Physics and Engineering of Radiation Detection

650 Chapter 11. Dosimetry and Radiation Protection

whereD(L) represents the normalized dose distribution as a function ofLET.Itis
given by

D(L)=

1

ρ

LΦ(L), (11.5.4)

with Φ(L) being the fluence distribution as a function ofLET.
One problem with the use ofLETin microdosimetry is that it does not properly
characterize the differences in the biological effectiveness of different radiation types.
In other words, the biological effectiveness of two types of radiation could be different
even though they might have sameLET. This implies that one should be careful
in using this quantity to derive dosimetric inferences. Because of this particular
reason, the statistical quantities, such as specific energy and lineal energy are more
commonly used.

A.2 SpecificEnergy.........................

The specific energy is defined as the ratio of the energy imparted by radiation to
the matter in a volume to the mass of the matter, that is

z=

E

m

, (11.5.5)

wheremrepresents the mass of the matter andEis the energy imparted. Since the
energy impartation is a statistical process and suffers from random fluctuations, the
specific energy has similar uncertainties associated with it.

A.3 LinealEnergy..........................

The lineal energy is defined as the ratio of the energy imparted to the medium in a
single event to the average chord length, that is

y=

E

̄l. (11.5.6)

whereEis the energy imparted in a single event and ̄lis the average chord length.
The lineal energy is generally measured and computed in units ofkeV μm−^1 .To
understand the average chord length we first note that any particle track in a medium
leaves a number of randomly oriented chords behind. The average length of these
chords is what is represented by the parameter ̄l. In general, both the chord lengths
and their orientations are randomly distributed.
Note that, as with specific energy, here too the imparted energy is a random
variable. Therefore the lineal energy is also a statistical quantity and is described
by its own frequency distribution functionf(y). Now, just likeLET,wecanuse
this distribution to determine the average track lineal energy, that is

y ̄t=

∫

yf(y)dy, (11.5.7)

where we have assumed that the distributionf(y) has been normalized. Similarly
we can also define a dose average lineal energy by

y ̄d=

∫

yD(y)dy, (11.5.8)