K-Shell Photoabsorption Studies of the Carbon Isonuclear Sequence*

Photoabsorption cross sections for the isonuclear C - C$^{3+}$ ions have been computed using an R-matrix method with the inclusion of important Auger broadening effects. Comparison with existing C$^+$, C$^{2+}$, and C$^{3+}$ experimental results for the lowest $1s\rightarrow 2p,3p$ resonances shows good agreement in general for the resonance strengths and widths, but the computed resonance positions differ from the observed positions by as much as 0.45~eV. Higher $np$ resonances and the above-threshold K-shell photoionization cross sections are also computed in order to produce an entire absorption profile as a function of X-ray photon energy. These computed cross sections are used to model the {\em Chandra} X-ray absorption spectrum of the blazar Mkn 421 near the carbon K-edge, thereby obtaining instrumental and interstellar carbon-ion abundances.