Interaction of Particles with Matter Alfons Weber STFC & University of Oxford Graduate Lecture 2009

Table of Contents Bethe-Bloch Formula Multiple Scattering Energy loss of heavy particles by Ionisation Multiple Scattering Change of particle direction in Matter Cerenkov Radiation Light emitted by particles travelling in dielectric materials Transition Radiation Light emitted on traversing matter boundary Dec 2009 Alfons Weber

For which detectors is energy loss important? Dec 2009 Alfons Weber

Bethe-Bloch Formula Describes how heavy particles (m>>me) loose energy when travelling through material Exact theoretical treatment difficult Atomic excitations Screening Bulk effects Simplified derivation ala MPhys course Phenomenological description Dec 2009 Alfons Weber

Bethe-Bloch (1) Consider particle of charge ze, passing a stationary charge Ze Assume Target is non-relativistic Target does not move Calculate Momentum transfer Energy transferred to target ze b y r θ x Ze X or Y? Dec 2009 Alfons Weber

Bethe-Bloch (2) Efficient target? Force on projectile Change of momentum of target/projectile Energy transferred Efficient target? Dec 2009 Alfons Weber

Bethe-Bloch (3) Consider α-particle scattering off Atom Mass of nucleus: M=A*mp Mass of electron: M=me But energy transfer is Energy transfer to single electron is Dec 2009 Alfons Weber

Bethe-Bloch (4) Energy transfer is determined by impact parameter b Integration over all impact parameters b db ze Dec 2009 Alfons Weber

Bethe-Bloch (5) Calculate average energy loss There must be limits material dependence is in the calculation of the limits Dec 2009 Alfons Weber

Bethe-Bloch (6) Simple approximations for From relativistic kinematics Inelastic collision Results in the following expression Dec 2009 Alfons Weber

Bethe-Bloch (7) This was just a simplified derivation Incomplete Just to get an idea how it is done The (approximated) true answer is with ε screening correction of inner electrons δ density correction (polarisation in medium) Dec 2009 Alfons Weber

Energy Loss Function Dec 2009 Alfons Weber

Average Ionisation Energy Dec 2009 Alfons Weber

Density Correction Density Correction does depend on material with x = log10(p/M) C, δ0, x0 material dependant constants Dec 2009 Alfons Weber

Different Materials (1) Dec 2009 Alfons Weber

Different Materials (2) Dec 2009 Alfons Weber

Particle Range/Stopping Power Dec 2009 Alfons Weber

Energy-loss in Tracking Chamber Who is who? Dec 2009 Alfons Weber

Straggling (1) So far we have only discussed the mean energy loss Actual energy loss will scatter around the mean value Difficult to calculate 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 Dec 2009 Alfons Weber

Straggling (2) Simple parameterisation Landau function Better to use Vavilov distribution Dec 2009 Alfons Weber

Straggling (3) Dec 2009 Alfons Weber

δ-Ray δ-Rays Energy loss distribution is not Gaussian around mean. In rare cases a lot of energy is transferred to a single electron If one excludes δ-rays, the average energy loss changes Equivalent of changing Emax δ-Ray Dec 2009 Alfons Weber

Restricted dE/dx Some detector only measure energy loss up to a certain upper limit Ecut Truncated mean measurement δ-rays leaving the detector Dec 2009 Alfons Weber

Electrons Electrons are different light Bremsstrahlung Pair production Dec 2009 Alfons Weber

More next time... Dec 2009 Alfons Weber

Multiple Scattering Particles don’t only loose energy … … they also change direction Dec 2009 Alfons Weber

MS Theory Average scattering angle is roughly Gaussian for small deflection angles With Angular distributions are given by Dec 2009 Alfons Weber

Correlations Multiple scattering and dE/dx are normally treated to be independent from each Not true large scatter  large energy transfer small scatter  small energy transfer Detailed calculation is difficult, but possible Wade Allison & John Cobb are the experts Dec 2009 Alfons Weber

