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

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Nov Table of Contents Bethe-Bloch Formula 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

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

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

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

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Nov Bethe-Bloch (3) Consider α-particle scattering off Atom Mass of nucleus: M=A*m p Mass of electron:M=m e But energy transfer is Energy transfer to single electron is

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

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Nov Bethe-Bloch (5) Calculate average energy loss There must be limit for E min and E max All the physics and material dependence is in the calculation of this quantities

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

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Nov 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, because of polarisation in medium

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Nov Energy Loss Function

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Nov Average Ionisation Energy

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

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Nov Different Materials (1)

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Nov Different Materials (2)

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Nov Particle Range/Stopping Power

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

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Nov 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

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

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Nov Straggling (3)

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Nov 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 E max δ-Ray

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Nov Restricted dE/dx Some detector only measure energy loss up to a certain upper limit E cut Truncated mean measurement δ-rays leaving the detector

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Nov Electrons Electrons are different light Bremsstrahlung Pair production

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

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

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Nov 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

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Nov Correlations (W. Allison) 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 k L log k T whole atoms at low Q 2 (dipole region) electrons at high Q 2 electrons backwards in CM nuclear small angle scattering (suppressed by screening) nuclear backward scattering in CM (suppressed by nuclear form factor) Log p L or energy transfer (16 decades) Log p T transfer (10 decades) Log cross section (30 decades)

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Nov 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

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

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

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

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Nov Different Cherenkov Detectors Threshold Detectors Yes/No on whether the speed is β>1/n Differential Detectors β max > β > β min Ring-Imaging Detectors Measure β

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Nov Threshold Counter Particle travel through radiator Cherenkov radiation

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

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Nov Ring Imaging Detectors (1)

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Nov Ring Imaging Detectors (2)

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

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

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

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

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Nov Transition Radiation Detector

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Nov Table of Contents Bethe-Bloch Formula 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

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Nov Bibliography PDG 2004 (chapter 27 & 28) and references therein Especially Rossi Lecture notes of Chris Booth, Sheffield R. Bock, Particle Detector Brief Book Or just it!

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Nov Plea I need feedback! Questions What was good? What was bad? What was missing? More detailed derivations? More detectors? More… Less…

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