Classical limit of the interacting boson Hamiltonian

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

“…A stability analysis of this surface leads to a set of conditions, Eqs. (34), (37) and (38), which are necessary and sufficient for the occurrence of a minimum with an intrinsic shape with octahedral symmetry.…”

“…(34), (37) and (38) are the necessary and sufficient conditions for the energy surface E(β 2 , β 4 , γ 2 , γ 4 , δ 4 ) to have a local minimum with octahedral symmetry. It is not necessarily a unique minimum and it may not be the global one.…”

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

“…The parametrization of the Hamiltonian (1) is very appropriate because the phase transition appears approximately at the same value of the control parameter (ξ) for any value of N [4]. This critical point, ξ c , can be obtained easily from the expression for the energy given in [24] as…”

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

“…The classical limit of the IBM may be found by using the coherent state or intrinsic state formulism [16,17,27]. Usually, the ground state of a system described by the IBM is written as a condensate of bosons with…”

“…However, the operatorsS + ρ andS − ρ used in the third term of (20) are only well defined in the U(6) ⊃ U(5) ⊃ O(5) basis, and there is the O(5) seniority number τ mixing in the coherent state |c . Therefore, one can not derive the energy surface described by (20) in the classical limit using (34) or using the method proposed in [27] directly. Moreover, since the quantum number of the angular momentum is also not a good quantum number in (34), the coherent state (34) may be expanded in terms of any complete set of U(6) ⊃ U(5) ⊃ O(5) basis vectors for given N. Due to the multiplicity occurring in the O(5) ↓ O(3) reduction, we expand (34) …”