Calculation of the unoccupied4flevel in europium metal

Hartree-Fock-Wigner-Seitz band calculations, employing crystal potentials constructed from relativistic atomic wave functions via the renormalized-atom method, are used to estimate ${\Delta }_{+}(f^7\to f^8)$, the unoccupied $4f$-level position relative to the Fermi level in Eu metal. It is found that ${\Delta }_{+}\simeq 8.6$ eV, which, in conjunction with other calculations, leads to a value of 10.5 eV for the $4f$ Coulomb interaction energy $U$. Both results are consonant with recent measurements. Sensitivity of the ${\Delta }_{+}$ estimate to the choice of input atomic configurations is also examined.