Environmental Engineering Reference
In-Depth Information
intersection of electron states takes place at the distance between nuclei
e
2
R
c
D
EA
,
(2.85)
J
where EA is the electron binding energy in negative ion
B
(the electron affinity
of atom
B
)and
J
is the ionization potential of atom
A
. The transition transferring
the electron from the field of one atomic particle to the other takes place near the
intersection distance
R
c
.
Resonant collision processes are characterized by
0 at infinite distances
between colliding particles, and a small Massey parameter corresponds to these
processes at finite distances between particles. Hence, resonant processes proceed
effectively. One can consider a resonant process as an interference of the states
between which the transition proceeds. Then the transition probability is approxi-
mately1ifthephaseshiftis
R
Δ
ε
Δ
ε
D
1. Thus, the cross section of a resonant
process is of the order of
R
0
,where
R
0
is the collision impact parameter for which
the phase shift is of the order of unity, that is [44],
(
R
)
dt
/
„
R
0
, w e
Z
Δ
ε
(
R
)
dt
„
σ
π
1 .
(2.86)
Letusconsiderasanexampletheexcitationtransferprocess
A
C
A
.
A
!
A
C
This process can cause broadening of spectral lines. The interaction potential of
the atoms in the ground and excited states is
U
D
2
R
3
,where
D
is the matrix
element of the dipole moment operator between these states and
R
is the distance
between the atoms. From (2.86), the cross section of this process (
R
0
,where
σ
(
D
2
/
R
0
)(
R
0
/
v
)
„
)is
CD
2
„
v
σ
D
,
(2.87)
2
/(
m
e
e
2
) is the Bohr radius, and
where
C
1. Because
D
ea
0
,where
a
0
D„
e
2
/
v
, from this it follows that the cross section of resonant excitation transfer
is much larger than a typical atomic cross section,
„
a
0
.
In the case of a nonresonant excitation transfer process
σ
A
C
B
B
!
A
C
the process is effective if the excitation energies for atoms
A
and
B
are nearby
in accordance with the Massey criterion (2.83). As an example, we represent in
Figure 2.20 the rate constant for the process of excitation transfer from metastable
helium atoms to neon atoms in 2s states (for Pashen notations of levels) [128]. This
process is the basis of operation for the He-Ne laser using a He-Ne mixture. In a
gas discharge plasma, metastable helium levels are excited effectively, and transfer
of their excitation to neon atoms creates an inverse population of levels that is
necessary for laser operation.
