  Radiative charge exchange collisions between a carbon atom C(${}^3$P) and a
helium ion He+, both in their ground state, are investigated theoretically.
Detailed quantum chemistry calculations are carried out to obtain potential
energy curves and transition dipole matrix elements for doublet and quartet
molecular states of the HeC+ cation. Radiative charge transfer cross sections
and rate coefficients are calculated and are found at thermal and lower
energies to be large compared to those for direct charge transfer. The present
results might be applicable to modelling the complex interplay of [C II] (or
C+), C, and CO at the boundaries of interstellar photon dominated regions
(PDRs) and in xray dominated regions (XDRs), where the abundance of He+ affects
the abundance of CO.
