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

Low Frequency Carbon Radio Recombination Lines I: Calculations of Departure Coefficients