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!