Contributions of SU(3) higher-order interaction operators to rotational bands in the interacting boson model

Rotational bands are commonly used in the analysis of the spectra of atomic nuclei. The early version of the interacting boson model of Arima and Iachello has been foundational to the description of rotations in nuclei. The model is based on a unitary spectrum generating algebra U(6) and an orthogonal (angular momentum) symmetry algebra SO(3). A solvable limit of the model contains SU(3) in its dynamical symmetry chain. The corresponding Hamiltonian is written as a linear combination of linear and quadratic Casimir invariants of all the algebras in the chain. The limit of exact dynamical symmetry, however, is rarely fulfilled by realistic systems, so the symmetry needs be broken. A suitable mechanism to do so is the partial dynamical symmetry approach. Prompted by these facts, the aim of this work is to construct higher-order SU(3) interaction terms in both the limit of exact and broken symmetry, which can be used in the description of rotational bands of nuclei. For this task, a systematic algebraic approach, loosely referred here to as the projection operator technique, will be extensively used to obtain those operators that make up the n-body terms in the corresponding Hamiltonians. This novel technique is thus proved to be quite efficient for these purposes.

Automated summary

This article introduces the commonly used properties of rotational bands in the analysis of atomic nuclear spectra, and details the interaction boson model of Arima and Iachello and its description of nuclear rotation. The article also proposes the partial dynamical symmetry approach to address the symmetry issues in realistic systems, and introduces the algebraic method called the projection operator technique for constructing higher-order interaction terms.