Interaction of Particles with Matter

1. Interaction of Particleswith Matter Alfons Weber STFC & University of OxfordGraduate Lecture 2009

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 Alfons Weber

3. For which detectors is energy loss important? Alfons Weber

4. 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 Alfons Weber

5. 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? Alfons Weber

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

7. 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 Alfons Weber

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

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

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

11. 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 (polarisation in medium) Alfons Weber

12. Energy Loss Function Alfons Weber

13. Average Ionisation Energy Alfons Weber

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

15. Different Materials (1) Alfons Weber

16. Different Materials (2) Alfons Weber

17. Particle Range/Stopping Power Alfons Weber

18. Energy-loss in Tracking Chamber Who is who? Alfons Weber

19. 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 Alfons Weber

20. Straggling (2) • Simple parameterisation • Landau function • Better to use Vavilov distribution Alfons Weber

21. Straggling (3) Alfons Weber

22. 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 Alfons Weber

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

24. Electrons • Electrons are different light • Bremsstrahlung • Pair production Alfons Weber

25. More next time... Alfons Weber

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

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

28. 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 Alfons Weber

29. 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! Alfons Weber

30. 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 Alfons Weber

31. Cherenkov Radiation • Moving charge in dielectric medium • Wave front comes out at certain angle slow fast Alfons Weber

32. Cherenkov Radiation (2) • How many Cherenkov photons are detected? Alfons Weber

33. 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 Alfons Weber

34. Threshold Counter • Particle travel through radiator • Cherenkov radiation Alfons Weber

35. Differential Detectors • Will reflect light onto PMT for certain angles only  β Selection Alfons Weber

36. Ring Imaging Detectors (1) Alfons Weber

37. Ring Imaging Detectors (2) Alfons Weber

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

39. 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 Alfons Weber

40. 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 Alfons Weber

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

42. Transition Radiation Detector Alfons Weber

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

44. Atlas TRT (II) Alfons Weber

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

46. 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 Alfons Weber

47. 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! Alfons Weber

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