Environmental Engineering Reference
In-Depth Information
imental form of the rate constant for this process testifies to the role of the ion-
atom exchange interaction.
Three body recombination of positive and negative ions follows the scheme
A
C
C
B
C
A
C
C
!
B
C
C
.
(2.90)
The process gives rise initially to a bound state of the positive and negative ions
A
C
and
B
, then a valence electron transfers from the field of atom
B
to the field of
ion
A
C
, and the bound state decays into two atoms
A
and
B
. The second stage of
the process occurs spontaneously during the approach of the negative and positive
ions, so the three body recombination is determined by formation of the bound
state of these ions.
We can estimate the rate constant for process (2.90) using the Coulomb interac-
tion between the ions and a polarization interaction between each ion and atom.
Assuming the atomic mass to be comparable to the mass of one of the ions, we use
estimation (2.40) for the cross section of the atom-ion collision and the Thomson
formula (2.68) for the rate constant for the three body recombination process. As a
result, we have
T
3
α
1/2
e
6
e
2
M
D
N
i
K
.
(2.91)
Criterion (2.69) for the validity of the Thomson theory gives
[
C
]
e
2
(
e
2
)
1/2
T
3/2
α
1 .
(2.92)
Inserting the atom polarizability
, which is about several atomic units, into for-
mula (2.92), we find that at room temperature the number density [
C
]mustbe
much less than 10
20
cm
3
. Hence, the criterion for the three body character of re-
combination of positive and negative ions is fulfilled if the gas pressure is of the
order of 1 atm.
α
2.3.3
Three Body Processes Involving Excited Atoms
Three body processes in a dense plasma may change the composition of this plas-
ma. In particular, if excited atoms partake in this process, the formation of excited
molecules may change both the radiative properties of this plasma and the subse-
quent rate of decay of excited states. As an example of this type, we consider the
formation of excited (metastable and resonantly excited) molecules in inert gases.
Atoms of these gases have a
n
p
6
valence electron shell, and excited states have an
n
p
5
(
n
1)s electron shell. The process of formation of excited molecules proceeds
according to the scheme
C
A
C
A
2
C
2
A
!
A
.
(2.93)
Table 2.13 contains the rate constants for process (2.93) at room temperature.
