1.3 interaction of radiation with matter 1 by archana sharma cern geneva switzerland march 2009...
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1.3 Interaction of Radiation with Matter1
Gaseous Particle Detectors:
1.3 Interaction of Radiation with Matter
Chapter I 5th March 2009 1.1 Introduction 1.2 Units and Definitions, Radiation Sources 1.3 Interaction of Radiation with Matter
Chapter II 12th March 2009 2.1 General Characteristics of gas detectors, Electronics for HEP detectors2.2: Transport Properties 2.3: Wire-based Detectors
Tool
Interaction with atomic electrons. Particle loses energy; atoms are excited or ionized.
Interaction with atomic electrons. Particle loses energy; atoms are excited or ionized.
Interaction with atomic nucleus. Particle undergoes multiple scattering. Could emit a bremsstrahlung photon.
Interaction with atomic nucleus. Particle undergoes multiple scattering. Could emit a bremsstrahlung photon.
If particle’s velocity is greater than the speed of light in the medium -> Cherenkov Radiation. When crossing the boundary between media, ~1% probability of producing a Transition Radiation X-ray.
If particle’s velocity is greater than the speed of light in the medium -> Cherenkov Radiation. When crossing the boundary between media, ~1% probability of producing a Transition Radiation X-ray.
Electromagnetic Interaction of Particles with MatterElectromagnetic Interaction of Particles with Matter
Material with atomic mass A and density ρ contains n atoms
Material with atomic mass A and density ρ contains n atoms
Probability, p of incoming particle hitting an atom
Probability, p of incoming particle hitting an atom
A volume with surface S and thickness dx contains N=nSdx atoms
A volume with surface S and thickness dx contains N=nSdx atoms
Probablity that a particle hits exactly one atom between x and (x + dx)
Probablity that a particle hits exactly one atom between x and (x + dx)
Mean free path Mean free path Average collisions/cmAverage collisions/cm
S
dx
Cross-sectionCross-section
Differential cross-section is the cross-section from an incoming particle of energy E to lose an energy between E and E’
Differential cross-section is the cross-section from an incoming particle of energy E to lose an energy between E and E’
Total cross-sectionTotal cross-section
Probability (P(E)) that a particle of energy, E, loses between E’ and E’ + dE’ in a collision
Probability (P(E)) that a particle of energy, E, loses between E’ and E’ + dE’ in a collision
Average number of collisions/cm causing an energy loss between E’ and E’+dE’
Average number of collisions/cm causing an energy loss between E’ and E’+dE’
Average energy loss per cmAverage energy loss per cm
Differential Cross-sectionDifferential Cross-section
Linear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss.
Linear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss.
Part
icle
Data
G
roup
Stopping Power of muons in Copper
Bethe-Bloch Formula
Energy loss through ionization and atomic excitation
Energy loss through ionization and atomic excitation
Stopping Power Stopping Power
Linear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss.
Linear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss.
Part
icle
Data
G
roup
Stopping Power of muons in Copper
Bethe-Bloch Formula
Energy loss through ionization and atomic excitation
Energy loss through ionization and atomic excitation
Stopping Power Stopping Power
1.3 Interaction of Radiation with Matter8
Bethe-Bloch Formula
Describes how heavy particles (m>>me) lose energy when travelling through a material
Exact theoretical treatment difficultAtomic excitationsScreeningBulk effects
Phenomenological description
Describes how heavy particles (m>>me) lose energy when travelling through a material
Exact theoretical treatment difficultAtomic excitationsScreeningBulk effects
Phenomenological description
Part
icle
Data
G
roup
Bethe-Bloch Formula
m – electronic massv – velocity of the particle (v/c = )N – number density of atomsI – ‘Effective’ atomic excitation energy – average value found empiricallyGas is represented as a dielectric medium through which the particle propagates And probability of energy transfer is calculated at different energies – Allison Cobb
1.3 Interaction of Radiation with Matter
ze
Ze
br
θx
y
A very roughBethe-Bloch Formula
Consider particle of charge ze, passing a stationary charge ZeAssume
Target is non-relativisticTarget does not move
CalculateMomentum transfer Energy transferred to target
Consider particle of charge ze, passing a stationary charge ZeAssume
Target is non-relativisticTarget does not move
CalculateMomentum transfer Energy transferred to target
