1. Particle and Radiation Detectors: Advances & Applications
Lectures: Hans-Jürgen Wollersheim

2. Particle Interaction with Matter
Aurora Borealis
Ionization

3. 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

4. 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

5. 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

6. 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, & 𝑚𝑎𝑠𝑠>0

7. What is a Particle?
Strong force
Electromagnetic force
Weak force

8. 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

9. 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

10. 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 = [MeV fm]

11. 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

12. 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= 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

13. 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)

14. 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.

15. 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

16. Literature
Recommended Textbook
Recommended Textbook

17. 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 = m. Nuclear sizes are on the order of femtometers which in the nuclear context are usually called fermis:
1 fermi = 1 fm = 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 = ·10-27 kg = MeV/c2
electron mass = MeV/c2; proton mass = MeV/c2; neutron mass = MeV/c2
Mass data: nucleardata.nuclear.lu.se/database/masses/

18. Some Nuclear Units

19. 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 − 𝛽 2 = 𝑇 𝑙𝑎𝑏 + 𝑚 0 ∙ 𝑐 2
𝛽= 𝑇 𝑙𝑎𝑏 ∙ 𝐴 1 ∙ 𝑇 𝑙𝑎𝑏 ∙ 𝐴 1 + 𝑇 𝑙𝑎𝑏
beam velocity:
Lorentz contraction factor:
𝛾= 1− 𝛽 2 −1 2
𝛾= 931.5∙ 𝐴 1 + 𝑇 𝑙𝑎𝑏 ∙ 𝐴 1
𝛽∙𝛾= 𝑇 𝑙𝑎𝑏 ∙ 𝐴 1 ∙ 𝑇 𝑙𝑎𝑏 ∙ 𝐴 1

20. Quality of Measurements: Resolution𝑧 ∆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

21. 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

22. 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

23. 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

24. 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

25. Luminosity 𝐿= 𝑁 𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑙𝑒𝑠 ∙ 𝑁 𝑡𝑎𝑟𝑔𝑒𝑡 𝑛𝑢𝑐𝑙𝑒𝑖
accelerator current: 1 nA What is the number of projectiles?
1 particle / s ≡ ·10-19 C/s
6.25·109 particles / s ≡ 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 = cm2] ≈ 102 [s-1]