Relation betweenE(5)models and the interacting boson model

Abstract

The connections between the E(5) models [the original E(5) using an infinite square well, E(5)-β 4 , E(5)-β 6 , and E(5)-β 8 ], based on particular solutions of the geometrical Bohr Hamiltonian with γ -unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the U(5)-O(6) transition line is used and a numerical fit to the different E(5) models energies is performed, later on the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce very well all these E(5) models. The agreement is the best for E(5)-β 4 and reduces when passing through E(5)-β 6 , E(5)-β 8 , and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest-lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed.

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

“…It is expected that a suitable IBM Hamiltonian, like the U(5), O (6), and SU(3) limiting cases, may fit the E(5) critical point nuclei better, especially when relatively higher excited levels are taken into consideration, though it is commonly believed that the BMM may be regarded as the large-N limit of the IBM [16][17][18]. The purpose of this work is to establish an extended Hamiltonian near the critical point of the U(5)-O(6) transitional region of the IBM, of which the solution should be closer to that of the E(5) model with finite N. Namely, the model is suitable to describe the E(5) critical symmetry nuclei as reported in [5][6][7][8][9], while the model in the large-N cases may be close to those of the E(5)-β 2n type models similar to the results reported in [15].…”

“…Arias et al did initial work along this line [13,14], showing that for the low-lying part of the spectrum the results of the consistent-Q type U(5)-O(6) Hamiltonian in the IBM at the critical point are close to those of the E(5) model for cases with a small number of bosons, while the IBM Hamiltonian for large N cases reproduces low-lying parts of the spectrum and electromagnetic transition rates of a BMM Hamiltonian with a β 4 potential. A detailed study on the connections between the E(5), E(5)-β 4 , E(5)-β 6 , and E(5)-β 8 models based on particular solutions of the BMM with such γ-unstable potentials and the IBM fit with relatively large N (= 60) were also carried out [15], which further confirms the above conclusions.…”

“…We present results of the low-lying level energies and the reduced E2 transitional rates of the model with N = 1000 bosons in Tables IV and V, respectively. Since numerical results of the IBM fit to the E(5) results with N = 60 are also available [15], the EXT results with N = 60 are also shown in Tables IV and V in comparison with the corresponding results of the IBM fit provided in [15]. It can be observed from Table IV that the EXT results are always better than those of the CQ, especially for higher excited states.…”

“…It can be observed from Table IV that the EXT results are always better than those of the CQ, especially for higher excited states. In fact, the tendency that higher levels become too low in energy in the CQ in comparison to the corresponding E(5) results is not altered in the IBM fits shown in [15], while it is overcome in the EXT. The quality of the EXT fit becomes better with the increasing of N when N ≤ 60.…”

“…It is clearly shown in Table V Table V of Ref. [15]. Anyway, the EXT does not provide with results of the E(5) model in finite-N cases.…”