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**Interaction of Particles with Matter**

Alfons Weber CCLRC & University of Oxford Graduate Lecture 2004

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**Table of Contents Bethe-Bloch Formula Multiple Scattering**

Nov 2004 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 2004 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

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Nov 2004 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 b y r θ x Ze

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**Bethe-Bloch (2) Force on projectile**

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

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**Bethe-Bloch (3) Consider α-particle scattering off Atom**

Nov 2004 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

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**Bethe-Bloch (4) Energy transfer is determined by impact parameter b**

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

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**Bethe-Bloch (5) Calculate average energy loss**

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

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**Bethe-Bloch (6) Simple approximations for**

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

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**Bethe-Bloch (7) This was just a simplified derivation**

Nov 2004 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 2004 Energy Loss Function

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**Average Ionisation Energy**

Nov 2004 Average Ionisation Energy

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**Density Correction Density Correction does depend on material with**

Nov 2004 Density Correction Density Correction does depend on material with x = log10(p/M) C, δ0, x0 material dependant constants

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**Different Materials (1)**

Nov 2004 Different Materials (1)

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**Different Materials (2)**

Nov 2004 Different Materials (2)

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**Particle Range/Stopping Power**

Nov 2004 Particle Range/Stopping Power

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**Application in Particle ID**

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

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**Straggling (1) So far we have only discussed the mean energy loss**

Nov 2004 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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**Straggling (2) Simple parameterisation Landau function**

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

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Nov 2004 Straggling (3)

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**δ-Ray δ-Rays Energy loss distribution is not Gaussian around mean.**

Nov 2004 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

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

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**Electrons Electrons are different light Bremsstrahlung**

Nov 2004 Electrons Electrons are different light Bremsstrahlung Pair production

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

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

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Nov 2004 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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**Correlations (W. Allison)**

Nov 2004 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 Log pT transfer (10 decades) 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!

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**Signals from Particles in Matter**

Nov 2004 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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**Cherenkov Radiation (1)**

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

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**Cherenkov Radiation (2)**

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

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**Cherenkov Radiation (3)**

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

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**Different Cherenkov Detectors**

Nov 2004 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

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**Threshold Counter Particle travel through radiator Cherenkov radiation**

Nov 2004 Threshold Counter Particle travel through radiator Cherenkov radiation

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**Differential Detectors**

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

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**Ring Imaging Detectors (1)**

Nov 2004 Ring Imaging Detectors (1)

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**Ring Imaging Detectors (2)**

Nov 2004 Ring Imaging Detectors (2)

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**Ring Imaging Detectors (3)**

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

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Nov 2004 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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**Transition Radiation (2)**

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

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**Transition Radiation (3)**

Nov 2004 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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**Transition Radiation Detector**

Nov 2004 Transition Radiation Detector

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**Table of Contents Bethe-Bloch Formula Multiple Scattering**

Nov 2004 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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**Bibliography PDG 2004 (chapter 27 & 28) and references therein**

Nov 2004 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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**Plea I need feedback! Questions A.Weber@rl.ac.uk What was good?**

Nov 2004 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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