sound

Particle Interaction with Matter Bremsstrahlung or ‘braking radiation’ Spectrum of the X-rays emitted by an X-ray tube with a rhodium target, operated at 60 kV. The continuous curve is due to bremsstrahlung, and the spikes are characteristic K lines for rhodium. Bremsstrahlung

First Detectors – photographic plates First X-ray image by Wilhelm Conrad Roentgen (1895) Henri Bequerel’s first “picture” of Uranium (1896) 𝛾−𝑟𝑎𝑦𝑠 𝛽−𝑟𝑎𝑦𝑠

The Physics of Particle Detectors What is a particle? What is a detector? How to detect a particle? The theoretical answer: “a particle is an irreducible representation of the inhomogeneous Lorentz group” (E. Wiegner) That means: →𝑆𝑝𝑖𝑛 0, 1 2 , 1, 3 2 & 𝑚𝑎𝑠𝑠>0

What is a Particle? Strong force Electromagnetic force Weak force

Physics of Particle Detection Every effect of particles or radiation can be used as working principle for a particle detector. Claus Grupen Precise knowledge of the processes leading to signals in particle detectors is necessary. The detectors are nowadays working close to the limits of theoretically achievable measurement accuracy – even in large systems. Werner Riegler

How do we see Particles? light bulb → accelerator A light bulb shines on a hand and the different reflections make the fine structure visible. With a magnifying glass or microscope more details can be seen, but there is a fundamental limit: The wavelength of the light (1/1000 mm) determines the size of the resolvable objects. available wavelength 𝐸= ℎ𝑐 𝜆 → electromagnetic waves LW 3000 m MW 300 m KW 30 m UKW 3 m GPS 0.3 m Infrared 10-6 m light 5·10-7 m 2 eV UV 10-7 m 10 eV X-ray 10-10 m 104 eV γ-ray 10-12 m 106 eV light bulb → accelerator magnifying glass or microscope → detector

Energy, Wavelength and Resolution Small objects (smaller than λ) do not disturb the wave → small object is not visible Large objects disturb the wave → large object is visible Louis de Broglie wavelength versus resolution all particles have wave properties: 𝜆= ℎ 𝑝 = ℎ𝑐 𝐸 𝑘𝑖𝑛 ∙ 𝐸 𝑘𝑖𝑛 +2 𝑚 0 𝑐 2 de Broglie wavelength 10-1m 10-9m 10-10m 10-14m 10-15m h·c = 1239.84 [MeV fm]

Detection and Identification of Particles Detection = particle counting (is there a particle?) Identification = measurement of mass and charge of the particle (most elementary particle have 𝑍𝑒=±1) How: - charged particles are deflected by B fields such that: 𝜌= 𝑝 𝑍𝑒𝐵 ∝ 𝑝 𝑍 = 𝛾 𝑚 0 𝛽𝑐 𝑍 𝑝=𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑚 0 =𝑟𝑒𝑠𝑡 𝑚𝑎𝑠𝑠 𝛽𝑐=𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 - particle velocity measured with time-of-flight (ToF) method ToF for known distance Ionization − 𝑑𝐸 𝑑𝑥 =𝑓 𝛽 Cherenkov radiation Transition radiation 𝛽∝ 1 ∆𝑡

Detection and Identification of Particles Detection = particle counting (is there a particle?) Identification = measurement of mass and charge of the particle (most elementary particle have 𝑍𝑒=±1) How: - kinetic energy determined via a calorimetric measurement 𝛾= 1 1+ 𝛽 2 𝐸 𝑘𝑖𝑛 = 𝛾−1 𝑚 0 𝑐 2 - for Z=1 the mass is extracted from 𝐸 𝑘𝑖𝑛 and 𝑝 - to determine Z (particle charge) a Z-sensitive variable is e.g. the ionization energy loss 𝑑𝐸 𝑑𝑥 ∝ 𝑧 2 𝛽 2 𝑙𝑛 𝑎∙ 𝛽 2 𝛾 2 a = material-dependent constant

