98 Chapter 2. Interaction of Radiation with Matter
saw earlier, are fairly complicated, but their overall effect on a beam of photons and
the material through which it passes can be characterized by some simple relations.
Before we go on to define these relations, let us have a qualitative look at the passage
of a photon beam through matter.
A photon beam consists of a large number of photons moving in a straight line.
The beam may or may not be monochromatic, such as, all the photons in the beam
may or may not have the same energy. Of course the termsameis somewhat loosely
defined here since even a so called monochromatic photon beam has some variations
in energy around its mean value. Depending on their energy, each photon in the
beam may undergo one of the several interactions we discussed earlier. It is hard,
even impossible, to say with absolute certainty that a photon with a certain energy
will definitely interact with an atom and in a defined way. The good thing is that the
gross interaction mechanisms of a large number of photons can be quite accurately
predicted with the help of statistical quantities such as cross section.
In radiation measurements, a photon beam is relatively easier to handle as com-
pared to a beam of massive particles. The reason is that the interaction of photons
with matter is localized or discrete. That is, a photon that has not interacted with
any other particle does not loose energy and remains a part of the beam. This means
that the energy of all non-interacting photons in a beam remains constant as the
beam passes through the material. However the intensity of the beam decreases as
it traverses the material due to loss of interacting photons.
It has been found that at any point in a material, the decrease in intensity of a
photon beam per unit length of the material depends on the intensity at that point,
that is
dI
dx∝−I
⇒
dI
dx= −μtI, (2.3.32)wheredIis the change in intensity as the beam passes through the thicknessdx
(actuallydI/dxrepresents the tangents of theIversusxcurve at each point).μtis
the total linear attenuation coefficient. It depends on the type of material and the
photon energy. Integrating the above equation gives
I=I 0 e−μtx, (2.3.33)whereI 0 is the intensity of the photon beam just before it enters the material and
Iis its intensity at a depthx.
It is interesting to note the similarity of the above equation with the radioactive
decay law we studied in the previous chapter. In fact, in analogy with the half and
mean lives of radioisotopes, mean free pathλmand half-thicknessx 1 / 2 have been
defined for photon beam attenuation in materials.
λm =1
μt(2.3.34)
x 1 / 2 =ln(2)
μt(2.3.35)
Theterm mean free pathwas defined earlier in the chapter. Now, using equation
2.3.33 we can assign quantitative meaning to it. The reader can easily verify that the