110 Chapter 2. Interaction of Radiation with Matter
2.4.B Passage of Charged Particles through Matter
There is a fundamental difference between the interaction of charged particle beams
and photon beams with matter. We saw earlier that whenever a photon interacts
with material, it is either absorbed or scattered and consequently removed from the
beam. On the other hand, when a charged particle interacts with matter it does
not get removed from the beam except for the rare cases where it gets scattered to
a very large angle.
There are a number of electronic and nuclear mechanisms through which charged
particles can interact with particles in the medium. However the net result of all
these interactions is a reduction in the energy of the particles as they pass through
the medium. Although the underlying interaction mechanisms are fairly complicated
but fortunately the rate of this energy loss can be fairly accurately predicted by a
number of semi-empirical relations developed so far.
The rate at which a charged particle loses energy as it passes through a material
depends on the nature of both the incident and the target particles. This quantity
is generally referred to in the literature as thestopping powerof the material. It
should be noted that stopping power does not represent the energy loss per unit
time rather the energy that a charged particle loses per unit length of the material
it traverses. Generally speaking, any charged particle can have either electronic,
nuclear, or gravitational interaction with the particles of the material through which
it passes. However the gravitational interaction is too low to be of any significance
and is generally ignored. The total stopping power is then just the sum of the
stopping powers due to electronic and nuclear interactions.
Stotal = −dE
dx
−dE
dx= Selectronic+Snuclear (2.4.6)Here the negative sign signifies the fact that the particles lose energy as they pass
through the material. For most practical purposes the nuclear component of the
stopping power can also be ignored as it is generally only a fraction of the total
stopping power. For particles such as electrons, this statement is always valid since
they are not affected at all by the strong nuclear force. For heavy positive charges,
such asα-particles, this holds if the particle energy is not high enough for it to pen-
etrate so deep into the atom that the short range nuclear forces of nuclear particles
become appreciable. Hence the stopping power can be written as a function of the
electronic component only.
−dE
dx≈Selectronic (2.4.7)The first successful attempt to derive a relation for the energy loss experienced by
an ion moving in the electromagnetic field of an electron was made by Neil Bohr. He
argued that such an expression can be obtained by simply considering the impulses
delivered by the ion to the electron as it passes through its electromagnetic field.
This consideration led him to the following relation.
[
−dE
dx]
Bohr=
4 πq^2 e^4 Ne
mev^2ln[
γ^2 mev^3 f(Z)
qe^2