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Physical Review C

Application of a number-conserving boson expansion theory to Ginocchio’s SO(8) model

Chao-Te Li, V. G. Pedrocchi, Taro Tamura

Published May 1, 1986• 4 citations
Publisher

Abstract

A boson expansion theory based on a number-conserving quasiparticle approach is applied to Ginocchio's SO(8) fermion model. Energy spectra and E2 transition rates calculated by using this new boson mapping are presented and compared against the exact fermion values. A comparison with other boson approaches is also given.
DOI
10.1103/physrevc.33.1762

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To see how closely an interacting-boson-model-like model can be approached, we systematically develop a similarity transformation that unitarizes the simple correspondence version of the Dyson boson mapping of the Ginocchio SO(8) model. For a large region of Hamiltonian parameter space, a one-body plus two-body Hermitian boson Hamiltonian of the interacting-boson-model form is achieved. The similarity transformation consists of a dynamical part and a normalizing part. The dynamical transformation results in a one-body plus two-body Hermitian Hamiltonian and simple transition operators. The normalizing transformation commutes with the dynamically transformed Hamiltonian. This enables the transition rates to be calculated without introducing dual bases. However, the resulting boson model differs from the phenomenological interacting boson model in that transition rates are not calculable from the absolute squares of matrix elements. Dynamically transformed operators are given explicitly, and normalizing transformations for SO(6) and seniority limits are obtained in closed form.
We discuss microscopic ground of the IBM from the quasiparticle viewpoint, paying attention to the effects of nucleon-number conservation. The OAI mapping is revisited, showing for a single-j system how the number conservation effects are taken into account. The number-conserving quasiparticle approximation exploited by Li is applied to incorporate the number conservation effects. The significance of the number conservation is confirmed via the tests in the Ginocchio model and in a 2j system. An effective boson number is evaluated based on the number-conserving quasiparticle method. It is shown that the nucleon-number conservation effects are well incorporated in the IBM, even for systems with non-degenerate single-particle orbits.
It is shown how the boson mapping formalism may be applied as a useful manybody tool to solve a fermion problem. This is done in the context of generalized Ginocchio models for which we introduce S-, D-, and G-pairs of fermions and subsequently construct the sdg-boson realizations of the generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are solved beyond the explicit symmetry limits. Phase transitions to rotational structures are obtained, also in situations where there is no underlying SU(3) symmetry.