11.2. Quantities Related to Dosimetry 621
condition, which is not always possible to satisfy. However the good news is that
even if one does not account for these anomalies the computed dose values are
generally correct by more than 95% for well designed dosimeters. A well designed
dosimeter usually refers to a chamber with walls made of a lowZmaterial such as
graphite. If the walls are made of highZmaterials, the Bragg-Gray theory gives false
results. The reason for this anomaly lies in the way the right hand side of equation
11.2.34 is computed. In Bragg-Gray theory this quantity, that is the stopping power
ratio, is calculated by using the spectrum of the electron fluence, which has been
computed in the continuous slowing down approximation. In this approximation
the production ofδ-electrons during the slowing down process of primary electrons
is completely neglected. Now, if theseδ-electrons are also taken into account then
the total electron fluence is much larger, especially at the low end of the energy
spectrum. This effect is more pronounced if the walls of the cavity are made of high
Zmaterials, which favor the production ofδ-electrons.
G.2 Spencer-AttixCavityTheory
The main shortcoming of the Bragg-Cavity theory, the fact that it does not take
into account theδ-electrons, was overcome by the Spencer-Attix Cavity theory. In
this theory theδ-electrons are divided into two distinct groups based on the energy
they possess. The first group contains theδ-electrons that are locally absorbed
and thus do not contribute to the electron fluence. The other group represents the
rest of theδ-electrons that have energy high enough to escape the local absorption.
These electrons do contribute to the total electron fluence. The energy level used
to distinguish between these two groups is traditionally represented by the symbol
. Although there are different ways in which this energy can be defined, the
original definition proposed by Spencer and Attix is still the most widely used. This
definition is based on the idea that should correspond to the energy needed by an
electron to cross the cavity. This implies that depends on the cavity dimensions
and can therefore be easily calculated.
The result of includingδ-electrons in the fluence spectrum is that the total elec-
tron fluence assumes a higher value. Note that the basic formula to compute the
dose in the Spencer-Attix cavity theory is the same as in the Bragg-Gray cavity
theory, that is
Dmed
Dcav=
( ̄
L
ρ)med,cav,. (11.2.39)
where, as in the case of Bragg-Gray equation, the term on the right hand side
represents the ratio of the stopping powers in the medium to that in the cavity, that
is (
L ̄
ρ
)med,cav,≡
(
L/ρ ̄)
( med,^
L/ρ ̄)
cav,. (11.2.40)
The stopping power as defined here is different from the one calculated in the Bragg-
Gray cavity theory. Here it is evaluated consideringδ-electrons as well. In terms of
conventional notation for stopping power, we can write the equivalence
( ̄
L
ρ
)
≡
(
1
ρdE
dx)
unres