  The isotopic evolution of the ground-state nuclear shapes and the systematics
of one-quasiproton configurations are studied in odd-A Rubidium isotopes. We
use a selfconsistent Hartree-Fock-Bogoliubov formalism based on the Gogny
energy density functional with two parametrizations, D1S and D1M, and
implemented with the equal filling approximation. We find clear signatures of a
sharp shape transition at N=60 in both charge radii and spin-parity of the
ground states, which are robust, consistent to each other, and in agreement
with experiment. We point out that the combined analysis of these two
observables could be used to predict unambiguously new regions where shape
transitions might develop.
