Signatures of shape transitions in odd-$\mathit{A}$ 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.

Figure 1

Single-particle energies for protons and neutrons in ${}^{98}\mathrm{Sr}$ as a function of the axial quadrupole moment $Q_{20}$. The Fermi level is depicted as a thick dashed red line. The results have been obtained with the Gogny-D1S EDF.

Figure 2

Experimental (a) excitation energies and spin-parity assignments [12, 13, 14, 15, 23] compared with Gogny-D1S HFB-EFA results (b) for one-quasiproton states in odd-$A$ Rb isotopes. Prolate configurations are shown by black lines, oblate ones by red lines, and spherical ones by blue lines.

Figure 3

Gogny-D1S excitation energies of single-quasiproton prolate (a) and oblate (b) states in Rb isotopes. Hole states are plotted below zero energy and particle states are plotted above. The absolute ground states are indicated with circles.

Figure 4

Same as in Fig. 3, but for Gogny D1M.

Figure 5

Isotopic evolution of the quadrupole deformation parameter $\beta$ of the energy minima obtained from Gogny D1S and D1M calculations.

Figure 6

Gogny-D1S HFB results for $\delta \langle r_c^2\rangle$ (a) and $S_{2n}$ (b) in odd-$A$ Rb isotopes compared to experimental data from Refs. [25, 26] for masses and from Ref. [27] for radii. Results for prolate, oblate, and spherical minima are displayed with different symbols (see legend). Open circles correspond to ground-state results.

Figure 7

Same as in Fig. 6, but for Gogny D1M.