11
2
0
1
2x
Zzep dtF
c b
Projectile force
Change of momentum of target/projectile
Energy transferred
2 23
2 20 0
cos cos4 4x
Zze ZzeF
r b
2 2 2 4
2 2 20
1
2 2 (2 ) ( )
p Z z eE
M M c b
Bethe-Bloch Formula
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
2 2 2 4 2
2 2 20
1
2 2 (2 ) ( )
p Z z e ZE
M M c b M
2 4
2 2 2 20
2 1( )
(4 )ee
z eE b E
m c b
Bethe-Bloch Formula
1.3 Interaction of Radiation with Matter13
Energy transfer is determined by impact parameter b
Integration over all impact parametersb
dbze
2 (number of electrons / unit area )
=2 A
dnb
dbN
b Z xA
Bethe-Bloch Formula
1.3 Interaction of Radiation with MatterDec 2008 Alfons Weber 14
There must be limits Dependence on the material is in the calculation
of the limits of the impact parameters
max
max
min
min
max
min
2 2
2
2 2
2
2
20
dd ( ) 2 ln
d
ln
with 24
bbe
e bb
EeE
Ae
m cn ZzE b E b C x b
b A
m c ZzC x E
A
eC N
m c
Bethe-Bloch FormulaCalculate average energy loss
1.3 Interaction of Radiation with Matter15
Simple approximations for– From relativistic kinematics
– Inelastic collision
Results in the following expression
min 0 average ionisation energyE I
2 2 2 22
20
22 lne em c m cE ZzC
x A I
2 2 22 2 2
max 2
22
1 2
ee
e e
m cE m c
m mM M
Bethe-Bloch Formula
1.3 Interaction of Radiation with Matter16
This was a very 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)
2 2 2 222max
2 20
21 ( )2 ln
2 2 2e em c m c EE Zz
Cx A I
Bethe-Bloch Formula
1.3 Interaction of Radiation with Matter17
Energy Loss FunctionEnergy Loss Function
1 10 100 1000 10000
1.6
1.5
1.4
1.3
1.2
1.1
Minimum ionizing particles (mips)
Relativistic Rise
Fermi Plateau
Rel
To m
ips
1.3 Interaction of Radiation with Matter18
Diff
ere
nt
Mate
rials
Diff
ere
nt
Mate
rials
1.3 Interaction of Radiation with Matter19
Different Materials (2)Different Materials (2)
20
Average Ionisation EnergyAverage Ionisation Energy
Few eV to few tens of eVFew eV to few tens of eV
1.3 Interaction of Radiation with Matter21
Density Correction depends on material
with– x = log10(p/M)
– C, δ0, x0 material dependant constants
Density CorrectionDensity Correction2 2 2 22
2max2 2
0
21 ( )2 ln
2 2 2e em c m c EE Zz
Cx A I
1.3 Interaction of Radiation with Matter22
Part
icle
Range/S
topp
ing
Pow
er
Part
icle
Range/S
topp
ing
Pow
er
1.3 Interaction of Radiation with Matter23
Energy-loss in Tracking ChambersEnergy-loss in Tracking Chambers
The Bethe Bloch Formula tool for Particle IdentificationThe Bethe Bloch Formula tool for Particle Identification
1.3 Interaction of Radiation with Matter24
Mean energy loss Actual energy loss will scatter around the
mean valueDifficult to calculate
– parameterization exist in GEANT and some standalone software libraries
– Form of distribution is important as energy loss distribution is often used for calibrating the detector
StragglingStraggling
1.3 Interaction of Radiation with Matter25
Energy LossIs a statisticalprocess
Simple parameterisation– Landau function
2
2
1 1( ) exp ( )
22
with e
f e
E E
m c ZzC x
A
StragglingStraggling
1.3 Interaction of Radiation with MatterDec 2008 Alfons Weber 26
StragglingStraggling
1.3 Interaction of Radiation with Matter27
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 changesEquivalent of changing Emax
δ-raysδ-rays
1.3 Interaction of Radiation with Matter28
Some detectors only measure energy loss up to a certain upper limit Ecut
– Truncated mean measurement– δ-rays leaving the detector
2 2 2 22
2 20
2
max
212 ln
2
( ) 1
2 2
cut
e e cut
E E
cut
m c m c EE ZzC
x A I
E
E
Restricted dE/dxRestricted dE/dx
1.3 Interaction of Radiation with Matter29
Electrons are different light– Bremsstrahlung– Pair production
ElectronsElectrons
1.3 Interaction of Radiation with Matter30
Multiple ScatteringMultiple Scattering
Particles not only lose energy …
but also they also change direction
1.3 Interaction of Radiation with Matter31
Average scattering angle is roughly Gaussian for small deflection angles
With
Angular distributions are given by
00 0
0
13.6 MeV1 0.038ln
radiation length
x xz
cp X X
X
2
2 20 0
2
200
1exp
2 4
1exp
22
space
plane
plane
dN
d
dN
d
Multiple ScatteringMultiple Scattering
1.3 Interaction of Radiation with Matter32
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– Allison & Cobb
Correlation bet dE/dx and MSCorrelation bet dE/dx and MS
Integrate the Bethe-Bloch formula to obtain the range
Integrate the Bethe-Bloch formula to obtain the rangeUseful for low energy hadrons and muons with momenta below a few hundred GeV
Useful for low energy hadrons and muons with momenta below a few hundred GeV
Radiative Effects important at higher momenta. Additional effects at lower momenta.
