Spectral properties of a tractable collective Hamiltonian

TL;DR

This paper analyzes the spectral properties of a simplified collective Hamiltonian with quartic potential terms, exploring vibrational and rotational structures, and introduces transitional Hamiltonians within a Cartan-Weyl framework.

Contribution

It presents a detailed analysis of a tractable collective Hamiltonian with quartic potential terms, including limits and transitional models, using a novel Cartan-Weyl based method.

Findings

Spectral properties of the Hamiltonian are characterized.

Physically significant limits are analyzed and compared with approximation schemes.

Transitional Hamiltonians between limits are constructed and discussed.

Abstract

The spectral properties of a tractable collective model Hamiltonian are studied. The potential energy is truncated up to quartic terms in the quadrupole deformation variables, incorporating vibrational, $\gamma$-independent rotational and axially deformed rotational structures. These physically significant limits are analysed in detail and confronted with well-established approximation schemes. Furthermore, transitional Hamiltonians in between the limits are presented and discussed. All results are obtained within a recently presented Cartan-Weyl based framework to calculate $SU(1,1)\times SO(5)$ embedded quadrupole collective observables.