Predominance of Triaxial Shapes in Transitional Super-Heavy Nuclei: Ground-State Deformation and Shape Coexistence along the Flerovium (Z=114) Chain of Isotopes.

We present the first triaxial beyond-mean-field study of even-even super-heavy nuclei. Calculations for the even Flerovium isotopes towards the supposed N=184 neutron shell closure were performed using the effective finite-range density-dependent Gogny force. They include the restoration of the particle-number and angular-momentum symmetries and the mixing of different shapes using the generator coordinate method. The importance of the γ degree of freedom is highlighted by comparing the triaxial to axial-symmetric calculations performed within the same framework. For the three even Fl isotopes between the prolate ^{288}Fl and the oblate ^{296}Fl triaxial ground-state shapes are predicted, whereas axial-symmetric calculations suggest a sharp prolate-oblate shape transition between ^{290}Fl and ^{292}Fl. A novel type of shape coexistence, namely, that between two different triaxial shapes, is predicted to occur in ^{290}Fl. Finally, the existence of a neutron shell closure at N=184 is confirmed, while no evidence is found for Z=114 being a proton magic number.