Environmental Engineering Reference
In-Depth Information
where
n
is the principal quantum number of a bound electron in the initial state,
and an average is performed over other quantum numbers of this electron. The
parameter
σ
K
in this formula is
e
2
„
π
3
p
3
64
c
a
0
D
10
18
cm
2
.
σ
D
7.9
(2.123)
K
Correspondingly, according to the principle of detailed balance (2.116), when the
final atomic state is a highly excited state with principal quantum number
n
,for
the photorecombination cross section, formula (2.122) gives
e
2
„
3
2
a
0
n
3
π
3
p
3
32
2
ω
σ
D
.
(2.124)
rec
c
ω
(
ω
ω
0
/
n
2
)
The Kramers formula corresponds to the limit when both transition states may be
described classically [157]. Transitions between excited states conform to this limit,
and this follows from general tables of parameters of radiative transitions of an
electron that is under the action of the central field [158].
It is of interest to use the Kramers formula (2.122) for photoionization of the
hydrogen atom in the ground state when the classical description of a transfer-
ring electron is not valid. In this case, according to this classical description, the
threshold photoionization cross section is to
K
of (2.123), which is 25% higher
than the accurate value (2.119) of this quantity. This means that two limiting cases
under consideration are able to give correct estimations of radiative parameters for
real cases. Note that when the electron shell of an atom contains several valence
electrons, general characteristics of the above dependencies are conserved [159].
In the same manner as photorecombination, one can consider the process of
electron photoattachment to an atom that proceeds according to the scheme
σ
A
C„
ω
e
C
A
!
.
(2.125)
In particular, Figure 2.29 shows the cross sections of electron photoattachment to
halogen atoms [160], and we can use the principle of detailed balance (2.116) for
these processes, where the statistical weights of the halogen atom and its negative
ion are 6 and 1, respectively, so this formula gives the following connection between
the cross section of photoattachment
σ
at
and the cross section of photodetachment
σ
det
of the negative ion:
)
2
3(EA
C
ε
σ
D
σ
det
,
(2.126)
at
ε
where
ε
is the electron energy, EA is the atom electron affinity, and the photon
energy is
„
ω
D
EA
C
ε
because of the energy conservation. Since for these halo-
gen atoms EA
at
is less by
roughly by six orders of magnitude than the cross section of photodetachment
>
3 eV, the cross section of electron photoattachment
σ
σ
det
of the negative ion in this range of electron energies.