Correlations (W. Allison) nuclear small angle scattering (suppressed by screening) nuclear backward scattering in CM (suppressed by nuclear form factor) electrons at high Q2 whole atoms at low Q2 (dipole region) Log cross section (30 decades) log kL 2 18 17 7 log kT Log pL or energy transfer (16 decades) electrons backwards in CM Example: Calculated cross section for 500MeV/c  in Argon gas. Note that this is a Log-log-log plot - the cross section varies over 20 and more decades! Log pT transfer (10 decades) Dec 2009 Alfons Weber

Signals from Particles in Matter Signals in particle detectors are mainly due to ionisation Gas chambers Silicon detectors Scintillators Direct light emission by particles travelling faster than the speed of light in a medium Cherenkov radiation Similar, but not identical Transition radiation Dec 2009 Alfons Weber

Cherenkov Radiation Moving charge in dielectric medium Wave front comes out at certain angle slow fast Dec 2009 Alfons Weber

Cherenkov Radiation (2) How many Cherenkov photons are detected? Dec 2009 Alfons Weber

Different Cherenkov Detectors Threshold Detectors Yes/No on whether the speed is β>1/n Differential Detectors βmax > β > βmin Ring-Imaging Detectors Measure β Dec 2009 Alfons Weber

Threshold Counter Particle travel through radiator Cherenkov radiation Dec 2009 Alfons Weber

Differential Detectors Will reflect light onto PMT for certain angles only  β Selection Dec 2009 Alfons Weber

Ring Imaging Detectors (1) Dec 2009 Alfons Weber

Ring Imaging Detectors (2) Dec 2009 Alfons Weber

Ring Imaging Detectors (3) More clever geometries are possible Two radiators  One photon detector Dec 2009 Alfons Weber

Transition Radiation Transition radiation is produced, when a relativistic particle traverses an inhomogeneous medium Boundary between different materials with different diffractive index n. Strange effect What is generating the radiation? Accelerated charges Dec 2009 Alfons Weber

Transition Radiation (2) Before the charge crosses the surface, apparent charge q1 with apparent transverse vel v1 After the charge crosses the surface, apparent charges q2 and q3 with apparent transverse vel v2 and v3 Dec 2009 Alfons Weber

Transition Radiation (3) Consider relativistic particle traversing a boundary from material (1) to material (2) Total energy radiated Can be used to measure γ Dec 2009 Alfons Weber

Transition Radiation Detector Dec 2009 Alfons Weber

ATLAS TRTracker ATLAS Experiment Inner Detector: pixel, silicon and straw tubes Combination of Central Tracker and TR for electron identification Dec 2009 Alfons Weber

Atlas TRT (II) Dec 2009 Alfons Weber

Electrons with radiator Electrons without radiator Atlas TRT (III) only electron produce TR in radiator e± / π separation Electrons with radiator Electrons without radiator Bod -> J/yKos TRT senses ionisation transition radiation High threshold hits Dec 2009 Alfons Weber

Table of Contents Bethe-Bloch Formula Multiple Scattering Energy loss of heavy particles by Ionisation Multiple Scattering Change of particle direction in Matter Cerenkov Radiation Light emitted by particles travelling in dielectric materials Transition radiation Light emitted on traversing matter boundary Dec 2009 Alfons Weber

Bibliography This lecture http://www-pnp.physics.ox.ac.uk/~weber/teaching PDG 2008 (chapter 27 & 28) and references therein Especially Rossi Lecture notes of Chris Booth, Sheffield http://www.shef.ac.uk/physics/teaching/phy311 R. Bock, Particle Detector Brief Book http://rkb.home.cern.ch/rkb/PH14pp/node1.html Or just it! Dec 2009 Alfons Weber

Plea I need feedback! Questions Alfons.Weber@stfc.ac.uk What was good? What was bad? What was missing? More detailed derivations? More detectors? More… Less… Alfons.Weber@stfc.ac.uk Dec 2009 Alfons Weber