Bohr Hamiltonian with Davidson potential for triaxial nuclei

TL;DR

This paper develops an analytical solution to the Bohr Hamiltonian for triaxial nuclei using a Davidson potential, providing spectra and transition rates that span from vibrational to rotational behaviors, and identifies the critical point of shape phase transition.

Contribution

It introduces a new analytical approach for triaxial nuclei with Davidson potential and links it to the Z(5) critical point solution.

Findings

Analytical spectra and B(E2) rates for triaxial shapes

Identification of the Z(5) solution as a critical point

Comparison with experimental data

Abstract

A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving a Davidson potential in beta and a steep harmonic oscillator in gamma, centered around gamma=30 degrees, is developed. Analytical expressions for spectra and B(E2) transition rates ranging from a triaxial vibrator to the rigid triaxial rotator are obtained and compared to experiment. Using a variational procedure it is pointed out that the Z(5) solution, in which an infinite square well potential in beta is used, corresponds to the critical point of the shape phase transition from a triaxial vibrator to the rigid triaxial rotator.