Physics and Engineering of Radiation Detection

11.4. Active Dosimetry 641

This is all good as long as we wanted to measure the doseinside the chamber.
How we relate this dose to the material surrounding the chamber is something that
can be dealt with by the Bragg-Gray cavity theory. Note that even if the detection
medium and the material surrounding the chamber are under exact same conditions,
the dose calculated from the above expression does not represent the expected dose
in the medium. To apply the Bragg-Gray cavity theory we make use of equation
11.2.34. Substituting the expression forDairin this equation gives

Dmed = Dair

( ̄

L

ρ

)med

air

=

QairWair

eMair

( ̄

L

ρ

)med

air

kt. (11.4.8)

The above equation, though very simple, gives a fairly accurate measure of the
dose, provided the chamber walls are not made of highZelements and the chamber
size is small. As mentioned earlier in the chapter, the dose computed from the
Bragg-Gray theory has a few sources of error, the most important of which are
listed below.

Measuring mass of air in the chamber is not trivial since it has dependence on

temperature and pressure. This is further complicated by the fact that, due

to non-uniformity of the electric field inside the chamber, the charge collec-

tion efficiency deviates from the ideal case. This is compensated in the above

equation by taking aneffective massof air instead of the absolute mass.

The Bragg-Gray theory assumes continuity between the two media. Since

ionization chambers have walls therefore this assumption is not strictly valid

specially for the walls that are made of highZelements.

The irradiation might not be uniform as assumed by the Bragg-Gray theory.

The uncertainties due to these errors are included in the correction factorktin
the above equation with the exception of wall correction, which is generally done
separately. The wall correction is actually a two step process. The first step involves
estimating the dose in the wall material using Bragg-Gray equation 11.4.8. that is

Dwall=

QairWair

eMair

( ̄

L

ρ

)wall

air

kt. (11.4.9)

The dose in the surrounding medium can then be obtained by simply multiplying
the above equation by the ratio of the mass energy absorption coefficients of the
medium and the wall. This gives

Dmed=

QairWair

eMair

( ̄

L

ρ

)wall

air

(μm,en)medwallkt, (11.4.10)

where

(μm,en)medwall≡

(μm,en)med

(μm,en)wall

, (11.4.11)