Radiative Effects important at higher momenta. Additional effects at lower momenta.
RangeRange
Electrons: bremsstrahlung
Photons: pair production
ppn
np
pn
n n
ppn
pn
e
γe
Characteristic amount of matter traversed for these interactions is the radiation length (X0)
Characteristic amount of matter traversed for these interactions is the radiation length (X0)
ppn
np
pn
n n
ppn
pn
e
e
γ
Presence of nucleus required for the conservation of energy and momentum
Presence of nucleus required for the conservation of energy and momentum
Photon and Electron InteractionsPhoton and Electron Interactions
also
Energy Loss in Lead
Radiation LengthRadiation Length
Mean distance over which an electron loses all but 1/e of its energy through bremsstralung
Mean distance over which an electron loses all but 1/e of its energy through bremsstralung
7/9 of the mean free path for electron-positron pair production by a high energy photon
7/9 of the mean free path for electron-positron pair production by a high energy photon
A charged particle of mass M and charge q=Z1e is deflected by a nucleus of charge Ze (charge partially shielded by electrons)
A charged particle of mass M and charge q=Z1e is deflected by a nucleus of charge Ze (charge partially shielded by electrons)The deflection accelerates the charge and therefore it radiates bremsstrahlung
The deflection accelerates the charge and therefore it radiates bremsstrahlung
Partial screening of nucleus by electrons
Energy Loss by electronsEnergy Loss by electrons
Elastic scattering of a nucleus is described byElastic scattering of a nucleus is described by
Energy loss through bremsstrahlung is proportional to the electron energy
Energy loss through bremsstrahlung is proportional to the electron energy
Ionization loss is proportional to the logarithm of the electron energy
Ionization loss is proportional to the logarithm of the electron energy
Critical energy (Ec) is the energy at which the two loss rates are equal
Critical energy (Ec) is the energy at which the two loss rates are equal
Electron in Copper: Ec = 20 MeVMuon in Copper: Ec = 400 GeV!
Electron in Copper: Ec = 20 MeVMuon in Copper: Ec = 400 GeV!
Electron Critical EnergyElectron Critical Energy
1. Atomic photoelectric effect
2. Rayleigh scattering3. Compton scattering of an
electron4. Pair production (nuclear
field)5. Pair production (electron
field)6. Photonuclear interaction
1. Atomic photoelectric effect
2. Rayleigh scattering3. Compton scattering of an
electron4. Pair production (nuclear
field)5. Pair production (electron
field)6. Photonuclear interaction
Light element:Carbon
Heavy element:Lead
At low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant.
At low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant.
Energy Loss by electronsContributing ProcessesEnergy Loss by electronsContributing Processes
photo electric cross section
Strong dependence of ZAt high energies ~ Z5
photo electric cross section
Strong dependence of ZAt high energies ~ Z5
Probability that a photon interaction will result in a pair production
Differential Cross-sectionDifferential Cross-section
Total Cross-sectionTotal Cross-section
Photon Pair ProductionPhoton Pair Production
What is the minimum energy for pair production?
