Physics and Engineering of Radiation Detection

3.8. Detector Efficiency 207

which the electric lines of force are passing through. Hence the electric field intensity
due to a sheath of charges is given by

Eδx=

eEγN 0

2 Wv+hb

e−μρxδx

(

1 −e−μρx

)

. (3.7.36)

Now to obtain the space charge induced electric field at the edges of the volume
enclosed by the electrodes we integrate the above relation over all wholex.

E+ =

eEγN 0

2 Wv+hb

∫d

x=0

e−μρx

(

1 −e−μρx

)

dx

=

eEγN 0

4 Wv+μρhb

[

1+e−^2 μρd− 2 e−μρd

]

(3.7.37)

Equations 3.7.37 and 3.7.28 can be used to determine the effective electric field
inside a gaseous detector illuminated with a photon beam. The factorshandbin
equation 3.7.37 can be determined from the cross sectional area of the photon beam,
diffusion coefficientDof the filling gas for positive ions, and the charge integration
timeτof the readout circuitry through the relations

h = h∗+2

√

6 Dτ (3.7.38)

and b = b∗+2

√

6 Dτ, (3.7.39)

whereh∗andb∗are the height and breadth of the incident photon beam.

3.8 DetectorEfficiency

Now that we know about the different sources of error and their impact on detector
performance, we can appreciate the fact that it is not practically possible to build
a detector that is 100% efficient. If we could, such a detector would detect and
measure the radiationas it isand not as itsees it. We can intuitively think that the
detection efficiency of a gas filled detector would depend on many factors, such as
detector geometry, type of filling gas, gas pressure and temperature, type of incident
radiation, type of electronic circuitry etc. etc. The intuition is correct and leads to
the problem that with so many parameters, it is fairly difficult, if not impossible,
to analytically calculate the absolute efficiency of the system. However if we are
really hard pressed to do that, the easier way to proceed would be to decompose the
overall efficiency in components related to different parameters or sets of parameters.
The individual efficiencies would then be easier to handle analytically. To make
this strategy clearer, let us follow the path of a radiation beam through a parallel
plate ionization chamber. As the beam passes through the entrance window of
the chamber, a part of it gets parasitically absorbed in the window material. This
implies that we can assign an efficiency to the system that tells us how effective
the window is innotabsorbing the radiation. Let us call itηw. The beam of
particles then passes through the filling gas of the chamber and deposits some of
its energy. Now, a number of factors affect this absorption of energy by the gas
molecules. Let us lump them together in an absorption efficiency and represent it
byηg. The absorbed energy can produce electron ion pairs through processes that
we know are not 100% efficient (see chapter 2). Let us represent this efficiency by