Investigation of $${}^{{178{-}186}}$$ Pt Isotopic Chain by Using $${Z}$$ (5) and Interacting Boson Model-2

In this paper, we considered the possibility of the $$U$$ (5)– $$O$$ (6) transitional behavior in the region between the oblate and prolate limits. To this aim and also to determine the energy spectra, transition probabilities and energy surfaces of $${}^{178{-}186}$$ Pt isotopic chain, we have used three different formalisms. We found that, the $$SU(1,1)$$ -based transitional Hamiltonian in interacting boson model-2 version, reproduces the experimental data with high accuracy when the effect of $$U$$ (5) symmetry is increased. Also, the results suggest the advantages of $$Z$$ (5) critical symmetry formalism in description of $${}^{\mathrm{178}}$$ Pt nucleus. We also got an obvious relation between the control parameter of transitional Hamiltonians and the quadrupole deformation and energy ratios.