Alternative solvable description of the E(5) critical point symmetry in the interacting boson model

Abstract

A solvable extended Hamiltonian that includes multi-pair interactions among s-and d-bosons up to infinite order within the framework of the interacting boson model is proposed to gain a better description of E(5) model results for finite-N systems. Numerical fits to low-lying energy levels and reduced E2 transition rates within this extended version of the theory are presented for various N values. It shows that the extended Hamiltonian within the IBM provides a better description of the E(5) model results for small N cases, while the results of the model in the large-N cases are close to those of the E(5)-β 2n type models studied previously.

Investigation of quantum phase transitions in thespdfinteracting boson model based on dual algebraic structures for the four-level pairing model

“…The best fit which we are considering guarantees that the parameters are well determined. We have therefore computed the positive and negative parity energy spectra for the transitional region via Hamiltonian (16). As per the examples of our present technique and suggested results, the energy spectra and some ( ) B E1 and ( ) B E2 values of the Ru isotopes which are determined within the spdf−IBM framework are presented in figures 2-8, excluding roots that can be obtained from S k symmetry.…”

“…The Bethe ansatz method is a process of diagonalizing which depends on a set of dimensionless parameters which denote these parameters by x i so values of the parameters x i depend on the pair number N. By using equation (19) and the commutation relations of equation (1) which leads to a set of BAEs, the c-numbers x i ʼs are determined by These yield the eigenvalues ( ) E k of Hamiltonian equation (16) in the form…”

“…The importance of the p boson and f boson in transitional deformed nuclei has been investigated by Maino et al, Engel and Iachello, and Zamfir and Kusnezov [10,14,15] who describe analytical and phenomenological studies such as pygmy and giant dipole resonances, collective octupole states and low-lying E1 strength. An alternative solvable description of the critical point symmetry in the interacting boson model within the framework of ( ) SU 1, 1 Lie algebra is reported in [16], but this model is related to a description of positive parity levels. In order to clarify the structural change at the critical point of the phase transition, and to investigate negative parity states, the Hamiltonian must be diagonalized numerically similar to what has been done in [6,17].…”

Simultaneous description of low-lying positive and negative parity states in spd, sdf and spdf interacting boson model

“…Alternative solvable description of the critical point symmetry in the IBM within framework of SU(1, 1) Lie algebra is reported in Ref. 22, but this model is related to the description of positive parity levels. In order to clarify the structural change at the critical point of the phase transition, and investigation of negative parity states the Hamiltonian must be diagonalized numerically similar to what we have done in Refs.…”