Environmental Engineering Reference
In-Depth Information
Figure 2.11 gives the values of the function
f
(
x
) which follow from measuring
cross sections of atom ionization by electron impact if an atom contains valence
s
electrons. The Thomson model gives a value that differs from the values obtained
from measurements. In particular, at
x
1.6 the value of
f
(
x
) according to the
Thomson model is twice the measured value, and at
x
D
100 the value of
f
(
x
)ac-
cording to the Thomson model is half the measured value. In addition, the Thom-
son model gives the maximum
f
(
x
)at
x
D
D
2, whereas according to measurements
this maximum is observed at
x
5. Nevertheless, the Thomsonmodel gives the
correct behavior of the ionization cross section and is useful for certain estimations
because of its simplicity. In particular, according to the Thomson model the ioniza-
tion cross section is linear with respect to the energy excess
D
4
J
near the threshold
and this differs slightly from the precise energy dependence [48], although practi-
cally the difference between the correct and model energy dependencies for the
ionization cross section is not of importance.
There is another deficiency of the Thomson formula (2.60). In the course of its
derivation we assume a bound electron to be motionless. If we do not make this
assumption,theninthelimitofhighenergiesofanincidentelectronweobtain
ε
Figure 2.11
The reduced cross sections
of ionization of atoms and ions by elec-
tron impact with valence
- [103]; 11 - [104]; 12 - [105]. Approxima-
tion
x
C
8)] is
given by the solid curve and approximation
f
f
(
x
)
D
10(
x
1)/[
π
x
(
electrons versus
the reduced electron energy. Experiment:
1 - [95]; 2 - [96]; 3 - [97]; 4 - [98]; 5 - [99];
6 - [100]; 7 - [100]; 8 - [101]; 9 - [102]; 10
s
(
x
)
D
10(
x
1)/[
π
(
x
C
0.5)(
x
C
8)] is
represented by the dashed curve.
