Structural evolution in germanium and selenium nuclei within the mapped interacting boson model based on the Gogny energy density functional

The shape transitions and shape coexistence in the Ge and Se isotopes are studied within the interacting boson model (IBM) with the microscopic input from the self-consistent mean-field calculation based on the Gogny-D1M energy density functional. The mean-field energy surface as a function of the quadrupole shape variables $\beta$ and $\gamma$, obtained from the constrained Hartree-Fock-Bogoliubov method, is mapped onto the expectation value of the IBM Hamiltonian with configuration mixing in the boson condensate state. The resultant Hamiltonian is used to compute excitation energies and electromagnetic properties of the selected nuclei $^{66-94}$Ge and $^{68-96}$Se. Our calculation suggests that many nuclei exhibit $\gamma$ softness. Coexistence between prolate and oblate, as well as between spherical and $\gamma$-soft, shapes is also observed. The method provides a reasonable description of the observed systematics of the excitation energy of the low-lying energy levels and transition strengths for nuclei below the neutron shell closure $N=50$, and provides predictions on the spectroscopy of neutron-rich Ge and Se isotopes with $52\leq N\leq 62$, where data are scarce or not available.