  In the first paper of this series, we study the level population problem of
recombining carbon ions. We focus our study on high quantum numbers
anticipating observations of Carbon Radio Recombination Lines to be carried out
by the LOw Frequency ARray (LOFAR). We solve the level population equation
including angular momentum levels with updated collision rates up to high
principal quantum numbers. We derive departure coefficients by solving the
level population equation in the hydrogenic approximation and including low
temperature dielectronic recombination effects. Our results in the hydrogenic
approximation agree well with those of previous works. When comparing our
results including dielectronic recombination we find differences which we
ascribe to updates in the atomic physics (e.g., collision rates) and to the
approximate solution method of the statistical equilibrium equations adopted in
previous studies. A comparison with observations is discussed in an
accompanying article, as radiative transfer effects need to be considered.
