Lattice-constant dependence of4flevels in Sm metal: Evidence for a bulk valence transition

We have calculated $4f$-level positions in samarium metal as functions of Wigner-Seitz radius $r_{\mathrm{WS}}$ and find that the $4f^6$ state, which is empty at normal pressure, becomes occupied at larger $r_{\mathrm{WS}}$, signaling a trivalent-to-divalent transition. The valence change is estimated to occur for a volume expansion of approximately 8%. One-electron estimates of the $4f$ excitation energies fail to show this behavior. The Coulomb term $U$ is confined to a narrow energy interval over the $r_{\mathrm{WS}}$ range considered.