Interaction of Particles and γ-Radiation with Matter Different type of interactions with charged and neutral particles Difference “scale” of processes for electromagnetic and strong interactions Detection of charged particles (Ionization, Bremsstrahlung, Cherenkov …) Detection of γ-rays (Photo / Compton effect, pair production) Detection of neutrons (strong interaction) Detection of neutrinos (weak interaction)

Energy loss – dE/dx Particles interact differently with matter. Important for detectors is the energy loss per path length. The total energy loss per path length is the sum of all contributions. − 𝑑𝐸 𝑑𝑥 𝑡𝑜𝑡 =− 𝑑𝐸 𝑑𝑥 𝑐𝑜𝑙𝑙 − 𝑑𝐸 𝑑𝑥 𝑟𝑎𝑑 − 𝑑𝐸 𝑑𝑥 𝑝ℎ𝑜𝑡𝑜𝑒𝑓𝑓 − 𝑑𝐸 𝑑𝑥 𝑐𝑜𝑚𝑝𝑡𝑜𝑛 − 𝑑𝐸 𝑑𝑥 𝑝𝑎𝑖𝑟 − 𝑑𝐸 𝑑𝑥 ℎ𝑎𝑑𝑟𝑜𝑛 ⋯ Depending on the particle type, the particle energy and the material some processes dominate, other do not occur. For instance only charged particles will interact with electrons of atoms and produce ionization, etc.

Tentative outline of detector lecture Charged particle interaction in matter relevant formulas Bethe-Bloch formula interaction of β-particles in matter Bremsstrahlung Synchrotron radiation Interaction of gamma-rays in matter photoelectric effect Compton scattering e+e- pair production Semiconductor detectors bond model for semiconductors doping: n- and p-type silicon Silicon surface barrier detector micro-strip detector Germanium detector Scintillation detectors organic and inorganic scintillators Liouville’s theorem photomultiplier tube neutron detector Gas detectors ionization detectors ionization chamber proportional counter multi-wire proportional chamber time projection chamber Geiger-Müller counter Electronics signal processing constant fraction discriminator coincidences Segmented detectors Doppler effect Euroball, Miniball, AGATA Neutral particles neutrons neutrino Imaging

Literature Recommended Textbook Recommended Textbook

Some Nuclear Units Nuclear energies are very high compared to atomic processes, and need larger units. The most commonly used unit is the MeV. 1 electron Volt = 1 eV = 1.6·10-19 Joules 1 MeV = 106 eV; 1 GeV = 109 eV; 1 TeV = 1012 eV However, the nuclear size are quite small and need smaller units: Atomic sizes are on the order of 0.1 nm = 1 Angstrom = 10-10 m. Nuclear sizes are on the order of femtometers which in the nuclear context are usually called fermis: 1 fermi = 1 fm = 10-15 m Atomic masses are measured in terms of atomic mass units with the carbon-12 atom defined as having a mass of exactly 12 amu. It is also common practice to quote the rest mass energy E=m0c2 as if it were the mass. The conversion to amu is: 1 u = 1.66054·10-27 kg = 931.494 MeV/c2 electron mass = 0.511 MeV/c2; proton mass = 938.27 MeV/c2; neutron mass = 939.56 MeV/c2 Mass data: nucleardata.nuclear.lu.se/database/masses/

Some Nuclear Units

Relevant Formulae 𝐸= 𝑇 𝑙𝑎𝑏 + 𝑚 0 ∙ 𝑐 2 𝑚∙ 𝑐 2 = 𝑇 𝑙𝑎𝑏 + 𝑚 0 ∙ 𝑐 2 The relevant formulae are calculated if A1, Z1 and A2, Z2 are the mass number (amu) and charge number of the projectile and target nucleus, respectively, and Tlab is the laboratory energy (MeV) 𝐸= 𝑇 𝑙𝑎𝑏 + 𝑚 0 ∙ 𝑐 2 𝑚∙ 𝑐 2 = 𝑇 𝑙𝑎𝑏 + 𝑚 0 ∙ 𝑐 2 𝑚 0 ∙ 𝑐 2 1− 𝛽 2 = 𝑇 𝑙𝑎𝑏 + 𝑚 0 ∙ 𝑐 2 𝛽= 𝑇 𝑙𝑎𝑏 2 +1863∙ 𝐴 1 ∙ 𝑇 𝑙𝑎𝑏 931.5∙ 𝐴 1 + 𝑇 𝑙𝑎𝑏 beam velocity: Lorentz contraction factor: 𝛾= 1− 𝛽 2 −1 2 𝛾= 931.5∙ 𝐴 1 + 𝑇 𝑙𝑎𝑏 931.5∙ 𝐴 1 𝛽∙𝛾= 𝑇 𝑙𝑎𝑏 2 +1863∙ 𝐴 1 ∙ 𝑇 𝑙𝑎𝑏 931.5∙ 𝐴 1

