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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

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

Yu Liu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.

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In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.
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.
Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form that can be diagonalized for large number of bosons. We present results for the low-energy spectrum and the transition probabilities for systems up to 10,000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a ${\ensuremath{\beta}}^{4}$ potential.
The U (5)– O (6) transitional behaviour of the interacting Boson model in the large- N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B ( E 2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviours of these quantities are greatly enhanced with an increase in the total number of bosons N ; in particular, the fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n d in the first excited 0 + state and the ground state, and another quantity related to the isomer shift behave similarly in both the O (6)– U (5) large- N and U (5)– SU (3) phase transitions.
The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number NNN. The remnants of these types of degeneracies in finite-NNN systems have been preliminarily identified from the low-lying spectra of 150Nd^{150}\mathrm{Nd}150Nd. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.
The apparent persistence of symmetry in the face of strong symmetry-breaking interactions is examined in a many-boson model. The model exhibits a transition between two phases associated with U(5) and O(6) symmetries, respectively, as the value of a control parameter progresses from 0 to 1. The remarkable fact is that, in spite of strong mixing of the symmetries for intermediate values of the control parameter, the model continues to exhibit the characteristics of its closest symmetry limit for all but a relatively narrow transition region that becomes progressively narrower as the boson number increases. This phenomenon is explained in terms of quasidynamical symmetry.