Free-electron-gas exchange correlation in the calculated multiplet splittings ofs-core levels in3dtransition metals and rare-earth elements

A local approximation to the exchange-correlation effects is used in a detailed calculation of the $s$-core binding-energy splittings for the $3d$ transition elements and rare-earth series. Our approach to the many-body problem is a single-particle model based on an effective wave equation with the mass operator instead of the simpler exchange operator of Hartree-Fock theory. By treating the exchange-correlation effects (mass operator) in a form of an effective local potential in the free-electron gas, the splittings are calculated in the framework of the self-consistent-field method applied to free ions. The results are in good agreement with x-ray photoemission experimental data taken for $3d$ transition and rare-earth ionic compounds and metals.