202 Chapter 3. Gas Filled Detectors
smaller than the energy of the original electron.
e+(XY..V Z) → (XY..V Z)−∗
(XY..V Z)−∗ → (XY..V Z)∗+e′ withEe′<Ee (3.7.11)Here (XY..V Z) represents a polyatomic molecule. In a proportional counter, the
energy and the point of generation of the second electron may or may not be suitable
to cause an avalanche. This uncertainty can therefore become a significant source
of nonlinearity in the detector’s response if the concentration of such molecular
contaminants in the filling gas is not insignificant.
Not all polyatomic molecules emit secondary electrons during the process of de-
excitation. Some molecules dissociate into smaller molecules such that each of the
fragments is stable. Such a reaction can be written as
e+(XY..V Z) → (XY..V Z)−∗
(XY..V Z)−∗ → (XY)∗+(VZ)−(stable) or (3.7.12)
(XY..V Z)−∗ → (XY..V)∗+Z−(stable). (3.7.13)It is also possible for a fragmented part of the molecule to go in a metastable state
and then decay to ground state by emitting an electron or by further dissociating
according to
e+(XY..V Z) → (XY..V Z)−∗
(XY..V Z)−∗ → (XY)∗+(VZ)−∗
(XY)∗+(VZ)−∗ → (XY)∗+(VZ)∗+e or (3.7.14)
(XY)∗+(VZ)−∗ → (XY)∗+V∗+Z−. (3.7.15)B.3 CapturewithoutDissociation.................
In this process the polyatomic molecule captures an electron and instead of dissoci-
ating into simpler molecules, it transfers its excess energy to another molecule. This
reaction can be written as
e+(XY) → (XY)−∗
(XY)−∗+Z → (XY)−+Z∗
Z∗ → Z+γ. (3.7.16)3.7.C EffectsofSpaceChargeBuildup
We noted earlier that the slow mobility of the positive charges towards cathode
produces a sheath of positive charge cloud between the electrodes. This sheath
moves slowly towards the cathode under the influence of the applied electric field.
The most prominent effect of this charge cloud is that it decreases the effective
electric field intensity and thereby affects the drift of electrons. To quantitatively
understand this effect, let us suppose that we have a parallel plate chamber in which
a cloud of positive ions is moving toward the cathode (see Fig.3.7.1).
Assuming that the positive charge densityρ+is constant throughout the sheath
of charges having a width ofδx, the equation of motion of this cloud of charges can