Nuclear Shape-Phase Transition From Spherical U(5) to Deformed $$\gamma$$-Unstable O(6) Dynamical Symmetries of Interacting Boson Model Applied to Ru, Pd, and Xe Isotopic Chains

Abstract

AbstractThe shape transition from spherical vibrator U(5) to $$\gamma$$ γ -unstable deformed rotor O(6) in even-even Ru, Pd, and Xe isotopic chains are studied in framework of sd interacting boson model (IBM1) using the coherent state formalism to obtain the potential energy surfaces (PES’s). The location of critical points in the transition are identified by analysis the PES’s in terms of the deformation parameter $$\beta$$ β and by using the catastrophe theory in terms of the two essential parameters $$(r_1, r_2)$$ ( r 1 , r 2 ) . By using the most general IBM1 Hamiltonian in Casimir form with neglecting the U(5) and SU(3) quadratic Casimir operators and introducing only one control parameter the PES leads to the same energy surface as the Q-consistent IBM Hamiltonian at $$\gamma =0$$ γ = 0 . For the studied isotopic chains, the $$\chi ^2$$ χ 2 -test is used to perform the fitting between the experimental and the corresponding calculated IBM for some selected energy levels and electric quadrupole transition probabilities B(E2) values using a simulated search program. A good agreement is produced for both energies and B(E2) transition rates. The present model calculations suggest that $$^{100}$$ 100 Ru, $$^{102}$$ 102 Pd and $$^{130}$$ 130 Xe nuclei are good candidates for the E(5) critical point symmetry.