1. Interactions of Particles with Matter
From Mauricio Barbi, TSI’07 lectures
Interactions of Particles with Matter
Interactions of Photons
Pair Production
 An electron-positron pair can be created when
(and only when) a photon passes by the Coulomb
field of a nucleus or atomic electron  this is
needed for conservation of momentum.
Threshold energy for pair production at
E = 2mc2 near a nucleus.
E = 4mc2 near an atomic electron
 Pair production is the dominant photon interaction process at high energies. Cross-
section from production in nuclear field is dominant.
First cross-section calculations made by Bethe and Heitler using Born approximation (1934).
 + e-  e+ + e- + e-
 + nucleus  e+ + e- + nucleus
Spring, 2009
Phys 521A

2. Interactions of Particles with Matter
From Mauricio Barbi, TSI’07 lectures
Interactions of Particles with Matter
Interactions of Photons
Pair Production
Photon pair conversion
probability (attenuation length is 9/7 X0)
Cross-section independent of photon energy (once well above threshold), ~ Z2
P=54%
Spring, 2009
Phys 521A

3. Photon absorbtion lengths
Interactions of Photons
Photon attenuation length for different elemental absorbers versus photon energy
Here λ = 9/7 X0
Spring, 2009
Phys 521A

4. Interactions of Particles with Matter
From Mauricio Barbi, TSI’07 lectures
Interactions of Particles with Matter
Summary of the basic EM interactions
e+ / e-
Ionisation
Bremsstrahlung
P.e. effect
Comp. effect
Pair production E g
dE/dx s Z
Z(Z+1) Z5
Spring, 2009
Phys 521A

5. Electromagnetic showers
Cascade of pair production and bremsstrahlung is known as an electromagnetic shower
number of low-energy photons (or electrons) produced is proportional to initial energy of electron or gamma
Energy collected in each of e± and γ is also proportional to initial energy
Spring, 2009
Phys 521A

6. Electromagnetic Shower Development
From Mauricio Barbi, TSI’07 lectures
Electromagnetic Shower Development
A simple shower model
Shower development:
Start with an electron with E0 >> Ec
 After 1X0 : 1 e- and 1  , each with E0/2
 After 2X0 : 2 e-, 1 e+ and 1  , each with E0/4 .
 After tX0 :
Maximum number of particles reached at E = Ec 
[ X0 ]
Number of particles
increases
exponentially with t
equal number of e+, e-, 
Depth at which the energy of a shower particle equals
some value E’
 Number of particles in the shower with energy > E’
Spring, 2009
Phys 521A

7. Electromagnetic showers
Radiation length X0 used to characterize longitudinal shower development
Peaks at depth of ~7 X0
Transverse shower size due to multiple Coulomb scattering; scales with Moliere radius (radius of cylinder containing 90% of shower energy) RM = X0Es/Ec where Es = me√4π/α ~ 21 MeV and Ec is the critical energy
Two dimensionless variables: t=x/X0 and y=E/Ec govern shower development
Spring, 2009
Phys 521A

8. Electromagnetic Shower Development
From Mauricio Barbi, TSI’07 lectures
Electromagnetic Shower Development
A simple shower model Cu
Longitudinal profile of an EM shower
Simulation of the energy deposit in copper as a function of the shower depth for incident electrons shows the logarithmic dependence of tmax with E.
EGS4* (electron-gamma shower simulation)
Number of particle decreases after maximum
*EGS4 is a Monte Carlo code for doing simulations of the transport of electrons and photons in arbitrary geometries.
Spring, 2009
Phys 521A

9. Electromagnetic Shower Development
From Mauricio Barbi, TSI’07 lectures
Electromagnetic Shower Development
Shower profile
From previous slide, one expects the longitudinal and transverse developments to scale with X0
EGS4 calculation
EGS4 calculation
Longitudinal development
10 GeV electron
Transverse development
10 GeV electron RM
 RM less dependent on Z than X0:
Spring, 2009
Phys 521A

10. Electromagnetic Shower Development
From Mauricio Barbi, TSI’07 lectures
Electromagnetic Shower Development
Energy deposition
The fate of a shower is to develop, reach a maximum, and then decrease in number of particles once E0 < Ec
Given that several processes compete for energy deposition at low energies, it is important to understand the fate of the particles in a shower.
 Most of energy deposition is by low energy e±’s.
60%
e± (< 4 MeV)
40%
e± (< 1 MeV)
EGS4 calculation
e± (>20 MeV)
Ionization dominates
Spring, 2009
Phys 521A

11. Shower images ICARUS, liquid argon drift chamber (measures ionization)
Play around with an online simulator from Sven Menke:
Spring, 2009
Phys 521A