1. Lecture 1.3: Interaction of Radiation with Matter

2. 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

3. Electromagnetic Interaction of Particles with Matter
From Riegler Lecture 2: Introduction
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.
Interaction with atomic nucleus. Particle undergoes multiple scattering. Could emit a bremsstrahlung photon.
Interaction with atomic electrons. Particle loses energy; atoms are excited or ionized.

4. Material with atomic mass A and density ρ contains n atoms
Cross-section
Material with atomic mass A and density ρ contains n atoms
A volume with surface S and thickness dx contains N=nSdx atoms S dx
Probability of incoming particle hitting an atom
Probablity that a particle hits exactly one atom between x and (x + dx)
Riegler Lecture #2
Ave collisions/cm
Mean free path

5. Differential Cross-section
Differential cross-section is the cross-section from an incoming particle of energy E to lose an energy between E and E’
Total cross-section
Probability (P(E)) that a particle of energy, E, loses between E’ and E’ + dE’ in a collision
From Riegler, Lecture #2
Average number of collisions/cm causing an energy loss between E’ and E’+dE’
Average energy loss per cm

6. Stopping Power of muons in copper
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.
Stopping Power of muons in copper
Bethe-Bloch Formula
PDG, Ch 27 p 3.
Particle Data Group
Energy loss through ionization and atomic excitation

7. Integrate the Bethe-Bloch formula to obtain the range.
Useful for low energy hadrons and muons with momenta below a few hundred GeV
PDG
Radiative Effects important at higher momenta. Additional effects at lower momenta.

8. Photon and Electron Interactions in Matter
Electrons: bremsstrahlung e
Presence of nucleus required for the conservation of energy and momentum e γ p n
PDG
Photons: pair production
Characteristic amount of matter traversed for these interactions is the radiation length (X0) e p n γ e

9. Radiation Length Energy Loss in Lead
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
pdg

10. 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
Riegler/PDG
Partial screening of nucleus by electrons

11. 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
PDG
Electron in Copper: Ec = 20 MeV
Muon in Copper: Ec = 400 GeV!

12. Contributing Processes Light element: Carbon
Photon Energy Loss
Contributing Processes
Light element: Carbon
Atomic photoelectric effect
Rayleigh scattering
Compton scattering of an electron
Pair production (nuclear field)
Pair production (electron field)
Photonuclear interaction (Giant Dipole Resonance)
PDG
Heavy element: Lead
At low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant.

13. Photon Pair Production
Probability that a photon interaction will result in a pair production
Differential Cross-section
Total Cross-section
PDG

14. 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
PDG
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

15. Electromagnetic Cascades
Visualization of cascades developing in the CMS electromagnetic and hadronic calorimeters
From CMS outreach site

16. Electromagnetic Cascades
Transverse shower size scales with the Molière radius
From PDG. Could do with a neater illustration
On average 10% of the shower energy lies outside a cylinder with radius RM. About 99% within 3.5RM.

17. Muon Energy Loss
For muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV.
Pair production, bremsstrahlung and photonuclear
Ionization energy loss
Mean range

18. Muon critical energy for the chemical elements
Muon Energy Loss
Critical energy defined as the energy at which radiative and ionization energy losses are equal.
From PDG
Muon critical energy for the chemical elements

19. 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
Riegler Lectures – thought it was a neat illustration

20. From Interactions to Detectors
Now that you know all the interactions, we can start talking about detectors!
From the Particle Adventure