Abstract
A systematic search of triaxial ground state and shape coexistence in Ru and Mo isotopes is done using the relativistic-Hartree-Bogoliubov formalism using density-dependent zero and finite range $NN$ interactions, and with separable pairing. Shape coexistence and triaxiality softness manifest themselves in a clear manner in Mo isotopes and only triaxiality softness is very clear in all of the Ru isotopes. Both point-coupling and meson-exchange models give similar results with few exceptions. A very good agreement is found with the available experimental data and with the macro-microscopic finite range droplet model. The findings are also in good agreement with the self-consistent Hartree-Fock-Bogoliubov calculations based on the interaction Gogny-D1S force.
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