Environmental Engineering Reference
In-Depth Information
where
is the atom polarizability. Then the cross section of ion capture by an atom
is given by (2.21) and has the form
α
s
α
e
2
σ
D
2
π
g
2
,
c
μ
where
g
is the relative ion-atom velocity and
is their reduced mass. The diffusion
cross section of ion-atom scattering in the case of their polarization interaction
exceeds this value by 10% and is [48-52]
μ
s
α
e
2
σ
(
g
)
D
2.2
π
.
(2.40)
μ
g
2
Note that this process usually has classical character, which was used in derivation
of (2.40). Indeed, the collision momentum
l
c
that corresponds to ion-atom capture
is given by
e
2
2
)
1/4
D
μ
g
(2
α
μ
ε
c
„
D
l
c
,
„
where
g
2
/2 is the energy of relative ion-atom motion. In particular, in the
case of collision between a helium atom and a helium ion (
ε
D
μ
1.38
a
0
,themassof
α
D
the helium atom is
m
He
D
7300
m
e
) at relative thermal energy (
ε
D
0.026 eV) this
formula gives
l
c
14, which confirms the classical character of ion-atom capture.
The resonant charge exchange process, involving an atomic ion and a parent
atom, is an ion collision process without energy transfer for the electron's degree
of freedom. This process proceeds according to the scheme
D
!
A
C
C
A
,
A
C
C
A
(2.41)
where the tilde marks a specific particle in this process. The resonant charge ex-
change process is important for transport of atomic ions in a parent gas because
the cross section of resonant charge exchange exceeds the cross section of elastic
ion-atom collisions at thermal collision energies.
The cross section of resonant charge exchange is large in slow ion-atom colli-
sions because of the interference character of this process. Indeed, let us demon-
strate this in the case of collision for a structureless ion or atom, where the valence
electron is found in the
s
state (e.g., H
C
HorHe
C
He). Then the eigenstate of
the quasimolecule
A
2
, that is, the system consisting of ion
A
C
and atom
A
at large
distance from each other, may be composed of the states in Figure 2.9, where the
ion belongs to the first or the second particle [53]. The wave functions
ψ
1
and
ψ
2
describe these states. Owing to the symmetry of this system, the eigenstate wave
functions of the quasimolecule conserve or change their sign as a result of electron
reflection with respect to the symmetry plane, that is, perpendicular to the axis
joining nuclei and passing through its middle. The wave functions
ψ
g
and
ψ
u
of
these states at large ion-atom distances are given by
1
p
2
(
1
p
2
(
ψ
D
ψ
C
ψ
2
),
ψ
D
ψ
ψ
2
),
g
1
u
1
