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Science China Physics Mechanics and Astronomy

Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation

Yu Zhang, Yu‐xin Liu, Zhanfeng Hou, Yang Ren Sun

Published Jan 5, 2011• 2 citations
Publisher
DOI
10.1007/s11433-010-4209-5

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A solvable extended Hamiltonian that includes multi-pair interac- tions 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. Similarly, an extended pairing Hamiltonian to de- scribe pairing interactions among valence nucleon monopole pairs up to infinite order in a spherical mean-field can also be built, which includes the extended pairing interaction model within a deformed mean-field theory as a special case. These mean-field plus pairing models are all constructed based on the local ~ E2 algebraic structure.
The phase diagram of two-level boson Hamiltonians, including the interacting boson model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.