Environmental Engineering Reference
In-Depth Information
From this we obtain for the recombination coefficient for electrons and multi-
charged ions for processes (2.79)
2
1
exp
.
3/2
2
g
ai
g
e
g
Z
π
„
Γ
/
„
E
a
T
e
α
D
(2.80)
m
e
T
e
Γτ
/
„C
One can summarize the qualitative features of electron capture in an autoioniz-
ing state. The process corresponds to excitation of valence or internal electrons of
the ion, accompanied by the capture of an incident electron in a bound state. The
energy of the incident electron coincides with the excitation energy of the autoion-
izing state
E
a
. The above expression for the capture rate constant
k
is obtained from
imposition of the condition of thermodynamic equilibrium among the atomic par-
ticles participating in the process. This requires the Maxwell distribution function
for kinetic energies of the electrons, which leads to the following criterion for the
validity of formula (2.80):
N
Z
k
N
e
k
ee
,
(2.81)
where
k
ee
is the rate constant for the elastic electron-electron collisions that estab-
lish the Maxwell distribution function of electrons. If we have some other energy
distribution function
f
(
ε
) for electrons of energy
ε
, normalized by the relation
R
f
(
ε
)
d
v
D
1, generalization of (2.80) gives
2
3
g
ai
g
e
g
Z
π
„
m
e
Γ
/
„
α
D
f
(
E
a
)
1
.
(2.82)
Γτ
/
„C
This expression also requires that criterion (2.81) be satisfied. This means that
the electron energy distribution function is a Maxwell one in its dominant part.
This makes it possible to introduce the electron temperature; but the tail of the
distribution function, responsible for excitation of the autoionizing state, may be
distorted.
2.2.7
Attachment of Electrons to Molecules
This process results in capture of an electron by a molecule in an autodetachment
level and subsequent decay of a forming negative ion in an autodetachment state,
usually by dissociation of this negative ion [120, 121]. Since this autodetachment
state is characterized by a long lifetime, transfer of excess electron energy to atoms
or molecules of a gas in collisions with them is impossible if the process of elec-
tron attachment occurs in a gas. In any case, the process of electron capture has a
resonant character and results in transition between two electronic states. An ex-
ample of the electron attachment process related to the CO
2
molecule is given in
Figure 2.14 [114], and the corresponding electronic states in Figure 2.15 [115] lead
to two resonances in this process.
Another example of this process is electron attachment to the oxygen molecule in
the ground electronic state O
2
(
3
Σ
g
) that proceeds through formation of the autode-
taching state O
2
(
2
Π
u
). Figure 2.18 shows the dependence on the electron energy
