Chemistry Reference
In-Depth Information
V
AB
−
(
is the interaction between the resonant
AB
−
state
and the electron-molecule scattering continuum, and
J
R
)
,
V
0
(
R
)
=
V
AB
(
R
)
,
V
dk
(
R
)
(
R
)
=
V
d
k
i
(
R
)
χ
ν
i
(
R
)
. Energy
conservation implies
E
=
k
i
/(
2μ
)
+
ω
ν
i
=
k
f
/(
2μ
)
+
ω
ν
f
with μ as the reduced
electron-molecule mass.
The shape of the vibrational excitation cross section depends on the imaginary
part of
F
[see (9.80) and (9.82)]. When it is large
compared to the inverse period of vibration in the resonant state, that is, for a short-
lived resonance, the cross section is smooth. For a long-lived resonance, that is,
when
(
R
,
R
;
E
)
, that is, on
(
R
,
R
;
E
)
is much smaller than the period of vibration, the cross sections
consist of a series of peaks reflecting the vibrational states of the resonant state.
This dependence of the cross section on the lifetime of the resonance is illustrated in
Figure 9.16.
When the energy exceeds the dissociation energy,
dissociation
may occur, either
indirectly through the resonant state, or directly through a transition to the continuum
of the nuclear motion of the molecule. The indirect process only contributes when the
target is initially in a highly excited vibrational state [91]. Usually, the direct process
dominates. For large enough energies, the adiabatic approximation applies and the
dissociation cross section is given by
(
R
,
R
;
E
)
=
(
2π
)
4
d
σ
ν
i
→
ω
f
2
d
|
T
ω
f
ν
i
(
f
,
i
)
|
f
(9.98)
k
i
with
dRF
∗
ω
f
(
T
ω
f
ν
i
(
f
,
i
)
=
R
)
t
(
f
,
i
,
R
)
F
ν
i
(
R
)
,
(9.99)
where
t
(
f
,
i
,
R
)
is the electronically elastic fixed-nuclei scattering amplitude and
F
ω
f
(
R
)
is a continuum nuclear wave function of the molecule.
E
E
σ
σ
0
-
0
0−0
V
d
E
E
V
0
V
0
V
d
(a)
R
(b)
R
FIGURE 9.16
Illustration of resonant vibrational excitation of a molecule for a large (a) and
a small (b) imaginary part of
F
(
R
,
R
;
E
)
. The dashed line indicates the dissociation threshold,
V
0
(
R
)
is the potential energy surface of the molecule,
V
d
(
R
)
is the potential of the auto-
detaching resonant state of the negatively charged molecule, and the insets show the typical
shape of the cross section for the two cases.
