Environmental Engineering Reference
In-Depth Information
hydrogen atom to the light velocity, and this testifies to the nonrelativistic character
of the motion of valence electrons in atoms. Another small parameter related to
radiative processes in plasmas is the ratio of the electric field of an electromagnetic
wave to a typical atomic field. With the exception of specific cases, this ratio is small,
and so radiative processes in atomic systems involving absorption or emission of
photons usually proceed slowly on atomic timescales.
In external fields, emission of a photon is accompanied by an transition of an
atom to a lower excited state or to the ground state. The lifetime
of an excited
atom with respect to this process is considerably longer than a typical atomic time.
The reciprocal quantity 1/
τ
(the rate of spontaneous radiation) with respect to a
characteristic atomic frequency is measured by the cube of the fine structure con-
stant, [
e
2
/(
τ
c
)]
3
, and hence is lower by at least six orders of magnitude than the
frequency of the emitted photons. In particular, the radiative lifetime of the first
resonantly excited state of the hydrogen atom, H(2p), is 2.4
„
10
9
s, whereas the
10
17
s. The weakness of typical
electromagnetic fields in plasmas allows us to ignore multiphoton processes. In
particular, we can ignore two-photon processes compared with single-photon pro-
cesses. The lowest excited state of the atom from which it is possible to have a
single-photon transition to the ground state is called a resonantly excited state. Ra-
diative transitions involving resonantly excited states of atoms are the main subject
of our consideration.
3
/(
me
4
)
characteristic atomic time is
„
D
2.4
2.4.2
Spontaneous and Stimulated Emission
Radiative transitions between discrete states of an atom or molecule are summa-
rized in a simple fashion in Figure 2.27. We designate by
n
ω
the number of pho-
tons in a given state. This value is increased by 1 as a result of a transition to the
ground (lower) state and is decreased by 1 after absorption of a photon. Because
the absorption rate is proportional to the number of photons present, we write the
probability of photon absorption by one atom per unit time in the form
w
(
o
,
n
ω
!
,
n
ω
1)
D
An
ω
,
(2.108)
Figure 2.27
Collision and radiative transitions between two states.
