The low-binding-energy satellite recently observed in the 3d core-level spectrum of metallic lanthanum is considered in view of the (Z+1) approximation. The position of the 4f level in the presence of a hole in the 3d core level in barium metal is also treated from that point of view. The implications of the shake-down, fn fn+1, and shake-up, fn fn-1, satellites in connection with core-level diagnostics for mixed-valence systems are discussed. The valence shift of the 3d core-level position between divalent, trivalent, and tetravalent metallic lanthanide systems is calculated. It is pointed out that these valence shifts have no connection with the Coulomb correlation parameter U. Finally, some expected intrinsic difficulties in connection with photoelectron spectroscopic studies of -cerium are pointed out. © 1981 The American Physical Society.