Robust Regularity in $\gamma$-Soft Nuclei and Its Microscopic Realization

$\gamma$ softness in atomic nuclei is investigated in the framework of energy density functionals. By mapping constrained microscopic energy surfaces for a set of representative nonaxial medium-heavy and heavy nuclei to a Hamiltonian of the proton-neutron interacting boson model (IBM-2) containing up to three-body interactions, low-lying collective spectra and transition rates are calculated. Observables are analyzed that distinguish between the two limiting geometrical pictures of nonaxial nuclei: the rigid-triaxial rotor and the $\gamma$-unstable rotor. It is shown that neither of these pictures is realized in actual nuclei, and that a microscopic description leads to results that are almost exactly in between the two geometrical limits. This finding points to the optimal choice of the IBM Hamiltonian for $\gamma$-soft nuclei.

Figure 1

Self-consistent energy surfaces of ${}^{134}\mathrm{Ba}$ (a) and ${}^{190}\mathrm{Os}$ (b) up to 5 MeV in energy from the minima with the DD-PC1 and with the Skyrme SkM* functionals, respectively. The corresponding mapped energy surfaces of the IBM with (c),(d) and without (e),(f) the three-body term of Eq. (2) are plotted.

Figure 2

The energy ratios (a) $S(4,3,2)$ and (b) $S(5,4,3)$, and (c) the $B(E2;3_1^{+}\to 2_2^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio, as functions of the product $N_{\pi }{N}_{\nu }$, for a characteristic set of nonaxial medium and heavy nuclei. IBM(3B) and IBM(2B) denote results obtained with the IBM Hamiltonians with up to three- and two-body terms, respectively. The Skyrme SkM* and relativistic DD-PC1 functionals are used. Data are from Refs. 29, 32, and D-F and W-J denote the limits of the rigid-triaxial and the $\gamma$-unstable [or O(6)] models, respectively.

Figure 3

Low-lying spectra and $B(E2)$ values (in Weisskopf units) of ${}^{190}\mathrm{Os}$. The bands calculated with IBM Hamiltonians with [IBM(3B)] and without [IBM(2B)] the three-body term of Eq. (2) are compared to experimental data [30]. The Skyrme SkM* EDF is used, and the boson effective charge is adjusted to reproduce the experimental value of $B(E2;2_1^{+}\to 0_1^{+})$.