**4.5. Testcase #5**

In this example we illustrate how PopRatio may be used to calculate the cooling rate due to collisional excitation of low-lying levels of a given atom or ion.

As an example we take the ion Fe^{+}, because iron is an
astrophysically abundant element.
The ion Fe^{+} may be the dominating ionization stage in low
ionization regions, and
may be an important gas coolant
[30].

The cooling rate is given by [4]:

Rewriting this in terms of the total Fe^{+} density
*n*_{Fe+} =
_{i} *n*_{i}
and the population ratios
*X*_{i} = *n*_{i+1} / *n*_{1}:

with the energies *E*_{i} expressed in cm^{-1}. The
Fe^{+} density will depend on its
fractional abundance and on the iron elemental abundance:

Here we calculate the *cooling function*, defined as the right hand
side of eq. (26).

Since Fe^{+} has a complicated electronic structure,
several levels must be taken into account in the calculation. We employ
a 16-level model ion,
allowing us to calculate the cooling function for electronic densities
as high as 10^{4} cm^{-3}.

To run this testcase the user does not need to modify function URAD, since no fluorescence transitions are loaded in.