Quadrupole collective dynamics from energy density functionals: Collective Hamiltonian and the interacting boson model

Microscopic energy density functionals have become a standard tool for nuclear structure calculations, providing an accurate global description of nuclear ground states and collective excitations. For spectroscopic applications, this framework has to be extended to account for collective correlations related to restoration of symmetries broken by the static mean field, and for fluctuations of collective variables. In this paper, we compare two approaches to five-dimensional quadrupole dynamics: the collective Hamiltonian for quadrupole vibrations and rotations and the interacting boson model (IBM). The two models are compared in a study of the evolution of nonaxial shapes in Pt isotopes. Starting from the binding energy surfaces of ${}^{192,194,196}\mathrm{Pt}$, calculated with a microscopic energy density functional, we analyze the resulting low-energy collective spectra obtained from the collective Hamiltonian, and the corresponding IBM Hamiltonian. The calculated excitation spectra and transition probabilities for the ground-state bands and the $\gamma$-vibration bands are compared to the corresponding sequences of experimental states.

Figure 1

Self-consistent binding-energy maps of ${}^{192,194,196}\mathrm{Pt}$ in the $\beta –\gamma$ plane ($0^{°}⩽\gamma ⩽{60}^{°}$), calculated with the RHB model using the DD-PC1 functional (left panels), and the corresponding mapped energy surface of the IBM, $E_{\mathrm{IBM}}({\beta }_B,{\gamma }_B)$. The IBM total energies are depicted in terms of $\beta$ and $\gamma$, where $\beta \propto {\beta }_B$ and $\gamma ={\gamma }_B$ (see text for definition).

Figure 2

Low-lying collective spectra of ${}^{192,194,196}\mathrm{Pt}$ nuclei, calculated with the collective Hamiltonian based on the DD-PC1 functional and the corresponding IBM Hamiltonian, in comparison with available data. For each nucleus, the $B$(E2) values (in Weisskopf units) obtained in the IBM are normalized to the $B(\mathrm{E}2;2_1^{+}\to 0_1^{+})$ predicted by the collective Hamiltonian. The experimental excitation spectra and $B$(E2) values are from Refs. [50] and [51], respectively.

Figure 3

Absolute squares of the IBM wave functions in the $\beta –\gamma$ plane for the yrast states $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$, and the bandhead of the $\gamma$ band $2_2^{+}$ of ${}^{192}\mathrm{Pt}$.

Figure 4

Same as described in the caption to Fig. 3, but for the eigenstates of the collective Hamiltonian.