Environmental Engineering Reference
In-Depth Information
Figure 2.29
The cross section of photoattachment of electrons to halogen atoms [160].
2.4.5
Bremsstrahlung in Ionized Gases Involving Electrons
Along with bound-bound and bound-free radiative transitions which are accom-
panied by photon emission, free-free transitions are possible in collisions of two
atomic particles, and below we consider bremsstrahlung resulting from electron
scattering by ions and atoms. In these processes electrons are free both before and
after collision. Our goal is to find the cross section of bremsstrahlung resulting
from electron scattering by ions and atoms, and we start from the classical formula
for radiation of an atomic particle. Then we use (2.112) for the radiative rate and
take the initial
i
and final
k
states of this transition to be classical. The total intensity
of this transition according to (2.112) is
ik
3
c
3
jh
D
ik
D
„
ω
τ
4
ω
4
3
c
3
jh
R
D
ik
2
2
I
ik
r
D
ij
D
ij
,
where
is the transition energy, and in the classical limit we change the matrix
element by the Furie component of the corresponding quantity. Note that this for-
mula includes summation over final states that are close in energy and accounts for
both states with
„
ω
0 (absorption). Restricting
ourselves to radiative processes with emission of photons, we conserve half of the
total radiation intensity in this sum, which in the classical limit gives
ω
>
0 (emission) and states with
ω
<
2
3
c
3
j
R
D
j
2
.
I
D
(2.127)
Since for a scattering electron
D
D
e
r
,where
r
is the electron radius vector, the
intensity of radiation due to scattering of an electron by an atomic particle is pro-
portional to the acceleration squared in the particle field.
