  Absolute cross sections for the K-shell photoionization of ground-state
Li-like carbon [C$^{3+}$(1s$^2$2s $^2$S)] ions were measured by employing the
ion-photon merged-beams technique at the Advanced Light Source. The energy
ranges 299.8--300.15 eV, 303.29--303.58 eV and 335.61--337.57 eV of the
[1s(2s2p)$^3$P]$^2$P, [1s(2s2p)$^1$P]$^2$P and [(1s2s)$^3$S 3p]$^2$P
resonances, respectively, were investigated using resolving powers of up to
6000. The autoionization linewidth of the [1s(2s2p)$^1$P]$^2$P resonance was
measured to be $27 \pm 5$ meV and compares favourably with a theoretical result
of 26 meV obtained from the intermediate coupling R-Matrix method. The present
photoionization cross section results are compared with the outcome from
photorecombination measurements by employing the principle of detailed balance.
