Environmental Engineering Reference
In-Depth Information
2.4.3
Radiative Transitions in Atoms
In considering radiation processes in a gas, we pay attention to two of them -
dipole radiative transitions in atoms and photorecombination radiation involving
electrons and ions of a plasma. We analyze interaction of atomic particles of an
ionized gas with a weak electromagnetic field as occurs in gas discharges, so the
intensity of this electromagnet field is small in comparison with the corresponding
atomic value, and therefore typical times for radiative transitions are large com-
pared with typical atomic times. One more small parameter affects this interaction
when valence electrons partake in radiative transitions and their typical velocity
is small compared with the speed of light
c
. A parameter of radiative transitions
with a small value is the fine structure constant
e
2
/(
α
D
„
c
)
D
1/137, where
e
is
is the Planck constant,
c
is the light velocity, and
e
2
/
the electron charge,
is a
typical atomic velocity of valence electrons in their orbits. If we characterize a ra-
diative transition between two atomic states by the radiative lifetime of the upper
state with respect to the radiative transition
„
„
τ
r
, for the strongest transitions this
o
r
3
10
17
s is the atomic time and
lifetime is
τ
τ
D
α
τ
0
,where
τ
D
2.42
r
0
10
11
s.
In addition, we will consider the strongest interaction between the radiation field
and an atomic system whose interaction operator has the form
V
o
r
τ
D
6.2
D
ED
[148],
where
E
is the electric field strength of the radiation field, and
D
is the dipole mo-
ment operator of the atomic system. Therefore, the strongest radiative transitions
are called dipole transitions and connect transition states with nonzero matrix el-
ements of the dipole moment operator. We restrict ourselves below to only such
radiative transitions. The upper excited state of a radiative transition is named a
resonantly excited state if the dipole radiative transition in the ground state is pos-
sible from this state. For example, for the helium atom this state is He(2
1
P
)and
for the resonantly excited argon atoms the states are Ar(3
3
P
1
)andAr(3
1
P
1
). Ta-
ble 2.21 lists parameters of radiative transitions involving the lowest excited states
of helium and argon atoms. Note that the radiative lifetime for these transitions
exceeds
o
r
, because the interaction is shared between many excited states and the
transition energy is less than the atomic one.
We also give the expression for the rate of dipole radiation [148, 150, 151], that
is, the lifetime
τ
r
of a resonantly excited state with respect to spontaneous radiative
transition to a lower state
1
τ
τ
4
ω
3
2
2
e
2
g
0
m
e
c
3
g
ω
2
g
0
r
D
c
3
jh
o
j
D
jij
D
f
o
.
(2.112)
3
„
Here indices
o
and
relate to lower and upper states of the radiative transition,
D
is the dipole momentum operator,
is the transition frequency,
g
0
and
g
are the
statistical weights of lower and upper transition states,
c
is the light velocity, and the
oscillator strength
f
o
for transition between states
o
and
ω
is given by [152, 153]
2
m
e
ω
2
m
e
ω
2
g
D
2
g
f
o
D
e
2
jh
o
j
D
jij
e
2
j
D
j
.
(2.113)
3
„
3
„
