Interaction%20of%20Particles%20with%20Matter

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Interaction of Particleswith Matter

• Alfons Weber
• CCLRC University of OxfordGraduate Lecture 2004

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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

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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

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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
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Bethe-Bloch (2)

• Force on projectile
• Change of momentum of target/projectile
• Energy transferred

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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

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Bethe-Bloch (4)

• Energy transfer is determined by impact parameter
  b
• Integration over all impact parameters

b
db
ze
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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

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Bethe-Bloch (6)

• Simple approximations for
• From relativistic kinematics
• Inelastic collision
• Results in the following expression

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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

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Energy Loss Function
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Average Ionisation Energy
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Density Correction

• Density Correction does depend on
  materialwith
• x log10(p/M)
• C, d0, x0 material dependant constants

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Different Materials (1)
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Different Materials (2)
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Particle Range/Stopping Power
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Application in Particle ID

• Energy loss as measured in tracking chamber
• Who is Who!

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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

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Straggling (2)

• Simple parameterisation
• Landau function
• Better to use Vavilov distribution

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Straggling (3)
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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
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Restricted dE/dx

• Some detector only measure energy loss up to a
  certain upper limit Ecut
• Truncated mean measurement
• d-rays leaving the detector

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Electrons

• Electrons are different ?light
• Bremsstrahlung
• Pair production

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Multiple Scattering

• Particles dont only loose energy
  they also change direction

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MS Theory

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

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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

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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!
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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

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Cherenkov Radiation (1)

• Moving charge in matter

slow
at rest
fast
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Cherenkov Radiation (2)

• Wave front comes out at certain angle
• Thats the trivial result!

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Cherenkov Radiation (3)

• How many Cherenkov photons are detected?

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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

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Threshold Counter

• Particle travel through radiator
• Cherenkov radiation

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Differential Detectors

• Will reflect light onto PMT for certain angles
  only ? ß Selecton

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Ring Imaging Detectors (1)
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Ring Imaging Detectors (2)
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Ring Imaging Detectors (3)

• More clever geometries are possible
• Two radiators ? One photon detector

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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

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Transition Radiation (2)

• Initially observer sees nothing
• Later he seems to see two charges moving apart?
  electrical dipole
• Accelerated charge is creating radiation

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Transition Radiation (3)

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

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Transition Radiation Detector
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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

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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!

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Plea

• I need feedback!
• Questions
• What was good?
• What was bad?
• What was missing?
• More detailed derivations?
• More detectors?
• More
• Less
• A.Weber_at_rl.ac.uk