**2.2. Fluorescence**

Sometimes we have the situation in which the atom or ion is in one of
its first *m*
lower-lying levels and then it is photoexcited to some higher-lying
level
(e.g., by an
UV radiation field). Next it decays - either spontaneously or by
stimulated emission - back to
some different level among the first *m* levels. We call this
process *fluorescence*.

In this case it is easy to eliminate the level from the linear system of equations (2), reducing its order by one.

Initially, for notation purposes let us define:

The statistical equilibrium equation (2) for some level *l*
belonging to the first *m* lower-lying levels is:

where we have written only the terms involving the level . Whereas the equation for level will be:

Solving for
*n*_{} in
eq. (11), substituting in eq. (10) and
introducing the *indirect excitation rate* from level *i* to
level *j* through level
as:

with
_{ij}^{} = 0; we can now rewrite
eq. (10) as,

And we have eliminated the equation involving
*n*_{}.
Extending this reasoning to eliminate a whole set of *µ*
higher-lying levels is straightforward.
One simply replaces the indirect excitation rates in eq. (13) by the
corresponding
*total indirect excitation rates*: