Environmental Engineering Reference
In-Depth Information
section of electron-atom scattering [44, 45]:
L
2
1
3
x
2
,
8
5
x
2
D
πα
q
2
La
0
σ
D
4
π
C
x
.
(2.32)
This cross section has a minimum if the wave vector is
q
min
D
6/5) and the minimal cross section is 25 times less than that at zero electron ener-
gy. Although this analysis using short-range and polarization electron-atom inter-
actions exhibits a deep minimum in the diffusion cross section of electron-atom
scattering at a negative electron-atom scattering length, in reality the minimal
cross section is lower than the cross section at zero electron energy by approxi-
mately two orders of magnitude.
Note that the above analysis relates to electron scattering by a structureless atom.
In the case of electron scattering by atoms with incomplete electron shells, differ-
ent channels of electron scattering are present in the scattering amplitude. As an
example, we consider electron scattering by an alkali metal atom in the ground
state, when the total electron-atom system may have spin
S
D
12
La
0
/(5
πα
)(
x
1, and scattering
proceeds independently for each channel, so at zero electron energy the diffusion
cross section of electron-atom scattering is
D
0
I
D
π
L
0
C
3
L
1
,
σ
(0)
D
σ
t
(0)
(2.33)
where
L
0
and
L
1
are the electron scattering lengths if the total spin of the electron-
atom system is 0 and 1, respectively. These scattering lengths are given in Table 2.4.
Note the importance of resonance
3
P
in electron scattering by alkali metal atoms.
The excitation energy of this autodetaching state
E
r
and its width
Γ
r
are given in
Ta b l e 2 . 4 .
2.1.8
Elastic Scattering of Charged Particles in a Plasma
Let us consider collision of two charged particles, for example, electron-electron
or electron-ion scattering. We first illustrate the Coulomb interaction of particles,
which leads to divergence of the diffusion cross section if particle collision pro-
ceeds in a vacuum. Taking the charge of both particles to be
e
and assuming the
classical character of particle collision, we find the connection between the scat-
tering angle
in the case of scattering into
small angles. Within the framework of standard model, this problem is reduced
to motion of one particle with reduced mass
#
and the collision impact parameter
in the Coulomb field
e
2
/
R
of the
force center, where
R
is the distance of the particle from the center (or the distance
between particles). Assuming in the zero approximation this particle moves along
a straight trajectory, we have for a change of its momentum as a result of collision
with a given impact parameter
μ
[1]
Z
1
e
2
dt
R
2
D
2
e
2
Δ
p
D
,
(2.34)
g
1
