Pairing and nonaxial-shape correlations in N=150 isotones

Abstract

Background: Rotational bands have been measured around $^{250}\mathrm{Fm}$ associated with strong deformed-shell closures. The ${K}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ excited band emerges systematically in $N=150$ isotones raging from plutonium to nobelium with even-$Z$ numbers, and a sharp drop in energies was observed in californium.Purpose: I attempt to uncover the microscopic mechanism for the appearance of such a low-energy ${2}^{\ensuremath{-}}$ state in $^{248}\mathrm{Cf}$. Furthermore, I investigate the possible occurrence of the low-energy ${K}^{\ensuremath{\pi}}={2}^{+}$ state, the $\ensuremath{\gamma}$ vibration, to elucidate the mechanism that prefers the simultaneous breaking of the reflection and axial symmetry to the breaking of the axial symmetry alone in this mass region.Method: I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states.Results: The Skyrme-type SkM* and SLy4 functionals reproduce the fall in energy but not the absolute value of the ${K}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ state at $Z=98$ where the proton two-quasiparticle excitation $[633]7/2\ensuremath{\bigotimes}[521]3/2$ plays a decisive role for the peculiar isotonic dependence. I find interweaving roles by the pairing correlation of protons and the deformed-shell closure at $Z=98$. The SkM* model predicts the ${K}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ state appears lower in energy in $^{246}\mathrm{Cf}$ than in $^{248}\mathrm{Cf}$ as the Fermi level of neutrons is located in between the [622]5/2 and the [734]9/2 orbitals. Except for $^{250}\mathrm{Fm}$ in the SkM* calculation, the ${K}^{\ensuremath{\pi}}={2}^{+}$ state is predicted to appear higher in energy than the ${K}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ state because the quasiproton [521]1/2 orbital is located above the [633]7/2 orbital.Conclusions: A systematic study of low-lying collective states in heavy actinide nuclei provides a rigorous testing ground for microscopic nuclear models. The present paper shows a need for improvements in the EDFs to describe pairing correlations and shell structures in heavy nuclei, that are indispensable in predicting the heaviest nuclei.