Transcript Lecture 1.3: Interaction of Radiation with Matter

Lecture 1.3:
Interaction of Radiation with
Matter
Outline
1. Energy loss by heavy particles
2. Multiple scattering through small angles
3. Photon and Electron interactions in matter
Radiation Length
Energy loss by electrons
Critical Energy
Energy loss by photons
Bremsstrahlung and pair production
4. Electromagnetic cascade
5. Muon energy loss at high energy
6. 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
A volume with surface S and
thickness dx contains N=nSdx atoms
NA 
A
S
Probability of incoming
particle hitting an atom
pN

Probablity that a particle
hits exactly one atom
between x and (x + dx)

Mean free path


0
0
x x
e dx  
 xP(x)dx   

S
 NA 

A
dx 
1

dx
dx
P(x)dx  (1 p)m p  em p 
1

Ave collisions/cm
1


NA 
A
x
e  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) 
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 '

Average number of collisions/cm
causing an energy loss between 
E’ and E’+dE’
d (E, E')
dE'
dE'
1 d (E, E')
dE '
 (E)
dE '
NA  d (E, E')
A
dE'
Average energy loss per cm

dE
N 
 A
dx
A
 E'
d (E, E')
dE'
dE'
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.
dE
S
dx
Bethe-Bloch Formula
dE 4e 4 z 2


NB
dx
m0v 2

 2m v 2
 v 2  v 2 
0
B  zln
 ln1 2  2 
I
 c  c 

Energy loss through
ionization and atomic
excitation


Particle Data Group
Stopping Power of muons in copper
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.
Photon and Electron Interactions in Matter
Electrons: bremsstrahlung
e
e
p np
n p
p nn
p
p
n p
n n
γ
Photons: pair production
γ
p np
n p
p nn
p
p
n p
n n
e
e
Presence of nucleus
required for the
conservation of energy
and momentum
Characteristic amount of
matter traversed for these
interactions is the
radiation length (X0)
Radiation Length
Mean distance over which an
electron loses all but 1/e of its
energy through bremsstralung
But also
7/9 of the mean free path for
electron-positron pair
production by a high energy
photon
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
Z2
0 (q)  Z2    e
Partial screening of
nucleus by electrons
rr
i( qr j )
r 3
 (rj )d r1K d 3rZ 2  Z2  F
2
0
j1
2
d  1 Z1 (Z 2  F)e02  1
 

4
d 40
2 p
 sin 2
Electron Critical Energy
Energy loss through
bremsstrahlung is proportional to
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
800MeV
Ec 
Z 1.2
Electron in Copper: Ec = 20 MeV
Muon in Copper: Ec = 400 GeV!
Photon Energy Loss
Contributing Processes
1. Atomic photoelectric effect
2. Rayleigh scattering
3. Compton scattering of an
electron
4. Pair production (nuclear field)
5. Pair production (electron field)
6. Photonuclear interaction (Giant
Dipole Resonance)
At low energies the photoelectric
effect dominates; with increasing
energy pair production becomes
increasingly dominant.
Light
element:
Carbon
Heavy
element:
Lead
Photon Pair Production
Probability that a photon interaction will result
in a pair production
Differential Cross-section
d
A

1 43 x(1 x)

dx X 0 N A
Total Cross-section


7
9
ANA
X0
Electromagnetic Cascades
Longitudinal Shower Profile
A high-energy electron or
photon incident on a thick
absorber initiates an
electromagnetic cascade
through bremsstrahlung
and pair production
Longitudinal development
scales with the radiation
length
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
Electromagnetic Cascades
Visualization of
cascades developing in
the CMS
electromagnetic and
hadronic calorimeters
Electromagnetic Cascades
Transverse shower size scales with
the Molière radius
RM  X 0
Es
Ec
E s  21 MeV

On average 10% of the shower
 energy lies outside a cylinder with
radius RM. About 99% within 3.5RM.
Muon Energy Loss
For muons the critical
energy (above which
radiative processes are
more important than
ionization) is at several
hundred GeV.
dE

 a(E)  b(E)E
dx
Ionization
energy loss
Mean range
Pair production,
bremsstrahlung
and photonuclear
 E b 
x 0  1b ln1 0 

a 
Muon Energy Loss
Critical energy defined as the energy at which radiative
and ionization energy losses are equal.
Muon critical
energy for the
chemical elements
Muon
Tomography
Luis Alvarez
used the
attenuation of
muons to look
for chambers
in the Second
Giza Pyramid
He proved that
there are no
chambers
present
From Interactions to Detectors
Now that you know all the interactions, we can start talking about
detectors!