Physics and Engineering of Radiation Detection

82 Chapter 2. Interaction of Radiation with Matter

Herem 0 c^2 is simply the rest energy of the particle. For an electron and a

proton it is 0. 511 MeVand 938MeVrespectively. If we use these numbers

thenTwill also be inMeVirrespective of the units we use forvandcas long

as both are in the same units. Hence the above relation can also be written as

Tth =

[(

1 −

(2. 3 × 108 )^2

(2. 99 × 108 )^2

)− 1 / 2

− 1

]

×E 0

=0. 565 ×E 0 ,

whereE 0 =m 0 c^2 is the rest energy of the particle. The required threshold

kinetic energies of electrons and protons are then given by

Tthe =0. 565 × 0. 511

=0. 289 MeV

Tthp =0. 565 × 938

= 539MeV.

The above example clearly shows that protons need much higher kinetic energy
than an electron to emit Cherenkov radiation. This, of course, is a consequence of
the heavier mass of the proton. In general, the heavier the particle the higher kinetic
energy it must possess to be able to emit Cherenkov radiation.

2.3 InteractionofPhotonswithMatter...................

Since photons are not subject to Coulomb or nuclear forces, their interactions are
localized at short distances. This means that although the intensity of a photon
beam decreases as it passes through a material and photons are removed from the
beam but the energy of individual photons that do not take part in any interaction
is not affected.

2.3.A InteractionMechanisms

Photons can primarily interact with material in three different ways: photoelec-
tric effect, Compton scattering, and pair production. Other possible interaction
mechanisms include Raleigh and Mie processes. These interaction mechanisms have
different energy thresholds and regions of high cross-sections for different materials.
Whenever a beam of photons of sufficient energy passes through a material, not all
of the photons in the beam go through the same types of interaction. With regard
to radiation detection, the key then is to look statistically at the process. For exam-
ple, if we want to know how most of the photons in the beam will interact with the
material, we can look at the cross section of all the interactions and find the one that
has the highest value at that particular photon energy. Most of the time, the cross
sections can either be determined through some semi-empirical relation or extracted
from a cross section table that are routinely published by researchers. Fig.2.3.1
shows different photon cross sections as a function of energy for carbon and lead.
Another excellent use of these cross sections is the estimation of the attenuation of