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 178−186Pt 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 178Pt nucleus. We also got an obvious relation between the control parameter of transitional Hamiltonians and the quadrupole deformation and energy ratios.
