Phenomena Associated with Charged-Particle Tracks - Atoms, Radiation, and-Radiation Protection - page 166

buildup of secondary electrons as the incident beam initially penetrates and ionizes
the target. With increasing absorber thickness the relative number that penetrate
falls off steadily out to about 110 µ m, and then tails off. Mean and extrapolated
ranges can be similarly defined as in Fig. 7.5. The csda range for 100-keV electrons
in water is 140 µ m.
7.7
Multiple Coulomb Scattering
We have seen how straggling affects the penetration of charged particles and in-
troduces some fuzziness into the concept of range. Another phenomenon, elas-
tic scattering from atomic nuclei via the Coulomb force, further complicates the
analysis of particle penetration. The path of a charged particle in matter—even a
fast electron or a heavy charged particle—deviates from a straight line because it
undergoes frequent small-angle nuclear scattering events.
Figure 7.7 illustrates how a heavy particle, starting out along the X -axis at the
origin O in an absorber might be deviated repeatedly by multiple Coulomb scatter-
ing until coming to rest at a depth X 0 . The total pathlength traveled, R ,whichis
the quantity calculated from Eq. (5.39) and given in the tables, is greater than the
depth of penetration X 0 . The latter is sometimes called the projected range. The
difference between R and X 0 for heavy charged particles is typically 1%, and so R
is usually considered to be the same as X 0 .
Another effect of multiple Coulomb scattering is to spread a pencil beam of
charged particles into a diverging beam as it penetrates a target, as illustrated in
Fig. 7.8. The magnitude of the spreading increases with the atomic number of the
material. When a pencil beam of 120-MeV protons penetrates 1 cm of water, for
example, about 4% of the particles emerge outside an angle ϕ = 1.5 ◦ in Fig. 7.8.
The arrangement in Fig. 7.8 is basically the same as that used by Ruther-
ford when he investigated alpha-particle scattering through thin metal foils (Sec-
tion 2.2). The occasional, unexpected, large-angle scattering of a particle led him to
the discovery of the nucleus.
Fig. 7.7 Schematic representation of the effect of multiple
Coulomb scattering on the path of a heavy charged particle that
starts moving from the origin O toward the right along the
X -axis. The displacement lateral to the X -axis is exaggerated for
illustrative purposes.