Six-dimensional Davidson potential as a dynamical symmetry of the symplectic interacting vector boson model

Abstract

A six-dimensional Davidson potential, introduced within the framework of the Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the Sp(12, R) ⊃ SU (1, 1) × SO(6) reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of SO (6) are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.

Phase structure of the interacting vector boson model

“…(a) U T (2) algebra. It is defined by the operator of a number of particles N = N p + N n (16) and the "T-spin" operators T 1 m , (m = 0, ±1) introduced through…”

“…For O(6) ⊂ U (6), the symmetric representation [N ] 6 of U (6) decomposes into fully symmetric (ω, 0, 0) 6 ≡ (ω) 6 IR's of O(6) according to the rule [13], [16] [N ] 6 = ω=N,N −2,...,0(1)…”

Simultaneous Description of Even-Even, Odd-Mass and Odd-Odd Nuclear Spectra

“…It was established [11] that the correct placement of the bands in the spectrum strongly depends on their bandheads' configuration, and in particular, on the minimal or initial number of bosons, N = N i , from which they are built. The latter determines the starting position of each excited band.…”

“…Additionally to the five parameters a, b, α 3 , β 3 , α 1 entering in Eq. (11) which are used to describe the energies of the even-even core nuclei, the number of adjustable parameters needed for the complete description of the collective spectra of both odd-A and odd-odd nuclei is three, namely γ, ζ and η. The first two are evaluated by a fit to the experimental data [12] of the GSB of the corresponding odd-A neighbor, while the last one is introduced in the final step of the fitting procedure for the odd-odd nucleus, respectively.…”

Unified dynamical symmetries in the symplectic extension of the interacting vector boson model

“…In the larger infinite boson spaces of the dynamical Sp (12, R) there are also new chains of subgroups, starting with noncompact symplectic subalgebras. We investigate the reduction Sp(2, R) ⊗ SO (6) ⊂ Sp (12, R), which allows the inclusion of a 6-dimensional Davidson potential [9], that is known to allow mixing of the rotational and vibrational modes, so in applications it reproduces very well the transitional behavior in nuclear spectra. The other reduction [10] we consider Sp(4, R) ⊗ SO(3) ⊂ Sp (12, R) allows the selection of states with fixed angular momentum L, given by the SO(3) irreducible representations (irreps).…”