Valence calculations of binding energies of mid-row lanthanides

Binding energies of mid-row lanthanides have been calculated by taking advantage of the $>$90\% $LS$ purity of the $4f^n$ subgroups of their neutral ground states \footnote{{\it Atomic Energy Levels -- The Rare-Earth Elements}, edited by W. C. Martin, R. Zalubas, and L. Hagan, Natl. Bur. Stand. Ref. Data Ser. Natl. Bur. Stand. (U.S.) Circ. No. 60 (U.S. GPO, Washington, D.C., 1978).}. As described in our recent work on Nd$^-$ \footnote{S. M. O'Malley and D. R. Beck, Phy. Rev. A 77, 012505 (2008).}, the $4f^n$ electrons were treated as core-like and restricted to a single $LS$ term throughout all Dirac-Fock and correlation configurations, resulting in manageable relativistic configuration-interaction calculations for these computationally complex systems. Several weakly bound $6p$ attachments ($<$200 meV) were found for each negative ion, and these were carefully analyzed with respect to approximate $LS$ total configuration as well as the $j$'s of the the $4f^n$ subgroup and $6p$ electron.