Chemistry Reference
In-Depth Information
formalisms are applied for the estimation of ionization cross sections, for example,
the formalism of Lotz [24], Gryzinski [25], Born-Bethe [26], Deutsch-Märk [27],
or Kim [28,29].
For example, the formalism by Gryzinski provides for the ionization cross section
the formula
ε
H
ε
nl
U
3
/
2
1
U
·
−
1
a
0
·
σ
nl
=
4π
·
ξ
nl
·
·
U
+
1
1
1
ln
2.7
2
3
·
1
2
U
·
+
−
·
+
(
−
1
/
2
U
1
)
(3.113)
with
U
ε
nl
, σ
nl
the ionization cross section of the
nl
sub-shell which emit the
electron, ε the energy of the impinging electron, ε
nl
the electron bond energy in the
nl
sub-shell, ξ
nl
the number of equivalent electrons in the
nl
sub-shell,
a
0
the Bohr
radius (5.29
≡
ε
/
·
10
−
11
m), ε
ion
the ionization energy of the hydrogen atom (13.6 eV).
In particular, the electron impact ionization of molecules provides different ion-
ization channels due to the dissociative ionization of the parent molecule. In the case
of the dissociative ionization of molecules, the partial ionization cross section σ
ion
n
)
for each positive fragment ion (
n
) is introduced. The summation over all partial
ionization cross sections provides the total ionization cross section σ
ion
total
(
ε
(
ε
)
of the
molecule
σ
ion
total
(
ε
)
=
σ
ion
n
(
ε
)
.
(3.114)
n
According to the difficulty in the cross section calculation the measurement of ion-
ization cross sections is unavoidable in many cases. For example, the electron impact
ionization of the CF
4
molecule produce no stable ionized parent molecule, but all
single charged fragment ions are observed, such as CF
3
,CF
2
,CF
+
,C
+
, and F
+
,see
Figure 3.22.
3.3.3.6 Cross Section of the Neutral-Neutral Reaction at Thermal Velocity
with Threshold Energy
The energy dependence of the collision cross section in reaction between neutral
particles near the threshold energy can be estimated using the conservation of the
angular momentum (3.115) and energy (3.116) for the case of neglecting interaction
potential, see also [36].
v
th
·
b
=
v
φ
·
b
eff
.
(3.115)
Here
v
th
is the thermal velocity and
v
φ
the angular component of the velocity at the
effective impact parameter
b
eff
for the reaction:
m
red
2
·
m
red
2
·
v
th
=
v
2
φ
+
ε
=
ε
thres
.
(3.116)
