The population of excited three-electron states in carbon ions after single-electron capture in 0.5-1.1 MeV/amu C 4+ (1s2s 3 S)-He collisions is analyzed theoretically by combining different methods. While the two-center basis generator method is used to calculate capture amplitudes on the single-particle level, all-electron structure calculations for the relevant C 3+ states and their radiative and Auger transition rates are performed on the multiconfiguration Dirac-Fock level. These data are then combined and fed into a set of classical rate equations for the decay dynamics. Total cross sections for the production of the 1s2s2p 4 P , 1s2s2p 2 P − , and 1s2s2p 2 P + states are calculated and their ratios compared with recent experimental data and previous calculations [D. Strohschein et al., Phys. Rev. A 77, 022706 (2008)]. It is found that the relative intensities of the 1s2s2p 4 P states are considerably larger than expected on the basis of pure spin statistics. The Auger transitions, which were not included in the previous calculations, have a significant effect on the final results in that they reduce the 1s2s2p 2 P intensities. Although our extended computations explain a significant part of the production of the 1s2s2p 4 P states, the experimentally observed enhancement of these states is still considerably larger than the theoretical one.1 R = 4 P /( 2 P − + 2 P + ) is used as a shorthand notation for R = Intensity[C 3+ (1s2s2p 4 P )]/(Intensity{C 3+ [1s(2s2p 3 P ) 2 P − ]} + Intensity{C 3+ [1s(2s2p 1 P ) 2 P + ]}).