Biomedical Engineering Reference
In-Depth Information
for example, ultimately produces a total of about 450 secondary electrons, a large
fraction of which occur with initial energies of less than 100 eV. The details of elec-
tron transport and charged-particle track structure and their relation to chemical
and biological effects will be considered in Chapter 13.
6.3
Radiative Stopping Power
The acceleration of a heavy charged particle in an atomic collision is usually small,
and except under extreme conditions negligible radiation occurs. A beta particle, on
the other hand, having little mass can be accelerated strongly by the same electro-
magnetic force within an atom and thereby emit radiation, called bremsstrahlung.
Bremsstrahlung occurs when a beta particle is deflected in the electric field of a nu-
cleus and, to a lesser extent, in the field of an atomic electron. At high beta-particle
energies, the radiation is emitted mostly in the forward direction, that is, in the
direction of travel of the beta particle. As indicated in Fig. 6.3, this circumstance
is observed in a betatron or synchrotron, a device that accelerates electrons to high
energies in circular orbits. Most of the synchrotron radiation, as it is called, is emit-
ted in a narrow sweeping beam nearly in the direction of travel of the electrons that
produce it.
Energy loss by an electron in radiative collisions was studied quantum mechani-
cally by Bethe and Heitler. If the electron passes near a nucleus, the field in which
it is accelerated is essentially the bare Coulomb field of the nucleus. If it passes at a
greater distance, the partial screening of the nuclear charge by the atomic electrons
becomes important, and the field is no longer coulombic. Thus, depending on how
close the electron comes to the nucleus, the effect of atomic-electron screening will
be different. The screening and subsequent energy loss also depend on the energy
of the incident beta particle. The maximum energy that a bremsstrahlung photon
can have is equal to the kinetic energy of the beta particle. The photon energy spec-
trum is approximately flat out to this maximum.
Fig. 6.3
Synchrotron radiation. At high energies, photons are
emitted by electrons (charge -
e
) in circular orbits in the
direction (crosshatched area) of their instantaneous velocity
v
.
The direction of the electrons' acceleration
a
is also shown.
