Improvements in the understanding of the spectrum and photodetachment of Ce$^-$*

We have undertaken new relativistic configuration interaction calculations of the electron affinity of the $4f~5d^2~6s^2$ $^4$H$_{7/2}$ Ce$^-$ ground state in an effort to resolve the differences among our earlier work\footnote{S. M. O'Malley and D. R. Beck, Phys. Rev. A {\bf 61}, 034501 (2000)} (428 meV), newer calculations\footnote{X. Cao and M. Dolg, Phys. Rev. A {\bf 69}, 042508 (2004)} (530 meV), and the much larger experimental value\footnote{V. T. Davis and J. S. Thompson, Phys. Rev. Lett. {\bf 88}, 073003 (2002)} (955 meV). Inclusion of correlation involving the $4f$ electron brings us in good agreement with the other calculation$^3$ (511 meV), but addition of core-valence effects that would further bind the system is prohibitively difficult: several eV of core-valence correlation disrupts the relative positioning of the valence correlation configurations, resulting in unacceptable (up to $\sim$30\%) losses in their energy contributions. Thus, instead of opening the core, we have made a series of photodetachment cross section calculations. These results, along with a reinterpretation of the experimental data$^4$, lead us to a new value for the Ce$^-$ electron affinity of $\sim$660 meV.