1. Interaction of Particles with Matter
Alfons Weber
STFC & University of Oxford Graduate Lecture 2009

2. Table of Contents Bethe-Bloch Formula Multiple Scattering
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
Dec 2009
Alfons Weber

3. For which detectors is
energy loss important?
Dec 2009
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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
Dec 2009
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?
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6. Bethe-Bloch (2) Efficient target? Force on projectile
Change of momentum of target/projectile
Energy transferred
Efficient target?
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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
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8. Bethe-Bloch (4) Energy transfer is determined by impact parameter b
Integration over all impact parameters b db ze
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9. Bethe-Bloch (5) Calculate average energy loss There must be limits
material dependence is in the calculation of the limits
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10. Bethe-Bloch (6) Simple approximations for
From relativistic kinematics
Inelastic collision
Results in the following expression
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11. 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 (polarisation in medium)
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12. Energy Loss Function
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13. Average Ionisation Energy
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14. Density Correction Density Correction does depend on material with
x = log10(p/M)
C, δ0, x0 material dependant constants
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15. Different Materials (1)
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16. Different Materials (2)
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17. Particle Range/Stopping Power
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18. Energy-loss in Tracking Chamber
Who is who?
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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
Dec 2009
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20. Straggling (2) Simple parameterisation Landau function
Better to use Vavilov distribution
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21. Straggling (3)
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22. δ-Ray 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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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
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24. Electrons Electrons are different light Bremsstrahlung
Pair production
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25. More next time...
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26. Multiple Scattering
Particles don’t only loose energy … … they also change direction
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27. MS Theory
Average scattering angle is roughly Gaussian for small deflection angles
With
Angular distributions are given by
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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
Dec 2009
Alfons Weber

29. 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
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!
Log pT transfer (10 decades)
Dec 2009
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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
Dec 2009
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31. Cherenkov Radiation Moving charge in dielectric medium
Wave front comes out at certain angle
slow
fast
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32. Cherenkov Radiation (2)
How many Cherenkov photons are detected?
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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
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34. Threshold Counter Particle travel through radiator Cherenkov radiation
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35. Differential Detectors
Will reflect light onto PMT for certain angles only  β Selection
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36. Ring Imaging Detectors (1)
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37. Ring Imaging Detectors (2)
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38. Ring Imaging Detectors (3)
More clever geometries are possible
Two radiators  One photon detector
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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
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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
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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
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42. Transition Radiation Detector
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43. ATLAS TRTracker ATLAS Experiment Inner Detector:
pixel, silicon and straw tubes
Combination of Central Tracker and TR for electron identification
Dec 2009
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44. Atlas TRT (II)
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45. Electrons with radiator Electrons without radiator
Atlas TRT (III)
only electron produce TR in radiator
e± / π separation
Electrons with radiator
Electrons without radiator
Bod -> J/yKos
TRT senses
ionisation
transition radiation
High threshold hits
Dec 2009
Alfons Weber

46. Table of Contents Bethe-Bloch Formula Multiple Scattering
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
Dec 2009
Alfons Weber

47. Bibliography This lecture
PDG 2008 (chapter 27 & 28) and references therein
Especially Rossi
Lecture notes of Chris Booth, Sheffield
R. Bock, Particle Detector Brief Book
Or just it!
Dec 2009
Alfons Weber

48. Plea I need feedback! Questions Alfons.Weber@stfc.ac.uk What was good?
What was bad?
What was missing?
More detailed derivations?
More detectors?
More…
Less…
Dec 2009
Alfons Weber