Many large-scale numerical simulations of astrophysical plasmas must a
lso reproduce the hydrogen ionization and the resulting emission spect
rum, in some cases quite accurately. We describe a compact model hydro
gen atom that can be readily incorporated into such simulations. It re
produces the recombination efficiency and line spectrum predicted by m
uch larger calculations for a very broad range of densities and temper
atures. Uncertainties in hydrogen collision data are the largest sourc
e of differences between our compact atom and predictions of more exte
nsive calculations and underscore the need for accurate atomic data.