4.5. Sources of Error in Liquid Filled Ionizing Detectors 237
The (∗) sign above represents the excited state of the molecule. The de-excitation
could be by emission of a photon or, in case of multi-atomic complex molecules, by
molecular dissociation into smaller fragments. The latter is a radiationless process.
A good example of such an impurity is the oxygen molecule, which is very commonly
found even in highly purified liquids.
There are also some molecular species that emit the electron after capturing it.
Such a reaction is written as
e+(XY)(XY)−. (4.5.2)where the () sign represents the fact that the process of electron capture is re-
versible. A common example of such an impurity is the carbon dioxide molecule.
To understand the deteriorating effect of electron capture by an impurity molecule
on the detector response, we first note that the capture introduces an effective
negative charge on the molecule. The reader should recall that the output signal of
an ionization chamber has two edges: a fast rising edge and a slow falling edge. The
fast rising edge is almost exclusively described by the movement of negative charges
towards the anode. The introduction of heavy and slow moving negative ions in
the electron population produces larger slope in the rising edge and can even reduce
the signal height (the signal height depends on the movement of both positive and
negative charges). Hence for liquids, having higher molecular density, the electron
capture process can be a source of nonlinearity in the detector response.
Let us now see how we can numerically describe this parasitic capture process.
The reader may recall that earlier in the Chapter we had described the survival of
electrons in a liquid by an exponential function of the form (cf. equation 4.3.4)
N=N 0 e−μcx, (4.5.3)whereN 0 represents the initial number of electrons,N is the number of electrons
that have survived after traversing a distancex. μcis the capture coefficient for
electrons in the liquid. The capture coefficient depends not only on the type of
the medium but also on the energy of electrons. In most situations the electrons
are in thermal equilibrium with the liquid molecules and therefore we can use the
capture coefficient at the mean thermal energy for the liquid under consideration.
Using equation 4.5.3 we can define the probability of capturePcand probability of
survivalPsthrough the relations
Pc =N 0 −N
N 0
=1−e−μcx (4.5.4)Ps =N
N 0
= e−μcx. (4.5.5)Sinceμcin the above relations has the units of inverse distance, we can define a
termcapture mean free pathλcthrough the relation
λc=1
μc