Biomedical Engineering Reference
In-Depth Information
the forward direction. The electrons are always ejected within
±
90
°
of the near-forward direction.
A Compton interaction leaves behind an ionized atom which, as with
photo-electric interactions, is likely to undergo further changes as its
electrons readjust themselves in their orbits - such as emitting
relatively low energy photons or electrons.
Pair production
The third principal interaction of photons is in near-collisions with the
atomic
nucleus
, which lead to extinction of the photon and the creation
of a pair of particles:
an electron and a posi-
tron (which is the anti-
particle of the electron)
as sketched in Figure
Figure 4.3. Schematic representation of
4.3. This Process, ter-
med pair production,
is a dramatic example
of Einstein's theory of
pair production. An electron and a positron
(positive charge) are created in the field of
the atomic nucleus.
the equivalence of energy and mass. Here, the energy of an incident
photon is transformed to create two particles, each of mass 0.511 MeV.
As a consequence, there is a threshold energy for pair production,
namely 2
0.511 MeV = 1.02 MeV. A photon of lesser energy simply
does not have the energy needed to produce a particle/anti-particle
pair. The energy relationship is
⋅
′
′
E
+
E
=
E
−
1
02
MeV
electron
positron
photon
where
E
photon
is the energy of the incident photon, and
E´
electron
and
E´
positron
, and
E
photon
are the energies, respectively, of the emitted
electron and positron. The electron and positron share the available
energy. They are produced at an angle of typically 0.511/T radians,
where T is the kinetic energy of the particle in MeV. Thus, very
approximately, a 4 MeV photon will produce electrons and positrons
half of which will lie within about
±
15
°
of the forward direction.
Dependence of photon interactions on photon energy
Figure 4.4 shows how the relative importance of each of the three
main modes of photon interaction varies with the energy of the
photon. The likelihood of a photo-electric interaction varies roughly
as (1/
E
photon
)
3
. As a result, photo-electric interactions are much more
important - indeed, are dominant - for low energy photons. Above
