Signatures of shape transitions in odd-A neutron-rich rubidium isotopes

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 self-consistent 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 the charge radii and spin parity of the ground states, which are robust, consistent with 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.