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

2. 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

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. Bethe-Bloch (6) Simple approximations for
Nov 2004
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
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

11. Nov 2004
Energy Loss Function

12. Average Ionisation Energy
Nov 2004
Average Ionisation Energy

13. 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

14. Different Materials (1)
Nov 2004
Different Materials (1)

15. Different Materials (2)
Nov 2004
Different Materials (2)

16. Particle Range/Stopping Power
Nov 2004
Particle Range/Stopping Power

17. Application in Particle ID
Nov 2004
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
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

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

20. Nov 2004
Straggling (3)

21. 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

22. 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

23. Electrons Electrons are different light Bremsstrahlung
Nov 2004
Electrons
Electrons are different light
Bremsstrahlung
Pair production

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

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

26. 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

27. 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!

28. 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

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

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

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

32. 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

33. Threshold Counter Particle travel through radiator Cherenkov radiation
Nov 2004
Threshold Counter
Particle travel through radiator
Cherenkov radiation

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

35. Ring Imaging Detectors (1)
Nov 2004
Ring Imaging Detectors (1)

36. Ring Imaging Detectors (2)
Nov 2004
Ring Imaging Detectors (2)

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

38. 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

39. 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

40. 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

41. Transition Radiation Detector
Nov 2004
Transition Radiation Detector

42. 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

43. 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!

44. 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…