What is the minimum energy for pair production?
A high-energy electron or photon incident on a thick absorber initiates an electromagnetic cascade through bremsstrahlung and pair production
A high-energy electron or photon incident on a thick absorber initiates an electromagnetic cascade through bremsstrahlung and pair production
Longitudinal Shower Profile
Longitudinal development scales with the radiation length
Longitudinal development scales with the radiation lengthElectrons eventually fall beneath critical energy and then lose further energy through dissipation and ionization
Electrons eventually fall beneath critical energy and then lose further energy through dissipation and ionization
Measure distance in radiation lengths and energy in units of critical energy
Measure distance in radiation lengths and energy in units of critical energy
Electromagnetic cascadesElectromagnetic cascades
Visualization of cascades developing in the CMS electromagnetic and hadronic calorimeters
Visualization of cascades developing in the CMS electromagnetic and hadronic calorimeters
Electromagnetic cascadesElectromagnetic cascades
For muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV.
For muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV.Ionization
energy loss
Pair production, bremsstrahlung and photonuclear
Mean rangeMean range
Muon Energy LossMuon Energy Loss
Muon critical energy for some elements
Critical energy defined as the energy at which radiative and ionization energy losses are equal.
Critical energy defined as the energy at which radiative and ionization energy losses are equal.
Muon Energy LossMuon Energy Loss
Luis Alvarez used the attenuation of muons to look for chambers in the Second Giza Pyramid
He proved that there are no chambers present
Luis Alvarez used the attenuation of muons to look for chambers in the Second Giza Pyramid
He proved that there are no chambers present
Muon Tomography
X-Ray Radiography for airport security
1.3 Interaction of Radiation with Matter46
Signals in particle detectors are mainly due to ionisationAnd excitation in a sensitive medium – gasAlso:Direct light emission by particles travelling faster than
the speed of light in a medium– Cherenkov radiation
Similar, but not identical– Transition radiation
Signals from Particles in a Gas DetectorSignals from Particles in a Gas Detector
1.3 Interaction of Radiation with Matter47
Moving charge in dielectric mediumWave front comes out at certain angle
1cos c n
slow fast
Cerenkov RadiationCerenkov Radiation
1.3 Interaction of Radiation with Matter48
How many Cherenkov photons are detected?
22
2
2
2 2 2
0 2 2
( )sin ( )d
1( ) 1 d
11
with ( ) Efficiency to detect photons of energy
radiator length
electron radius
ce e
e e
e
zN L E E E
r m c
zL E Er m c n
LNn
E E
L
r
Cerenkov Radiation (2)Cerenkov Radiation (2)
1.3 Interaction of Radiation with MatterDec 2008 Alfons Weber 49
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
Transition RadiationTransition Radiation
50
22 vq
vacuummedium
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
11 vq
33 qv
Transition Radiation (2)Transition Radiation (2)
1.3 Interaction of Radiation with Matter51
Consider relativistic particle traversing a boundary from material (1) to material (2)
Total energy radiated
Can be used to measure
22 2
22 2 2 2 2 2 2
d 1 1
d d / 1/ 1/
plasma frequency
p
p
N z
Transition Radiation (3)Transition Radiation (3)
From Interactions to DetectorsFrom Interactions to Detectors
1.3 Interaction of Radiation with Matter
1.3 Interaction of Radiation with Matter
1.3 Interaction of Radiation with Matter
Multiwire Proportional ChamberMultiwire Proportional Chamber
1.3 Interaction of Radiation with Matter
Multiwire Proportional Chamberand derivativesMultiwire Proportional Chamberand derivatives
1.3 Interaction of Radiation with Matter
Key Points: Lecture 1-3 Energy loss by heavy particlesMultiple scattering through small anglesPhoton and Electron interactions in
matterRadiation LengthEnergy loss by electronsCritical EnergyEnergy loss by photonsBremsstrahlung and pair production
Electromagnetic cascadeMuon energy loss at high energyCherenkov and Transition Radiation
1.3 Interaction of Radiation with Matter
Exercise: Lecture 1-3 • Estimate the range of 1 MeV alphas in
• Aluminium
• Mylar
• Argon
• Indicate major interaction processes in:
• 1 MeV in Al
• 10 MeV in Argon
• 100 keV in Iron
• 1 MeV in Al
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