Environmental Engineering Reference
In-Depth Information
2.2.6
Dielectronic Recombination
Dielectronic recombination of an electron and an ion proceeds through electron
capture into an autoionizing state of the combined system, and the subsequent de-
cay of the autoionizing state results from its radiative transition to a stable state.
This process is of importance for recombination of electrons and multicharged
ions because the radiative lifetime of the multicharged ion decreases strongly (pro-
portional to
Z
4
) with increase of its charge
Z
. The process of dielectronic recom-
bination consists of the following stages:
A
C
Z
[
A
C
(
Z
1)
]
,
[
A
C
(
Z
1)
]
!
A
C
Z
e
C
!
C
e
,
[
A
C
(
Z
1)
]
!
A
C
(
Z
1)
C„
ω
.
(2.79)
Denoting the rate constant for the first process as
k
, the radiative lifetime of the
autoionizing state as
, and the energy
of excitation of the autoionizing state [
A
C
(
Z
1)
]
above the ground state as
E
a
,
we obtain the expression for the recombination coefficient for an electron and a
multicharged ion for processes (2.79).
The balance equation for the number density
N
ai
of ions in a given autoionizing
state is
τ
, the width of the autoionizing level as
Γ
dN
ai
dt
D
N
ai
Γ
N
ai
1
τ
N
e
N
Z
k
„
,
where
N
e
is the electron number density and
N
Z
is the number density of ions of
charge
Z
. From this we find the number density of ions in the autoionizing state
N
ai
and the rate of recombination
J
D
N
ai
/
τ
to be
N
e
N
Z
k
N
ai
τ
D
N
e
N
Z
k
Γτ
N
ai
D
,
J
D
1
.
Γ
/
„C
1/
τ
/
„C
The recombination coefficient
α
for processes (2.79) according to definition is giv-
en by
J
N
e
N
Z
D
k
1
.
Assuming there is thermodynamic equilibrium between a given autoionizing
state and other ion states, we have for the number density of atoms in an autoion-
izing state according to the Saha formula (1.52)
α
D
Γτ
/
„C
m
e
T
e
2
3/2
exp
E
a
T
e
,
N
Z
N
e
N
ai
D
g
e
g
Z
g
ai
π
„
2
where
g
e
,
g
Z
,and
g
ai
are statistical weights for the participating atomic states, and
T
e
is the electron temperature. Thermodynamic equilibrium corresponds to
τ
!
1
and for the rate constant
k
for electron capture in this autoionizing state gives
2
exp
.
3/2
2
g
ai
g
e
g
Z
π
„
Γ
„
E
a
T
e
k
D
m
e
T
e
