  We present fluxes in both neutral carbon [CI] lines at the centers of 76
galaxies with FIR luminosities between 10^{9} and 10^{12} L(o) obtained with
Herschel-SPIRE and with ground-based facilities, along with the J=7-6, J=4-3,
J=2-1 12CO and J=2-1 13CO line fluxes. We investigate whether these lines can
be used to characterize the molecular ISM of the parent galaxies in simple ways
and how the molecular gas properties define the model results. In most
starburst galaxies, the [CI]/13CO flux ratio is much higher than in Galactic
star-forming regions, and it is correlated to the total FIR luminosity. The
[CI](1-0)/CO(4-3), the [CI](2-1) (2-1)/CO(7-6), and the [CI] (2-1)/(1-0) flux
ratios are also correlated, and trace the excitation of the molecular gas. In
the most luminous infrared galaxies (LIRGs), the ISM is fully dominated by
dense and moderately warm gas clouds that appear to have low [C]/[CO] and
[13CO]/[12CO] abundances. In less luminous galaxies, emission from gas clouds
at lower densities becomes progressively more important, and a multiple-phase
analysis is required to determine consistent physical characteristics. Neither
the CO nor the [CI] velocity-integrated line fluxes are good predictors of H2
column densities in individual galaxies, and X(CI) conversion factors are not
superior to X(CO) factors. The methods and diagnostic diagrams outlined in this
paper also provide a new and relatively straightforward means of deriving the
physical characteristics of molecular gas in high-redshift galaxies up to z=5,
which are otherwise hard to determine.
