Nuclear shape evolution and shape coexistence in Zr and Mo isotopes
The phenomena of shape evolution and shape coexistence in even–even $$^{88-114}$$ 88 - 114 Zr and $$^{90-116}$$ 90 - 116 Mo isotopes are studied by employing covariant density functional theory (CDFT) with density-dependent point-coupling parameter set, DD-PCX, and with separable pairing interaction. The results for the rms deviation in binding energies, two-neutron separation energy, the differential variation of two-neutron separation energy, and rms charge radii, as a function of neutron number, are presented and compared with available experimental data. In addition to the oblate–prolate shape coexistence in $$^{96-110}$$ 96 - 110 Zr isotopes, the correlations between shape transition and discontinuity in the observables are also examined. A smooth trend of charge radii in Mo isotopes is found to be due to the manifestation of triaxiality softness. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi level of neutron and proton, respectively. The rapid shape transition in Zr isotopes near N $$\approx $$ ≈ 60 is identified to be caused by the evolution of the shell structure associated with massive proton excitations to 1 $$\pi g_{9/2}$$ π g 9 / 2 orbit. The present calculations also predict a deformed semi-bubble structure in the $$^{100}$$ 100 Zr isotope.