doctoral thesis

14 CHAPTER 1. INTRODUCTION
this average value from event to event. The energy loss distribution is called the Landau
distribution [18] and is skewed towards high values (the Landau tail). Only for a
thick layer, where the energy loss exceeds one half of the original particle energy, the
distribution becomes roughly Gaussian [11].
1.2.2 Other Interaction Mechanisms of Radiation with Matter
The energy loss due to ionization and excitation is not the only interaction process
of radiation with matter. Charged particles can also lose energy by radiation (bremsstrahlung).
The energy loss connected with the processes of transition radiation and
˘Cerenkov radiation are negligible, nevertheless they are important processes for identification
of charged particles. Moreover, we distinguish three processes in which photons
interact with matter: the Photo Electric Effect, the Compton Effect and the Pair
Production.
Radiation Loss by Charged Particles
When the distance of closest approach of a fast charged particle becomes smaller than
the atomic radius, the deflection of its trajectory in the electric field of the nucleus
becomes the most important effect. Let dσ(Θ) ⏐ be the differential atomic cross
dΩ scat
section that a particle of momentum p and velocity v = βc undergoes a collision
which deflects its trajectory into the solid angle dΩ at angle Θ to its original direction
of motion. If one neglects both the finite dimension of the nucleus and the shielding
of its field by the atomic electrons, one obtains the well-known Rutherford scattering
formula [19, 20]
dσ(Θ)
dΩ
⏐
⏐ scat
= z2 Z 2 r 2 e
4
2 mec 1
βp sin4 . (1.15)
(Θ/2)
Then the term NA
⏐
ρ dσ(Θ) ⏐ gives the average number of collisions per length in
A dΩ scat
a medium of density ρ with scattering of the particle into dΩ. The multiple Coulomb
scattering distribution is roughly Gaussian for small angles but at larger angles it behaves
like Rutherford scattering, having larger tails than does a Gaussian distribution
[11, 21, 22].
In some cases a photon of energy comparable with that of the deflected particle is
emitted during the scattering process, e.g.
e − + nucleus → e − + γ + nucleus ′ .