Quality of Measurements: Resolution 𝑧 ∆𝑧 Resolution is generally defined as 1 standard deviation 1𝜎 for a Gaussian distribution, or full width half maximum (𝐹𝑊𝐻𝑀=∆𝑧). 𝜎 𝑧 = 𝐹𝑊𝐻𝑀 2.355 𝜎 𝑧 𝑧 = 𝑁 𝑁 = 1 𝑁 If the measurement is dominated by Poissonian fluctuations: Fano factor F: fluctuations on N are reduced by correlation in the production of consecutive e-hole pairs. For Germanium detectors 𝐹~0.1 𝜎 𝑧 𝑧 = 𝐹 𝑁

Statistical Error: Peak on top of Background The area above the background represents the total counts between the vertical lines P minus the trapezoidal area B (red hatched). If the total counts are (P+B) and the end-points of the horizontal line are B1 and B2 (width of B1 + B2 = width of B), then the net area is given by: 𝑷= 𝑷+𝑩 −𝑩 The standard deviation of ΔP is given by: 𝜟𝑷= 𝑷+𝟐∙𝑩

Solid angle d 1 Ci = 3.7·1010 Bq Ω 4𝜋 ≅ 𝜋 𝑟 2 4𝜋 𝑑 2 = 𝑟 2𝑑 2 Ω 4𝜋 ≅ 𝜋 𝑟 2 4𝜋 𝑑 2 = 𝑟 2𝑑 2 Ω = solid angle between source and detector (sr) For a point source: d (cm) r = 3cm Ω 4𝜋 % 5 7.13 55 10 2.11 2.25 15 0.97 1 Ω 4𝜋 = 1 2 ∙ 1− 𝑑 𝑑 2 + 𝑟 2

α-particles, heavy ions Radiation protection 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑑𝑜𝑠𝑒= 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 𝑚𝑎𝑠𝑠 1 𝐽𝑜𝑢𝑙𝑒 𝑘𝑔 =1 𝐺𝑟𝑎𝑦 (𝐺𝑦) The biological dose, sometimes also known as the dose equivalent is expressed in units of Sieverts [Sv]. This dose reflects the fact that the biological damage caused by a particle depends not only on the total energy deposited but also on the rate of energy loss per unit distance traversed by the particle. equivalent dose = energy dose · quality factor Q radiation quality factor Q X-ray, γ, β 1 thermal neutrons 2.3 fast neutrons 10 α-particles, heavy ions 20

Radiation protection range in air [m] radioactive source concrete Pb Al α´s β´s X-rays γ-rays neutrons Ω= 𝑎 2 4𝜋∙ 𝑅 2 = 𝜋∙ 𝑟 2 4𝜋∙ 𝑅 2

Luminosity 𝐿= 𝑁 𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑙𝑒𝑠 ∙ 𝑁 𝑡𝑎𝑟𝑔𝑒𝑡 𝑛𝑢𝑐𝑙𝑒𝑖 accelerator current: 1 nA What is the number of projectiles? 1 particle / s ≡ 1.6·10-19 C/s 6.25·109 particles / s ≡ 1 nA 28Si target thickness: 1 mg/cm2 How many target nuclei? 28 g/cm2 Silicon ≡ 6.02·1023 atoms/cm2 1 mg/cm2 Silicon ≡ 2.15·1019 atoms/cm2 Luminosity = 6.25·109 · 2.15·1019 = 1.34·1029 [s-1 cm-2] event rate [s-1] = luminosity [s-1 cm-2] · cross section [cm2] = 1.34∙1029 [s-1 cm2] ∙ cross section [~ mb = 10-27 cm2] ≈ 102 [s-1]