Exactly separable version of the Bohr Hamiltonian with the Davidson potential

TL;DR

This paper introduces an exactly solvable version of the Bohr Hamiltonian using a Davidson potential, accurately modeling energy levels and transition rates in deformed nuclei with minimal parameters.

Contribution

It develops an exactly separable solution to the Bohr Hamiltonian with a Davidson potential, unifying descriptions of multiple nuclear bands and addressing longstanding degeneracy issues.

Findings

Accurately reproduces energy spectra and transition rates for rare earth and actinide nuclei.

Provides insights into gamma stiffness and gamma-bandhead energy correlation.

Addresses degeneracy problems in the Interacting Boson Approximation model.

Abstract

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (beta_0, gamma stiffness). Insights regarding the recently found correlation between gamma stiffness and the gamma-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained.