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1.3 Interaction of Radiation with Matter 1 By Archana SHARMA CERN Geneva Switzerland March 2009 Troisieme Cycle EPFL Lausanne, Switzerland Gaseous Particle Detectors:

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1.3 Interaction of Radiation with Matter Chapter I 5 th March Introduction 1.2 Units and Definitions, Radiation Sources 1.3 Interaction of Radiation with Matter Chapter II 12 th March General Characteristics of gas detectors, Electronics for HEP detectors 2.2: Transport Properties 2.3: Wire-based Detectors Tool

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Interaction with atomic electrons. Particle loses energy; atoms are excited or ionized. Interaction with atomic nucleus. Particle undergoes multiple scattering. Could emit a bremsstrahlung photon. If particles velocity is greater than the speed of light in the medium -> Cherenkov Radiation. When crossing the boundary between media, ~1% probability of producing a Transition Radiation X-ray. Electromagnetic Interaction of Particles with Matter

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Material with atomic mass A and density ρ contains n atoms Probability, p of incoming particle hitting an atom A volume with surface S and thickness dx contains N=nSdx atoms Probablity that a particle hits exactly one atom between x and (x + dx) Mean free path Average collisions/cm S dx Cross-section

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Differential cross-section is the cross-section from an incoming particle of energy E to lose an energy between E and E Total cross-section Probability (P(E)) that a particle of energy, E, loses between E and E + dE in a collision Average number of collisions/cm causing an energy loss between E and E+dE Average energy loss per cm Differential Cross-section

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Linear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss. Particle Data Group Stopping Power of muons in Copper Bethe-Bloch Formula Energy loss through ionization and atomic excitation Stopping Power

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Linear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss. Particle Data Group Stopping Power of muons in Copper Bethe-Bloch Formula Energy loss through ionization and atomic excitation Stopping Power

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1.3 Interaction of Radiation with Matter 8 Bethe-Bloch Formula Describes how heavy particles (m>>m e ) lose energy when travelling through a material Exact theoretical treatment difficult Atomic excitations Screening Bulk effects Phenomenological description Describes how heavy particles (m>>m e ) lose energy when travelling through a material Exact theoretical treatment difficult Atomic excitations Screening Bulk effects Phenomenological description

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Particle Data Group Bethe-Bloch Formula m – electronic mass v – velocity of the particle (v/c = ) N – number density of atoms I – Effective atomic excitation energy – average value found empirically Gas is represented as a dielectric medium through which the particle propagates And probability of energy transfer is calculated at different energies – Allison Cobb

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1.3 Interaction of Radiation with Matter ze Ze b r θ x y A very rough Bethe-Bloch Formula 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 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

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11 Projectile force Change of momentum of target/projectile Energy transferred Bethe-Bloch Formula

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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 Bethe-Bloch Formula

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1.3 Interaction of Radiation with Matter 13 Energy transfer is determined by impact parameter b Integration over all impact parameters b db ze Bethe-Bloch Formula

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1.3 Interaction of Radiation with Matter Dec 2008Alfons Weber 14 There must be limits Dependence on the material is in the calculation of the limits of the impact parameters Bethe-Bloch Formul a Calculate average energy loss

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1.3 Interaction of Radiation with Matter 15 Simple approximations for –From relativistic kinematics –Inelastic collision Results in the following expression Bethe-Bloch Formula

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1.3 Interaction of Radiation with Matter 16 This was a very 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) Bethe-Bloch Formula

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1.3 Interaction of Radiation with Matter 17 Energy Loss Function Minimum ionizing particles (mips) Relativistic Rise Fermi Plateau Rel To mips

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1.3 Interaction of Radiation with Matter 18 Different Materials

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1.3 Interaction of Radiation with Matter 19 Different Materials (2)

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20 Average Ionisation Energy Few eV to few tens of eV

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1.3 Interaction of Radiation with Matter 21 Density Correction depends on material with –x = log 10 (p/M) –C, δ 0, x 0 material dependant constants Density Correction

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1.3 Interaction of Radiation with Matter 22 Particle Range/Stopping Power

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1.3 Interaction of Radiation with Matter 23 Energy-loss in Tracking Chambers The Bethe Bloch Formula tool for Particle Identification

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1.3 Interaction of Radiation with Matter 24 Mean energy loss Actual energy loss will scatter around the mean value Difficult to calculate –parameterization exist in GEANT and some standalone software libraries –Form of distribution is important as energy loss distribution is often used for calibrating the detector Straggling

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1.3 Interaction of Radiation with Matter 25 Energy Loss Is a statistical process Simple parameterisation –Landau function Straggling

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1.3 Interaction of Radiation with Matter Dec 2008Alfons Weber 26 Straggling

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1.3 Interaction of Radiation with Matter 27 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-rays

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1.3 Interaction of Radiation with Matter 28 Some detectors only measure energy loss up to a certain upper limit E cut –Truncated mean measurement –δ-rays leaving the detector Restricted dE/dx

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1.3 Interaction of Radiation with Matter 29 Electrons are different light –Bremsstrahlung –Pair production Electrons

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1.3 Interaction of Radiation with Matter 30 Multiple Scattering Particles not only lose energy … but also they also change direction

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1.3 Interaction of Radiation with Matter 31 Average scattering angle is roughly Gaussian for small deflection angles With Angular distributions are given by Multiple Scattering

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1.3 Interaction of Radiation with Matter 32 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 – Allison & Cobb Correlation bet dE/dx and MS

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Integrate the Bethe-Bloch formula to obtain the range Useful for low energy hadrons and muons with momenta below a few hundred GeV Radiative Effects important at higher momenta. Additional effects at lower momenta. Range

