Interaction of Particles with Matter Alfons Weber CCLRC

Interaction of Particles with Matter Alfons Weber CCLRC & University of Oxford Graduate Lecture 2004

Nov 2004 2 Table of Contents n Bethe-Bloch Formula n n Multiple Scattering n n Change of particle direction in Matter Cerenkov Radiation n n Energy loss of heavy particles by Ionisation Light emitted by particles travelling in dielectric materials Transition radiation n Light emitted on traversing matter boundary

Nov 2004 3 Bethe-Bloch Formula n n Describes how heavy particles (m>>me) loose energy when travelling through material Exact theoretical treatment difficult n n n Atomic excitations Screening Bulk effects Simplified derivation ala MPhys course Phenomenological description

Nov 2004 4 Bethe-Bloch (1) n Consider particle of charge ze, passing a stationary charge Ze ze r n Assume n n n b θ y x Ze Target is non-relativistic Target does not move Calculate n Energy transferred to target (separate)

Nov 2004 5 Bethe-Bloch (2) n Force on projectile n Change of momentum of target/projectile n Energy transferred

Nov 2004 6 Bethe-Bloch (3) n Consider α-particle scattering off Atom n n Mass of nucleus: Mass of electron: M=A*mp M=me n But energy transfer is n Energy transfer to single electron is

Nov 2004 7 Bethe-Bloch (4) n n Energy transfer is determined by impact parameter b Integration over all impact parameters b ze db

Nov 2004 8 Bethe-Bloch (5) n Calculate average energy loss n There must be limit for Emin and Emax n All the physics and material dependence is in the calculation of this quantities

Nov 2004 9 Bethe-Bloch (6) n n Simple approximations for n From relativistic kinematics n Inelastic collision Results in the following expression

Nov 2004 10 Bethe-Bloch (7) n This was just a simplified derivation n Incomplete Just to get an idea how it is done The (approximated) true answer is with n n ε screening correction of inner electrons δ density correction, because of polarisation in medium

Nov 2004 11 Energy Loss Function

Nov 2004 12 Average Ionisation Energy

Nov 2004 13 Density Correction n Density Correction does depend on material with n n x = log 10(p/M) C, δ 0, x 0 material dependant constants

Nov 2004 14 Different Materials (1)

Nov 2004 15 Different Materials (2)

Nov 2004 16 Particle Range/Stopping Power

Nov 2004 17 Application in Particle ID n n Energy loss as measured in tracking chamber Who is Who!

Nov 2004 18 Straggling (1) n n n So far we have only discussed the mean energy loss Actual energy loss will scatter around the mean value Difficult to calculate n n parameterization exist in GEANT and some standalone software libraries From of distribution is important as energy loss distribution is often used for calibrating the detector

Nov 2004 19 Straggling (2) n Simple parameterisation n Landau function n Better to use Vavilov distribution

Nov 2004 20 Straggling (3)

Nov 2004 21 δ-Rays n n Energy loss distribution is not Gaussian around mean. In rare cases a lot of energy is transferred to a single electron δ-Ray n n If one excludes δ-rays, the average energy loss changes Equivalent of changing Emax

Nov 2004 22 Restricted d. E/dx n Some detector only measure energy loss up to a certain upper limit Ecut n n Truncated mean measurement δ-rays leaving the detector

Nov 2004 23 Electrons n Electrons are different light n n Bremsstrahlung Pair production

Nov 2004 24 Multiple Scattering n Particles don’t only loose energy … … they also change direction

Nov 2004 25 MS Theory n Average scattering angle is roughly Gaussian for small deflection angles With n Angular distributions are given by n

Nov 2004 26 Correlations n n Multiple scattering and d. E/dx are normally treated to be independent from each Not true n n n large scatter large energy transfer small scatter small energy transfer Detailed calculation is difficult but possible n Wade Allison & John Cobb are the experts

Nov 2004 27 Correlations (W. Allison) nuclear small angle scattering (suppressed by screening) electrons at high Q 2 nuclear backward scattering in CM (suppressed by nuclear form factor) whole atoms at low Q 2 (dipole region) Log cross section (30 decades) 17 2 Log p. L orlog k. L energy transfer (16 decades) Example: Calculated cross section for 500 Me. V/c in Argon gas. Note that this is a Log-log plot - the cross section varies over 20 and more decades! electrons backwards in CM 18 7 log k. T Log p. T transfer (10 decades)

Nov 2004 28 Signals from Particles in Matter n Signals in particle detectors are mainly due to ionisation n n Direct light emission by particles travelling faster than the speed of light in a medium n n Gas chambers Silicon detectors Scintillators Cherenkov radiation Similar, but not identical n Transition radiation

Nov 2004 29 Cherenkov Radiation (1) n Moving charge in matter at rest slow fast

Nov 2004 30 Cherenkov Radiation (2) n Wave front comes out at certain angle n That’s the trivial result!

Nov 2004 31 Cherenkov Radiation (3) n How many Cherenkov photons are detected?

Nov 2004 32 Different Cherenkov Detectors n Threshold Detectors n n Differential Detectors n n Yes/No on whether the speed is β>1/n βmax > βmin Ring-Imaging Detectors n Measure β

Nov 2004 33 Threshold Counter n n Particle travel through radiator Cherenkov radiation

Nov 2004 34 Differential Detectors n Will reflect light onto PMT for certain angles only β Selecton

Nov 2004 35 Ring Imaging Detectors (1)

Nov 2004 36 Ring Imaging Detectors (2)

Nov 2004 37 Ring Imaging Detectors (3) n More clever geometries are possible n Two radiators One photon detector

Nov 2004 38 Transition Radiation n Transition radiation is produced when a relativistic particle traverses an inhomogeneous medium n n Boundary between different materials with different n. Strange effect n n What is generating the radiation? Accelerated charges

Nov 2004 39 Transition Radiation (2) n n n Initially observer sees nothing Later he seems to see two charges moving apart electrical dipole Accelerated charge is creating radiation

Nov 2004 40 Transition Radiation (3) n Consider relativistic particle traversing a boundary from material (1) to material (2) n Total energy radiated n Can be used to measure γ

Nov 2004 41 Transition Radiation Detector

Nov 2004 42 Table of Contents n Bethe-Bloch Formula n n Multiple Scattering n n Change of particle direction in Matter Cerenkov Radiation n n Energy loss of heavy particles by Ionisation Light emitted by particles travelling in dielectric materials Transition radiation n Light emitted on traversing matter boundary

Nov 2004 43 Bibliography n PDG 2004 (chapter 27 & 28) and references therein n n Lecture notes of Chris Booth, Sheffield n n http: //www. shef. ac. uk/physics/teaching/phy 311 R. Bock, Particle Detector Brief Book n n Especially Rossi http: //rkb. home. cern. ch/rkb/PH 14 pp/node 1. html Or just it!

Nov 2004 44 Plea n n I need feedback! Questions n n n n What was good? What was bad? What was missing? More detailed derivations? More detectors? More… Less… A. Weber@rl. ac. uk