Density-dependent Hartree-Fock description of nuclei in the rare earth and nickel regions

Motivated by recent high-resolution muonic x-ray and electron scattering experiments, the mean field approximation with a realistic effective interaction has been applied in the rare-earth and nickel regions. For rotational rare-earth nuclei, the approximation of a single axially symmetric deformed intrinsic state yields quantitative agreement with the experimental binding energies, deformations, elastic electron scattering, and inelastic electron scattering to $2^{+}$ states. Discrepancies in transitions to $4^{+}$ and $6^{+}$ states may indicate the limits of validity of the simple deformed intrinsic state approximation. The recent radius measurements in Fe, Ni, and Zn isotopes have made it possible to test the degree to which the systematics of polarization of the charge distributions of nonspherical nuclei may be understood through the mean-field approximation. Although certain significant qualitative features have been understood, it is shown that the deformations of nuclei in this region are insufficiently defined to validate approximation by a single intrinsic wave function.