Detectors in Particle Physics Experimental particle physics requires the detection of
….. particles!
First we need to understand how particles interact with
matter because we make detectors from matter.
Divide particles into several classes: 1 “Heavy” charged particles 2 Electrons 3 Photons 4 Neutrons
Heavy Charged particles
Heavy means M > melectron
How do heavy charged particles lose energy in material? 1
Inelastic scattering from atomic electrons
2
Elastic scattering from nuclei
3
Emission of Cerenkov radiation
4
Nuclear reactions
5
Bremstralung
Largest contribution comes from inelastic collisions with atomic electrons, resulting in both excitation and ionization.
Each interaction causes a deflection and results in a scattering angle
The stopping power, or mean energy loss of moderately relativistic heavy charged particles in matter is described by the Bethe-Bloch equation:
2 2 K = 4 πN A re me c
A,Z = Atomic mass/# of material €
I = mean excitation energy z2 = charge of incident particle β= v/c of incident particle TMAX = maximum KE that can be imparted to a single
free electron in a single collision
Density effect correction to ionization energy loss
Mean Excitation Energy
Charged particles 1
Energy loss depends on number of electrons in the absorber.
2
At v ~ 0.96c all particles reach minimum in dE/dx and are termed Minimum Ionizing Particles ( MIPS)
3
Below a MIP particle dE/dx goes like 1/v2. So as nonrelativistic particle slows down it loses more and more energy.
4
Range above MIP is called relativistic rise because as v/c -> 1 and ln term rises slowly.
5
Highly relativistic particles start to lose energy much more rapidly due to radiation losses.
Outside of Bethe-Bloch range
At low momentum dE/dx goes down again
Momentum where particles start to radiate photons depends on mass.
Electrons are a special case! dE dE dE = + dx TOTAL dx COLLISIONS dx RADIATION 1
Define Criticial Energy Ec ~ 600 MeV/Z as point when dE/dx due to collisions is equal to that due to radiation.
€
2
E < Ec Energy loss dominated by excitation and ionization of electrons and material. In this regime Bethe-Bloch can be used for e+/e- as long as it is modified for small electron mass. Electrons are scattered through larger angles than heavier charged particles. This means e+/e- path length is longer than heavier particles through same material.
3
E > Ec Energy loss dominated by Bremsstrahlung radiation due to acceleration of e+/e- as it passes by nucleus. Radiation length (X0) distance over which energy of electron is reduced by a factor of e.
€
−dE E = dx X0 E = E 0e
− xx
0
Typical Radiation Lengths Z
Density (g/cm3)
X0 cm
Liquid H2
1
0.071
887
Lead
82
11.35
0.56
Carbon
6
1.5
28
Electron has lost nearly all of its energy after 7 radiation lengths. And nearly all of this energy has gone into the radiated photons. Many of these photons have E > 1 MeV and go onto to pair produce. This creates a “shower”. The transverse dimension of electromagnetic shower is called Moliere radius RM.
mec 2 4 π α RM = X 0 EC
Lets talk more about Photons
Photons come from the decay of neutral particles or directly from the interaction or from Bremsstrahlung.
Three primary energy loss mechanisms 1.
2.
3.
Photoelectric -
Photon is absorbed by an atom and an electron from one of the shells is ejected.
-
Dominates at low (< 10 keV) energies
Compton (scattering from atomic electron) -
Photon scattered from an atomic electron.
-
Scattered photon energy is degraded and goes onto interact again
Pair-production -
Kinematically impossible at lower energies.
-
Possible at energies of 2mec2 and starts to dominate at this point, resulting in a photon cascade.
Except for #2 photons don’t lose energy – they are “lost”. Photons are generally attenuated and don’t talk about dE/dx of photons in matter.
Neutrons Don’t interact electromagnetically Interact mainly by strong interactions via very short range. 1 2 3 4
Elastic scattering from nuclei (dominant) Inelastic scattering from nuclei. Nucleus may become excited and decay via γ-ray emission. (E > 1MeV) Radiative capture n + (Z,A) γ + (Z,A+1) goes like inverse of neutron velocity. High energy hadron shower ( E > 100 Mev)
Neutrons travel a long way since interactions are rare Neutron interactions are very energy dependent “ 1
HIGH ENERGY
FAST 3 EPITHERMAL 2
> 100 MeV ~ 1 MeV ~ 0.1 eV -1000 keV
THERMAL/SLOW ~ 1/40 eV 5 COLD/ULTRACOLD ~ microeV 4
