Subatomic Physics

3.3. Photons 45
Equation (3.2) also shows that the specific energy loss does not depend on the mass
of the particle (provided it is much heavier than the electron) but only on its charge
and speed. The curves in Fig. 3.5 therefore are valid also for particles other than
the protons if the energy scale is appropriately shifted.
The range of a particle in a given substance is obtained from Eq. (3.2) by
integration:
� 0
dT
R =
. (3.4)
T0 (dT/dx)
Here T is the kinetic energy and the subscript 0 refers to the initial value. Some useful
information concerning range and specific energy loss is summarized in Fig. 3.6.
Two more quantities shown in Fig. 3.2, the spread in energy and the spread in
angle, are important in experiments, but they are not essential for a first view of the
subatomic world. We shall therefore not discuss them here; the relevant information
can be found in the references given in Section 3.6.
3.3 Photons
Photons interact with matter chiefly by three processes:
1. Photoelectric effect.
2. Compton effect.
3. Pair production.
A complete treatment of the three processes is rather complicated and requires the
tools of quantum electrodynamics. The essentialfacts,however,aresimple.Inthe
photoelectric effect, the photon is absorbed by an atom, and an electron from one
of the shells is ejected. In the Compton effect, the photon scatters from an atomic
electron. In pair production, the photon is converted into an electron–positron pair.
This process is impossible in free space because energy and momentum cannot be
conserved simultaneously when a photon decays into two massive particles. It occurs
in the Coulomb field of a nucleus which is needed to balance energy and momentum.
The energy dependences of processes 1–3 are very different. At low energies,
below tens of keV, the photoelectric effect dominates (which accounts for the sharp
edges), the Compton effect is small, and pair production is energetically impossible.
At an energy of 2mec 2 , pair production becomes possible, and it soon dominates
completely. Two of the three processes, photoelectric effect and pair production,
eliminate the photons undergoing interaction. In Compton scattering, the scattered
photon is degraded in energy. The all-or-nothing situation described in Section 3.1
and depicted in Fig. 3.1(b) is therefore a good approximation, and the transmitted
beam should show an exponential behavior, as described by Eq. (3.1). The
absorption coefficient µ is a sum of three terms,
µ = µphoto + µCompton + µpair
and each term can be computed accurately.
(3.5)