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Interaction of Particles with Matter

Interaction of Particles with Matter. Alfons Weber CCLRC & University of Oxford Graduate Lecture 2004. Table of Contents. Bethe-Bloch Formula Energy loss of heavy particles by Ionisation Multiple Scattering Change of particle direction in Matter Cerenkov Radiation

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Interaction of Particles with Matter

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  1. Interaction of Particleswith Matter Alfons Weber CCLRC & University of OxfordGraduate Lecture 2004

  2. 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

  3. 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

  4. 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

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

  6. 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

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

  8. 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

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

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

  11. Energy Loss Function

  12. Average Ionisation Energy

  13. Density Correction • Density Correction does depend on materialwith • x = log10(p/M) • C, δ0, x0 material dependant constants

  14. Different Materials (1)

  15. Different Materials (2)

  16. Particle Range/Stopping Power

  17. Application in Particle ID • Energy loss as measured in tracking chamber • Who is Who!

  18. 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

  19. Straggling (2) • Simple parameterisation • Landau function • Better to use Vavilov distribution

  20. Straggling (3)

  21. 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

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

  23. Electrons • Electrons are different light • Bremsstrahlung • Pair production

  24. Multiple Scattering • Particles don’t only loose energy …… they also change direction

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

  26. 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

  27. 17 2 log kL log kT 7 18 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 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!

  28. 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

  29. Cherenkov Radiation (1) • Moving charge in matter slow at rest fast

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

  31. Cherenkov Radiation (3) • How many Cherenkov photons are detected?

  32. 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

  33. Threshold Counter • Particle travel through radiator • Cherenkov radiation

  34. Differential Detectors • Will reflect light onto PMT for certain angles only  β Selecton

  35. Ring Imaging Detectors (1)

  36. Ring Imaging Detectors (2)

  37. Ring Imaging Detectors (3) • More clever geometries are possible • Two radiators  One photon detector

  38. 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

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

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

  41. Transition Radiation Detector

  42. 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

  43. Bibliography • PDG 2004 (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!

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

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