Chemistry Reference
In-Depth Information
describe the reaction between the neutral particle C and the molecule DE with
threshold energy ε
CD
thres
to produce the particle CD. By use of the cross section σ
CD
thres
1
ε
CDE
thres
ε
σ
CDE
thres
σ
CDE
eff
=
·
−
(3.157)
for ε
≥
ε
CDE
thres
and σ
CDE
=
0forε
<
ε
CDE
thres
, the calculation of the reaction rate coefficient
thres
k
CD
thres
results in
2
3
/
2
exp
1
∞
π
2
·
·
m
red
ε
T
k
B
T
2
ε
T
m
red
·
·
ε
CDE
thres
ε
T
k
CDE
thres
σ
CDE
eff
=
·
·
−
·
−
·
d
ε
T
π
·
k
B
T
ε
CDE
thres
8
exp
exp
.
√
T
·
k
B
T
ε
CDE
thres
k
B
T
ε
CDE
thres
k
B
T
=
σ
CDE
eff
·
m
red
·
−
∼
·
−
(3.158)
π
·
This corresponds to an expression like the Arrhenius function typically for many
chemical reactions with activation energy in thermochemistry.
3.5.4 R
ATE
C
OEFFICIENT FOR
E
LECTRON
I
MPACT
I
ONIZATION
The production rate of single charged positive ions due to direct electron impact
ionization of neutral atoms A in ground state
A
k
A
+
A
+
+
e
+
A
→
e
+
e
(3.159)
is calculated by use of the specific electron impact ionization cross section and
the electron velocity distribution function (nonthermal plasma conditions), and the
particle densities of electrons
n
e
and neutrals
n
A
.
dn
e
dt
dn
A
A
dt
+
=
σ
A
A
v
r
·
n
A
τ
eA
. (3.160)
+
=
·
n
e
·
n
A
=
k
A
+
A
·
n
e
·
n
A
=
ν
e
A
·
n
A
=
The corresponding electron ionization rate coefficient
k
A
A
results in:
∞
σ
A
A
v
r
k
A
+
A
=
·
=
f
e
(
v
r
)
·
v
r
·
σ
A
A
(
v
r
)
·
d
v
r
.
(3.161)
thres
.
Generally, the electron velocity distribution function in (3.161) has to be calculated
by a kinetic equation (Boltzmann equation). The necessary collision cross section in
dependence on the relative velocity is mostly taken from experimental data approxi-
mated by analytical functions, or if available by quantum mechanical calculation or
semiclassical formulas, see Section 3.8.
