Triaxiality softness and shape coexistence in Mo and Ru isotopes

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.

Figure 1

Potential energy surfaces of the Ru isotopes from neutron number $N=52$ to 68 in the ($\beta ,\gamma$) plane, obtained from a triaxial RHB calculations with the DD-ME2 parameter set. The color scale shown at the right has the unit of MeV, and scaled such that the ground state has a zero MeV energy.

Figure 2

The same as in Fig. 1, but with different parameter set DD-PC1.

Figure 3

Potential energy surfaces of the Mo isotopes from neutron number $N=50$ to 66 in the ($\beta ,\gamma$) plane, obtained from a triaxial RHB calculations with the DD-ME2 parameter set. The color scale shown at the right has units of MeV, and scaled such that the ground state has a 0 MeV energy.

Figure 4

The same as in Fig. 3, but with different a parameter set DD-PC1.

Figure 5

Binding energy per nucleon (a) and the total binding energy (b) of the Mo isotopes using both DD-ME2 and DD-PC1 as a function of neutron number. Comparison with FRDM [26] results and experimental data [22] are shown.

Figure 6

Binding energy per nucleon (a) and the total binding energy (b) of the Ru isotopes using both DD-ME2 and DD-PC1 as a function of neutron number. Comparison with FRDM [26] results and experimental data [22] are shown.

Figure 7

Two neutron separations energies of Mo and Ru isotopes using both DD-ME2 and DD-PC1 as a function of neutron number. Comparison with FRDM [26] results and experimental data [22, 23, 24, 25] are shown.

Figure 8

Neutron and proton radii of Mo and Ru isotopes using both DD-ME2 and DD-PC1 as a function of neutron number.

Figure 9

Charge radius for Mo and Ru isotopes using both DD-ME2 and DD-PC1 as a function of neutron number, compared to experimental data from Ref. [25].

Figure 10

$\delta {\langle r_c^2\rangle }^{50,N}$ for Mo and Ru isotopes using both DD-ME2 and DD-PC1 as a function of neutron number, compared to experimental data from Refs. [23, 24, 25].