  We have calculated the electronic structure of Eu for the bcc, hcp, and fcc
crystal structures for volumes near equilibrium up to a calculated 90 GPa
pressure using the augmented-plane wave method in the local-density
approximation. The frozen-core approximation was used with a semi-empirical
shift of the f-states energies in the radial Schr$\ddot{o}$dinger equation to
move the occupied 4f valence states below the $\Gamma_1$ energy and into the
core. This shift of the highly localized f-states yields the correct europium
phase ordering with lattice parameters and bulk moduli in good agreement with
experimental data. The calculated superconductivity properties under pressure
for the $\it bcc$ and $\it hcp$ structures are also found to agree with and
follow a $T_c$ trend similar to recent measurement by Debessai et al.$^1$
