Partial dynamical symmetry from energy density functionals

We show that the notion of partial dynamical symmetry is robust and founded on a microscopic many-body theory of nuclei. Based on the universal energy density functional framework, a general quantal boson Hamiltonian is derived and shown to have essentially the same spectroscopic character as that predicted by the partial SU(3) symmetry. The principal conclusion holds in two representative classes of energy density functionals: nonrelativistic and relativistic. The analysis is illustrated in application to the axially deformed nucleus ${}^{168}\mathrm{Er}$.

Figure 1

SCMF energy surfaces on the $\beta \text{−}\gamma$ plane for ${}^{168}\mathrm{Er}$, based on the nonrelativistic Skyrme SLy4 and SkP EDFs (first column) and the relativistic DD-PC1 and DD-ME2 EDFs (third column) with different values of pairing strengths $V_0$ in units of ${\mathrm{MeV}\mathrm{fm}}^3$. The corresponding mapped IBM energy surfaces are plotted on the second and fourth columns. Contour spacing is 0.25 MeV, and the global minimum is indicated by a solid circle.

Figure 2

Experimental [51] (EXP) and SU(3)-PDS [6] spectra for ${}^{168}\mathrm{Er}$, compared with the spectra resulting from EDF-based IBM calculations for the Skyrme SLy4 EDF with pairing strength $V_0=1250{\mathrm{MeV}\mathrm{fm}}^3$, and for the relativistic EDF DD-ME2 with $V_0=837{\mathrm{MeV}\mathrm{fm}}^3$.

Figure 3

SU(3) $(\lambda ,\mu )$ decomposition of states in the ground $\left(g\right),\gamma$, and $\beta$ bands for the SU(3)-PDS and various EDF-based calculations. Shown are probabilities larger than 0.5%. The histograms shown from left to right for each band, correspond to the $L_i$ states listed in the upper panels in the order top-to-bottom left to right.