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### Interaction of Particles with Matter Alfons Weber CCLRC & University of Oxford Graduate Lecture 2004 Table of Contents Bethe-Bloch Formula Energy loss of heavy ... – PowerPoint PPT presentation

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Title: Interaction%20of%20Particles%20with%20Matter

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

2
• Bethe-Bloch Formula
• Energy loss of heavy particles by Ionisation
• Multiple Scattering
• Change of particle direction in Matter
• Light emitted by particles travelling in
dielectric materials
• Light emitted on traversing matter boundary

3
Bethe-Bloch Formula
• Describes how heavy particles (mgtgtme) 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
?
x
Ze
5
Bethe-Bloch (2)
• Force on projectile
• Change of momentum of target/projectile
• Energy transferred

6
Bethe-Bloch (3)
• Consider a-particle scattering off Atom
• Mass of nucleus MAmp
• Mass of electron Mme
• 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
• e screening correction of inner electrons
• d 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, d0, 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
d-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 d-rays, the average energy loss
changes
• Equivalent of changing Emax

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

23
Electrons
• Electrons are different ?light
• Bremsstrahlung
• Pair production

24
Multiple Scattering
• Particles dont 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
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 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
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
• Similar, but not identical

29
• Moving charge in matter

slow
at rest
fast
30
• Wave front comes out at certain angle
• Thats the trivial result!

31
• How many Cherenkov photons are detected?

32
Different Cherenkov Detectors
• Threshold Detectors
• Yes/No on whether the speed is ßgt1/n
• Differential Detectors
• ßmax gt ß gt ßmin
• Ring-Imaging Detectors
• Measure ß

33
Threshold Counter

34
Differential Detectors
• Will reflect light onto PMT for certain angles
only ? ß 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 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
• Initially observer sees nothing
• Later he seems to see two charges moving apart?
electrical dipole
• Accelerated charge is creating radiation

40
• Consider relativistic particle traversing a
boundary from material (1) to material (2)
• Can be used to measure ?

41
42
• Bethe-Bloch Formula
• Energy loss of heavy particles by Ionisation
• Multiple Scattering
• Change of particle direction in Matter
• Light emitted by particles travelling in
dielectric materials
• 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?