A projection method to calculate the physical states from intrinsic states is put forward. Using this projection method, the physical states of the ground state band in the interacting boson model (IBM) SU(3) limit are calculated. The wave functions are expressed in terms of the building blocks of the IBM wave functions.
By utilizing the 1/N expansion technique, the SU(3)-symmetry breaking caused by boson
energies is discussed for the sdg Interacting Boson Model, and the analytical expressions of the
intrinsic states are given under the approximation in the order of 1/N. It is also shown that
the many body theories for a interacting boson system, such as Hartree-Bose method, Tamm-
Dancoff approximation and Cranked Hartree approximation, are all special cases of the 1/N
expansion technique.
An exactly soluble three-level model for a system of fermions with Hamiltonian formed from generators of the group SU(3) is studied. A basis for the representation of which the ground state is a member is constructed. It is demonstrated that in this representation, the generators can each be expanded in a series as functions of a pair of ``kinematical'' boson operators; the series are uniquely determined to satisfy the operator algebra and the invariants of the representation by a method of Marumori. It is seen that the lowest anharmonic approximation to the Hamiltonian and other operators yields excellent numerical agreement with exact results for all regimes of interaction strength considered. An alternative description of the system in terms of a dynamically more meaningful boson, called the ``physical'' boson, is shown to be appropriate for relatively weak coupling where one has a near harmonic spectrum.
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.
The microscopic basis of the Interacting Boson Model for deformed nuclei is discussed. The IBM Hamiltonian is constructed microscopically in the following two steps. In the first step, the collective nucleon pairs of J = 0/sup +/ (S), 2/sup +/ (D), etc. are mapped onto the corresponding bosons. Nucleon-nucleon interactions are also mapped onto boson-boson interactions. This mapping method for deformed nuclei was proposed recently, and it turned out that this method is consistent with the Hartree-Fock-Bogoliubov + angular momentum projection calculation. Low-lying collective states primarily consist of S and D pairs. Consequently, the corresponding boson states mainly consist of s and d bosons, while there are some admixture of g-bosons. In the second step, effects of these g-bosons are included within the s-d boson space by a unitary transformation which transforms a combination of d and g bosons into a new d-boson. By minimizing the coupling between new d and g bosons with an appropriate mixing angle, one can neglect the coupling and obtain the IBM Hamiltonian with s and d bosons. It is demonstrated that the s-d Hamiltonian thus derived indeed reproduces spectra of the original s-d-g Hamiltonian.
We observe an adiabatic separation of collective rotations built upon a subset of intrinsic vibrational states within the interacting boson model (IBM) in the parameter domains corresponding to axially deformed ground state. The effect is not limited only to the low-lying states and closely follows the variation of quantum and classical measures of regularity. It leads to the existence of rotational bands even close to the highest accessible energies in specific regions within the IBM symmetry triangle. We propose a more general effect of regular intrinsic dynamics on the adiabatic separation of intrinsic and collective motion.