Exactly separable version of the Bohr Hamiltonian with the Davidson potential

Abstract

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(β) + u(γ)/β 2 , with the Davidson potential u(β) = β 2 + β 4 0 /β 2 (where β 0 is the position of the minimum) and a stiff harmonic oscillator for u(γ) centered at γ = 0 • . In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, γ 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 (β 0 , γ stiffness). Insights regarding the recently found correlation between γ stiffness and the γ-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.

Bohr Hamiltonian with a deformation-dependent mass term for the Kratzer potential

“…1, are similar for small values of β, where the 1/β 2 term dominates in both cases, but they differ substantially at large values of β, where the tails of the wave functions behave as e −β 2 /2 [33] and e −β/2 [31,32] (iii) The DDM Bohr Hamiltonian with the Davidson potential works well for deformed nuclei, but fails in describing the nuclei lying at the critical point between the spherical and deformed regions [34,35], known to be examples of the X(5) critical point symmetry [36]. It is interesting to examine if the DDM Bohr Hamiltonian with the Kratzer potential overcomes this drawback.…”

“…(B4) of Ref. [33], in which the square of the radial integral appears. The radial integral for γ-unstable nuclei is given in Eq.…”

“…The same set of experimental data for spectra and B(E2) transition rates has been used as in the cases of the Deformation Dependent Mass (DDM) Davidson model [17], the Exactly Separable Davidson (ESD) model [33], and the Morse potential [48,49], in order to facilitate comparisons of the various models among themselves and to the data. The theoretical predictions for the levels are obtained from Eq.…”

Quantum phase transitions and structural evolution in nuclei

“…Many approaches have been developed [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62], mainly by Bonatsos and collaborators, that simulate critical point nuclei, or the evolution of structure near the critical point. We will not discuss these in detail here-they have been reviewed recently [63,64].…”

Relationship between X(5) models and the interacting boson model

“…In Refs. [44,45] the authors treated exactly separable versions of the Davidson potential and of the X(5) potential, respectively. Finally, in Ref.…”