Lattice-constant variation of the barium4flevel

The unoccupied $4f$-level position relative to the Fermi energy in barium metal, ${\Delta }_{+}(f^0\to f^1)$, is estimated as a function of lattice constant. Total energies for initial and final states are obtained via Hartree-Fock-Wigner-Seitz band calculations based on renormalized atom crystal potentials, and ${\Delta }_{+}$ is derived from differences between such energies. At normal pressure ${\Delta }_{+}$ spans an energy range centered at 10.6 eV with a width of 4.9 eV, values which are in reasonable accord with a recent experiment. The $4f$ excitation spectrum is found to move progressively higher in energy with decreasing lattice constant. Results are contrasted with one-electron band calculations and implications for the superconducting behavior of barium are discussed.