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Electrons: bremsstrahlung Photons: pair production p p n n p p n nn p p n p n e e γ e e Characteristic amount of matter traversed for these interactions is the radiation length (X 0 ) p p n n p p n nn p p n p n e e e e γ Presence of nucleus required for the conservation of energy and momentum Photon and Electron Interactions

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also Energy Loss in Lead Radiation Length Mean distance over which an electron loses all but 1/e of its energy through bremsstralung 7/9 of the mean free path for electron- positron pair production by a high energy photon

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A charged particle of mass M and charge q=Z1e is deflected by a nucleus of charge Ze (charge partially shielded by electrons) The deflection accelerates the charge and therefore it radiates bremsstrahlung Partial screening of nucleus by electrons Energy Loss by electrons Elastic scattering of a nucleus is described by

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Energy loss through bremsstrahlung is proportional to the electron energy Ionization loss is proportional to the logarithm of the electron energy Critical energy (E c ) is the energy at which the two loss rates are equal Electron in Copper: E c = 20 MeV Muon in Copper: E c = 400 GeV! Electron in Copper: E c = 20 MeV Muon in Copper: E c = 400 GeV! Electron Critical Energy

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1.Atomic photoelectric effect 2.Rayleigh scattering 3.Compton scattering of an electron 4.Pair production (nuclear field) 5.Pair production (electron field) 6.Photonuclear interaction 1.Atomic photoelectric effect 2.Rayleigh scattering 3.Compton scattering of an electron 4.Pair production (nuclear field) 5.Pair production (electron field) 6.Photonuclear interaction Light element: Carbon Heavy element: Lead At low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant. Energy Loss by electrons Contributing Processes Energy Loss by electrons Contributing Processes photo electric cross section Strong dependence of Z At high energies ~ Z 5 photo electric cross section Strong dependence of Z At high energies ~ Z 5

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Probability that a photon interaction will result in a pair production Differential Cross- section Total Cross-section Photon Pair Production What is the minimum energy for pair production?

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A high-energy electron or photon incident on a thick absorber initiates an electromagnetic cascade through bremsstrahlung and pair production Longitudinal Shower Profile Longitudinal development scales with the radiation length Electrons eventually fall beneath critical energy and then lose further energy through dissipation and ionization Measure distance in radiation lengths and energy in units of critical energy Electromagnetic cascades

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Visualization of cascades developing in the CMS electromagnetic and hadronic calorimeters Electromagnetic cascades

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For muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV. Ionization energy loss Pair production, bremsstrahlung and photonuclear Mean range Muon Energy Loss

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Muon critical energy for some elements Critical energy defined as the energy at which radiative and ionization energy losses are equal. Muon Energy Loss

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Luis Alvarez used the attenuation of muons to look for chambers in the Second Giza Pyramid He proved that there are no chambers present Luis Alvarez used the attenuation of muons to look for chambers in the Second Giza Pyramid He proved that there are no chambers present Muon Tomography

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X-Ray Radiography for airport security

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1.3 Interaction of Radiation with Matter 46 Signals in particle detectors are mainly due to ionisation And excitation in a sensitive medium – gas Also: Direct light emission by particles travelling faster than the speed of light in a medium –Cherenkov radiation Similar, but not identical –Transition radiation Signals from Particles in a Gas Detector

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1.3 Interaction of Radiation with Matter 47 Moving charge in dielectric medium Wave front comes out at certain angle slowfast Cerenkov Radiation

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1.3 Interaction of Radiation with Matter 48 How many Cherenkov photons are detected? Cerenkov Radiation (2)

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1.3 Interaction of Radiation with Matter Dec 2008Alfons Weber 49 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 Transition Radiation

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50 Before the charge crosses the surface, apparent charge q 1 with apparent transverse vel v 1 After the charge crosses the surface, apparent charges q 2 and q 3 with apparent transverse vel v 2 and v 3 Transition Radiation (2)

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1.3 Interaction of Radiation with Matter 51 Consider relativistic particle traversing a boundary from material (1) to material (2) Total energy radiated Can be used to measure Transition Radiation (3)

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From Interactions to Detectors

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1.3 Interaction of Radiation with Matter

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Multiwire Proportional Chamber

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1.3 Interaction of Radiation with Matter Multiwire Proportional Chamber and derivatives Multiwire Proportional Chamber and derivatives

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1.3 Interaction of Radiation with Matter Key Points: Lecture 1-3 Energy loss by heavy particles Multiple scattering through small angles Photon and Electron interactions in matter Radiation Length Energy loss by electrons Critical Energy Energy loss by photons Bremsstrahlung and pair production Electromagnetic cascade Muon energy loss at high energy Cherenkov and Transition Radiation Key Points: Lecture 1-3 Energy loss by heavy particles Multiple scattering through small angles Photon and Electron interactions in matter Radiation Length Energy loss by electrons Critical Energy Energy loss by photons Bremsstrahlung and pair production Electromagnetic cascade Muon energy loss at high energy Cherenkov and Transition Radiation

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1.3 Interaction of Radiation with Matter Exercise: Lecture 1-3 Estimate the range of 1 MeV alphas in Aluminium Mylar Argon Indicate major interaction processes in: 1 MeV in Al 10 MeV in Argon 100 keV in Iron 1 MeV in Al Exercise: Lecture 1-3 E stimate the range of 1 MeV alphas in A luminium M ylar A rgon I ndicate major interaction processes in: 1 MeV in Al 1 0 MeV in Argon 1 00 keV in Iron 1 MeV in Al

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