  The population of meta-stable levels is key to high precision density
diagnostics of astrophysical plasmas. In photo-ionized plasmas, density is used
to infer the distance from the ionizing source, which is otherwise difficult to
obtain. Perfecting models that compute these populations is thus crucial. The
present paper presents a semi-analytic hydrogenic approximation for assessing
the relative importance of different processes in populating atomic levels.
This approximation shows that in the presence of a radiation source, photo- and
collisional- excitations are both important over a wide range of plasma
temperatures and ionizing spectra, while radiative recombination is orders of
magnitude weaker. The interesting case of Fe$^{+21}$ with a collisional
radiative model with photo-excitation demonstrates this effect. The population
of the first excited meta-stable level in Fe$^{+21}$ is sensitive to the
electron number density in the critical range of
$n_e=10^{12}-10^{15}\,\rm{cm}^{-3}$; it was observed to be significantly
populated in the X-ray spectrum of the 2005 outburst of the X-ray binary
GROJ1655-40. The present model shows that photo-excitation is the predominant
process indirectly populating the meta-stable level. For the photo-ionized
plasma in the GROJ1655-40 outflow, the model indicates a measured value of
$n_e=(2.6 \pm 0.5)\times10^{13}\,\rm{cm}^{-3}$ implying a distance from the
source of $r=(4.4 \pm 0.4)\times10^{10}$\,cm. Finally, we show how the computed
critical density and distance of Fe$^{+21}$ yield the correct ionization
parameter of the ion, independent of ionization balance calculations.
