Exact solution of U(5)–O(6) transitional description in interacting boson model with two-particle and two-hole configuration mixing *

Abstract

The exact solution of the U(5)-O(6) transitional description in the interacting boson model with two-particle and two-hole configuration mixing is derived based on the Bethe ansatz approach. The Bethe ansatz equations are provided to determine the model's eigenstates and corresponding eigen-energies. N= 2 and N= 4 cases are considered as examples to demonstrate the solution features. As an example of the application, some low-lying level energies and B(E2) ratios of 108Cd are fitted and compared with the corresponding experimental data.

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

“…We can learn that in transition region for closely spaced levels < d >≈16.7, neighboring states contain information about the chaoticity, and the spectrum for this region is chaotic. These properties and trends are consistent with the nuclear system's chaoticity in closely spaced levels [84] that may cause strongly mixed wave function and modify the nuclear structure of many-body systems [85][86][87]. These neighboring states with strongly mixed wave functions with the same spin and parity are prevalent in the closely spaced levels.…”

Band mixing in 96,98Mo isotopes *

“…Due to the large space configuration, shellmodel calculations with multi particle-hole excitations are not simple. To determine the nuclear structure of band mixing in the collective valence shell and multi-particlehole excitations, the interacting boson model (IBM) has been proposed [9,10]. The mass region A 100 has been of considerable interest for features of the U (5) to SO (6) transition in even-even nuclei.…”

“…Given this information and the conclusions from Refs. [9,[33][34][35][36] regarding analytic expressions and exact eigen energies between the spherical and -soft shapes found by using the Bethe-ansatz within an infinite-dimensional Lie algebra, it would be helpful to describe the shape coexistence configuration and band mixing in Mo. We thus followed the method of Refs.…”

“…We thus followed the method of Refs. [9,33,34] and applied a simple two-state model to the energy spectra and electric transition rates in Mo. The exact solution and band mixing configurations have recently been shown to be successful in reproducing the lowest state band and E2 matrix elements.…”

“…The CMC calculation can be used to explore the normal 2p-0h proton configuration for U(5) vibrational nuclei and the three intruder phonons, with a 2p-4h or 4p-2h configuration across the Z = 40 sub-shell for O(6) -soft nuclei. To this end, we used the same formalism and calculations via the SU(1,1) Lie algebra and SU(1,1) coherent states [9,33,37] for the lowest states of band mixing connecting the and states and the and states.…”