Biomedical Engineering Reference
In-Depth Information
6
Interaction of Electrons with Matter
6.1
Energy-Loss Mechanisms
We treat electron and positron energy-loss processes together, referring to both
simply as “electrons” or “beta particles.” Their stopping powers and ranges are
virtually the same, except at low energies, as can be seen from Fig. 5.6. Energetic
gamma photons produced by the annihilation of positrons with atomic electrons
(Sect. 8.5) present a radiation problem with
β
+
sources that does not occur with
β
-
emitters.
Like heavy charged particles, beta particles can excite and ionize atoms. In ad-
dition, they can also radiate energy by bremsstrahlung. As seen from Fig. 5.6, the
radiative contribution to the stopping power (shown by the dashed line) becomes
important only at high energies. At 100 MeV, for example, radiation accounts for
about half the total rate of energy loss in water. We consider separately the colli-
sional stopping power
(-d
E
/d
x
)
col
and the radiative stopping power
(-d
E
/d
x
)
rad
for
beta particles. Beta particles can also be scattered elastically by atomic electrons, a
process that has a significant effect on beta-particle penetration and diffusion in
matter at low energies.
6.2
Collisional Stopping Power
The collisional stopping power for beta particles is different from that of heavy
charged particles because of two physical factors. First, as mentioned in Section 5.1,
a beta particle can lose a large fraction of its energy in a single collision with an
atomic electron, which has equal mass. Second, a
β
-
particle is identical to the
atomic electron with which it collides and a
β
+
is the electron's antiparticle. In
quantum mechanics, the identity of the particles implies that one cannot distin-
guish experimentally between the incident and struck electron after a collision.
Energy loss is defined in such a way that the electron of lower energy after collision
is treated as the struck particle. Unlike heavy charged particles, the identity of
β
-
