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

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% http://pdg.lbl.gov Spring, 2009 Phys 521A

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

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

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

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

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

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

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

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

Shower images ICARUS, liquid argon drift chamber (measures ionization) Play around with an online simulator from Sven Menke: http://www.mppmu.mpg.de/~menke/elss/home.shtml Spring, 2009 Phys 521A