Environmental Engineering Reference
In-Depth Information
2.2
Inelastic Processes Involving Electrons
2.2.1
Excitation and Quenching of Atoms by Electron Impact
The average electron energy in a gas is usually small compared with the excitation
energy of atoms, and therefore excitation of atoms in a weakly ionized gas proceeds
in the tail of the energy distribution function of electrons. Hence, we need the
threshold cross section of atom excitation by electron impact for the analysis of the
character of atom excitation in an ionized gas. In the other limiting case, when the
electron energy exceeds significantly the excitation energy, the cross section is given
by the Born approximation [2, 75-77]. The maximum cross sections corresponds
to excitation of resonantly excited states when the excitation cross section is given
by the Bethe formula [2, 75, 76, 78, 79]:
ε
Δ
ε
ε
Δ
ε
,
e
4
Δ
ε
π
Δ
ε
4
2
π
2
σ
D
a
0
j
(
D
x
)
0
j
Φ
D
f
0
Φ
0
2
ln
C
p
x
x
Φ
(
x
)
!
,
x
!1
.
(2.48)
Here indices 0 and
refer to the initial and final states of the excitation process,
ε
is the electron energy,
is the excitation energy,
e
is the electron charge,
a
0
is the
Bohr radius, (
D
x
)
0
is the matrix element for the atom dipole moment projection
between the transition states,
f
0
is the oscillator strength for this transition, and
C
is a constant. Thus, in the case of excitation of resonantly excited states, the exci-
tation cross section is expressed through parameters of radiative transitions for the
atom. This analogy follows from an analogy between the interaction operator of a
fast charged particle in an atom and the interaction operator of an electromagnetic
wave and an atom [76, 79-82].
One can continue this formula on the basis of experimental data to electron en-
ergies
Δ
ε
[83]. Then ac-
counting for the threshold dependence of the excitation cross section [2, 84], we
find for the cross section near the threshold for excitation of resonantly excited
states [83, 85, 86]
ε
which are comparable with the atom excitation energy
Δ
ε
a
p
e
4
f
0
Δ
ε
2
π
σ
(
ε
)
D
ε
Δ
ε
,
(2.49)
0
5/2
and the numerical coefficient from experimental data is [83, 85]
a
D
0.130
˙
0.007 .
(2.50)
Formulas (2.48)-(2.50) can be used for determination of the excitation rate con-
stants for atom excitation by electron impact in a gas discharge plasma [86, 87].
We determine below the cross section and rate constant for quenching of a reso-
nantly excited atom by a slow electron. Atom quenching is an inverse process with
