Lecture 1.3: Interaction of Radiation with Matter.
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Transcript of Lecture 1.3: Interaction of Radiation with Matter.
Lecture 1.3:Interaction of Radiation with Matter
Outline
1. Energy loss by heavy particles2. Multiple scattering through small angles3. Photon and Electron interactions in matter
Radiation LengthEnergy loss by electronsCritical EnergyEnergy loss by photonsBremsstrahlung and pair
production4. Electromagnetic cascade5. Muon energy loss at high energy6. Cherenkov and Transition Radiation
Electromagnetic Interaction of Particles with Matter
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.
If particle’s velocity is greater than the speed of light in the medium -> Cherenkov Radiation. When crossing the boundary between median, ~1% probability of producing a Transition Radiation X-ray.
Cross-section
Material with atomic mass A and density ρ contains n atoms
n NA
A
p NS
NA A
dx 1
dxProbability of incoming
particle hitting an atom
A volume with surface S and thickness dx contains N=nSdx atoms
P(x)dx (1 p)m p e m p 1
e x
dxProbablity that a particle hits exactly one atom between x and (x + dx)
Mean free path
xP(x)dx x
e x
dx 0
0
Ave collisions/cm
1
NAA
S
dx
Differential Cross-section
d(E, E ')
dE '
Differential cross-section is the cross-section from an incoming particle of energy E to lose an energy between E and E’
(E) d (E,E ')
dE 'dE 'Total cross-section
Probability (P(E)) that a particle of energy, E, loses between E’ and E’ + dE’ in a collision
P(E,E ')dE '1
(E)
d (E,E ')
dE 'dE '
Average number of collisions/cm causing an energy loss between E’ and E’+dE’Average energy loss per cm
NAA
d(E, E ')
dE '
dE
dx
NAA
E 'd (E,E ')
dE 'dE '
Stopping Power
S dE
dx
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
dE
dx
4e4z2
m0v2 NB
Bethe-Bloch Formula
B z ln2m0v
2
I ln 1
v 2
c 2
v 2
c 2
Energy loss through ionization and atomic excitation
Range
Integrate the Bethe-Bloch formula to obtain the range.
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.
Electrons: bremsstrahlung
Photons: pair production
ppn
np
pn
n n
ppn
pn
e
γe
Photon and Electron Interactions in Matter
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
Radiation Length
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
But also
Energy Loss in Lead
Energy Loss 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
Elastic scattering of a nucleus is described by
0(q) Z2 e i(r q r r j )0
2(r r j )d3r1K d3rZ 2
Z2 Fj1
Z 2
dd
1
40
Z1(Z2 F)e02
2p
21
sin4 2
Partial screening of nucleus by electrons
Electron Critical Energy
Energy loss through bremsstrahlung is proportional to the electron energyIonization loss is proportional to the logarithm of the electron energy
Critical energy (Ec) is the energy at which the two loss rates are equal
Ec 800MeV
Z 1.2 Electron in Copper: Ec = 20 MeVMuon in Copper: Ec = 400 GeV!
Photon Energy Loss
1. Atomic photoelectric effect2. Rayleigh scattering3. Compton scattering of an
electron4. Pair production (nuclear
field)5. Pair production (electron
field)6. Photonuclear interaction
(Giant Dipole Resonance)
Contributing ProcessesLight element:Carbon
Heavy element:Lead
At low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant.
Probability that a photon interaction will result in a pair production
79
ANA
X0
Photon Pair Production
ddx
A
X0NA
1 43 x(1 x)
Differential Cross-section
Total Cross-section
Electromagnetic Cascades
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 lengthElectrons 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
Electromagnetic Cascades
Visualization of cascades developing in the CMS electromagnetic and hadronic calorimeters
Electromagnetic Cascades
Transverse shower size scales with the Molière radius
RM X0
E s
E c
E s 21 MeV
On average 10% of the shower energy lies outside a cylinder with radius RM. About 99% within 3.5RM.
For muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV.
dE
dxa(E) b(E)E
Ionization energy loss
Pair production, bremsstrahlung and photonuclear
x0 1b ln 1
E0b
a
Mean
range
Muon Energy Loss
Muon critical energy for the chemical elements
Critical energy defined as the energy at which radiative and ionization energy losses are equal.
Muon 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
Muon Tomography
From Interactions to Detectors
Now that you know all the interactions, we can start talking about detectors!