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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 lambda (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 lambda from the linear system of equations (2), reducing its order by one.

Initially, for notation purposes let us define:

Equation 9 (9)

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

Equation 10 (10)

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

Equation 11 (11)

Solving for nlambda in eq. (11), substituting in eq. (10) and introducing the indirect excitation rate from level i to level j through level lambda as:

Equation 12 (12)

with Gammaijlambda = 0; we can now rewrite eq. (10) as,

Equation 13 (13)

And we have eliminated the equation involving nlambda. 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:

Equation 14 (14)

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