Nuclear Shape Transition, Triaxiality and Energy Staggering of Υ -Band States for Even–Even Xenon Isotopic Chain

Abstract: The positive-parity states of even–even Xe nuclei are inspected within the framework of modified O (6) limit of the interacting boson model (IBM). The effective three-body interaction [QQQ]³ where Q is the IBM O (6) quadrupole operator is introduced to exhibit the triaxiality nature. The shape of nuclear surface is quantified by the deformation parameters β, Υ by using the intrinsic coherent state. For each nucleus, the potential energy surfaces (PES) of the transition U (5)–Triaxiality– O (6) are resolved and analyzed and the critical phase transition points are identified. For each nucleus a fitting procedure is adopted to get the best model parameters by fitting some selected calculated energy levels and B(E2) transition rate ratios with experimental ones. These ratios are analyzed because they serve as effective order parameters in the shape phase transition. The nuclei in Xe isotopic chain evolve from spherical vibrator U (5) to Υ -soft rotor O (6) by increasing the boson number from N=3 (heavy isotope ¹³²Xe) to N=10 (light isotope ¹²⁰Xe) and the isotope ¹²⁶Xe represents the critical nucleus. The nucleus¹²⁸Xe has triaxial nature. To transact with high spin states in Υ -band in ^118-128Xe isotopic chain to investigate and exhibit the odd–even-spin energy staggering, we introduce the two-parameter collective nuclear softness rotor model (CNS2). Three different staggering indices are considered depending on the dipole transitions linking the two families of spins while the quadrupole transitions are within each spin family. Strong odd–even-spin energy staggering has been seen. As a link between the IBM and CNS2 models we observed that the energy difference (Formula Presented.) between the (Formula Presented.) -band and ground state band normalized to (Formula Presented.) decreases with increasing the mass number.