Physics and Engineering of Radiation Detection

620 Chapter 11. Dosimetry and Radiation Protection

that theδ-electrons (that is, secondary electrons) are not considered at all. This, as
we will shortly see, is one of the problems with this theory. The reader might recall
that the term mass stopping power was introduced in chapter 2 as well. Although
there we used a different notation but in effect both represent the same parameter,
that is
L ̄
ρ

≡

1

ρ

dE

dx

. (11.2.35)

Since the right side of equation 11.2.34 represents the ratio of stopping powers
therefore it is conventionally represented by

( ̄

L

ρ

)med

cav

≡

( ̄

L/ρ

)

( med

L/ρ ̄ )

cav

. (11.2.36)

The unrestricted mass collisional stopping power can be evaluated fairly accu-
rately for most materials and radiation types using energy spectrum that ignores
theδ-electrons. Hence if we measure the dose using a detector, which to a good ap-
proximation can be considered a Bragg-Gray cavity, we can determine the absorbed
dose expected in the medium under same conditions. Let us suppose we use a gas
filled ionization chamber to determine the absorbed dose in another material, say
water. We first need the ratio of the spectrum averaged mass collision stopping pow-
ers for water and gas. This can be evaluated from the known spectrum of electron
fluence. The second quantity that we need is the dose measured by the ionization
chamber. We know that an ionization chamber does not directly measure the dose
but it can be used to determine the total charge produced by the radiation. If the
total charge isdQgasthen the dose is given by

Dgas =

dEgas

dmgas

=

dQgas

dmgas

Wgas

e

, (11.2.37)

wheredEgasrefers to the total energy deposited in the mass elementdmgasandWgas
is the energy needed to produce a charge pair. If the gas is air thenWair/e≈ 33. 9
J/Cand the above relation reduced so

Dair=33. 9

dQgas

dmgas

. (11.2.38)

At first sight it might seem that determination of the absorbed dose is fairly straight-
forward. Unfortunately the situation is not that simple. The main problem lies in
the determination of mass of the gas. Since the electric field inside an ionization
chamber is not uniform, the charge collection is not the same at all locations. The
easiest way to account for these nonlinearities is to use an effective mass instead.
This effective mass is calculated by calibrating the detector.
Bragg-Gray cavity theory has many limitations. For example, it assumes that the
cavity is infinitesimally small, which certainly is not true. Another problem is that
it assumes that the walls of the cavity are of the same material as the medium. Since
most ionization chamber dosimeters are constructed with graphite walls therefore
they do not quite meet this condition. Uniform irradiation of the cavity is another