Triaxiality softness and shape coexistence in Mo and Ru isotopes Shakeb Ahmad 1 , * H. Abusara 2 , † and S. Othman 2* 1 Physics Section, Women’s College, Aligarh Muslim University, Aligarh-202002 and 2 Department of Physics, BirZeit University, Ramallah, Palestine Introduction A nucleus may take different shapes varying from spherical to quadrupole, octupole and higher order multipole deformations. These shapes are a consequence of the sensitive in- terplay between collective degrees of freedom and single particle energies . This interplay will lead to phase transition along an iso- topic and isotonic chain. Shape evolution for several isotopic chain in the mass region A ≈ 100 has been studied through the self- consistent mean-field (SCMF) approximation based on the Gogny-D1M energy density func- tional(EDF) [1], the potential energy surfaces (PES) using Skyrme HF+BCS [2], and Rel- ativistic Mean Field (RMF) with BCS pair- ing [3]. In particular, the structural evolu- tion of even-even Ru, Mo, Zr, Sr nuclei, and Ge, Se [1] nuclei have been studied within the SCMF approximation based on the Gogny- D1M energy density functional. This calcu- lation has fully explored the triaxial degrees of freedom and the shape coexistence in these nuclei. The spectroscopic properties have also been done for these nuclei with the help of a fermion-to-boson mapping procedure. This is very important as to clarify to which extent both triaxiality and shape coexistence are re- flected in the spectroscopic properties of these nuclei. In the present analysis, we have done a systematic calculation in the search of triaxial ground state properties and shape coexistence for 92-108 Mo and 96-112 Ru isotopes. The systematic constrained triaxial calculation is done in the self-consistent mean field model- the Relativistic-Hartree-Bogoliubov(RHB) * Electronic address: physics.sh@gmail.com † Electronic address: habusara@birzeit.edu with density-dependent zero and finite range N-N interactions. The model parameter used are the density-dependent DD-ME2 and. Pairing correlations are considered in the separable pairing model. A systematic comparison is made with calculated values and experimental data, Macro-microscopic Finite Range Droplet Model(FRDM) as well as with the self-consistent HFB calculations based on the interaction Gogny-D1S force. Results and Discussion Systematic constrained triaxial calculations mapping the quadrupole deformation space defined by β 2 and γ has been performed for 92-108 Mo and 96-112 Ru isotopes, using both DD-ME2 and DD-PC1 parameteriza- tions. For each nuclei two contour plots have been made one each parameterization to inves- tigate the location of a triaxial ground state, and the possibility of shape coexistence. The location of the ground state in the β − γ deformation space is indicated by the point (β 0 ,γ 0 ). Location of the ground state is shown in TABLE I for Ru and Mo isotopes and is ex- tracted from Fig.1. One can relate the smooth transition of the ground state along the iso- topic chains with the evolution of several ground state nuclear properties along an iso- topic chain. For that we study the evolution of binding energy (BE), proton radii (R p ) and neutron radii (R n ), two neutron separation en- ergies (S 2n ) and root mean square charge radii (R c ) with δ〈r 2 c 〉 50,N = 〈r 2 c 〉 N −〈r 2 c 〉 50 , for both Ru and Mo isotopic chain [4]. Conclusion We have used the Relativistic-Hartree- Bogoliubov (RHB) formalism with separable pairing to perform a systematic calculation along two isotopic chains, Ru and Mo, for the search of triaxial ground state and shape co- Proceedings of the DAE Symp. on Nucl. Phys. 62 (2017) 182 Available online at www.sympnp.org/proceedings