Spectral properties of a tractable collective Hamiltonian

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.

arXiv commentsubmitted to PRC

References in corpus (14)

• Quantum phase transitions in the interacting boson model
• Solutions of the Bohr hamiltonian, a compendium
• A computationally tractable version of the collective model
• An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces
• Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics
• Critical-Point Symmetry in a Finite System
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model
• First-Order Quantum Phase Transition in a Finite System
• Simplified approach to the application of the geometric collective model
• Quadrupole collective variables in the natural Cartan-Weyl basis
• X(5) Critical-Point Structure in a Finite System
• Vector coherent state theory of the generic representations of so(5) in an so(3) basis
• On the relation between $E(5)-$models and the interacting boson model
• The quadrupole collective model from a Cartan-Weyl perspective

Cited by in corpus (1)

• Exact diagonalization of the Bohr Hamiltonian for rotational nuclei: Dynamical gamma softness and triaxiality