Environmental Engineering Reference
In-Depth Information
the radiative lifetime for a given transition with wavelength
. Note that the ex-
cited states under consideration correspond to 4s and 4p valence electrons and a
3p hole, and the only quantum number of these states is the total momentum
J
that results from summation of momenta of the core (ion) and valence electrons.
Along with the Paschen notation, which is 2s
5
...2s
2
for states with a 4s valence
electron and 2p
10
...2p
1
for states with a 4p valence electron, the notation is given
for a certain scheme of the momentum summation. Namely, 4s and 4p correspond
to the total momentum 3/2 for the total core momentum, and 4s
0
and 4p
0
relate
to the case when the total core momentum is 1/2. The result of summation of the
total core momentum with the orbital momentum of an excited electron is given
in the square brackets, and the total atom momentum, which is a sum of this mo-
mentum and the spin of the valence electron, is given as a subscript. This scheme
of momentum summation is based on some hierarchy of interactions that is not
realized for a 4p valence electron and hence it is used to denote atomic levels.
λ
2.4.4
Photoionization and Photorecombination Processes
The photoionization process proceeds according to the scheme
A
C
,
„
ω
C
A
!
e
C
(2.114)
and the opposite process, the process of photorecombination, is
A
C
!„
ω
C
e
C
A
.
(2.115)
We first derive the connection between the cross sections of processes (2.114) and
(2.115) on the basis of the principle of detailed balance, which has the form
g
rec
σ
rec
j
i
D
g
ion
σ
ion
j
p
,
where
r
are the cross sections of photoionization and photorecombination,
respectively,
g
ion
and
g
rec
are the statistical weights for these states, and
j
e
and
j
p
are the fluxes of electrons and photons in these channels. Taking the statistical
weights as the number of states per electron or photon, we have
σ
i
and
σ
g
e
g
i
4
π
k
2
dk
(2
2
4
π
q
2
dq
(2
g
rec
D
,
g
ion
D
g
a
,
π
)
3
π
)
3
where
g
e
,
g
i
,and
g
a
are the statistical weights of an electron, an ion, and an atom
with respect their electronic states,
k
and
q
are the wave vectors of a photon and an
electron, the factor 2 accounts for two photon polarizations, and we consider the
ion to be motionless. Because one photon is located in this volume
Ω
,wehave
for a photon flux
j
p
D
c
/
Ω
andanelectronflux
j
e
D
v
e
/
Ω
,where
c
is the light
velocity and the electron velocity
v
e
D„
q
/
m
e
. Using the conservation of energy for
these transitions,
2
q
2
2
m
e
C
„
„
ω
D
J
,
