High-$K$ isomers in transactinide nuclei close to $N=162$

We extend our recent study of shape evolution, collective excitation spectra, and decay properties of transactinide nuclei [V. Prassa, T. Nikšić, and D. Vretenar, Phys. Rev. C 88, 044324 (2013)], based on the microscopic framework of relativistic energy density functionals, to two-quasiparticle (2qp) excitations in the axially deformed Rf, Sg, Hs, and Ds isotopes, with neutron number $N=160–166$. The evolution of high-$K$ isomers is analyzed in a self-consistent axially symmetric relativistic Hartree-Bogoliubov calculation using the blocking approximation with time-reversal symmetry breaking. The occurrence of a series of low-energy high-$K$ isomers is predicted, in particular the $9_{\nu }^{-}$ in the $N=160$ and $N=166$ isotopes, and the ${12}_{\nu }^{-}$ in the $N=164$ nuclei. The effect of the $N=162$ deformed-shell closure on the excitation of 2qp states is discussed. In the $N=162$ isotones we find a relatively low density of 2qp states, with no two-neutron states below 1.6 MeV excitation energy and two-proton states at $\approx 0.5$ MeV higher energy than the lowest 2qp states in neighboring isotopes. This is an interesting result that can be used to characterise the occurrence of deformed shell gaps in very heavy nuclei.

Figure 1

Self-consistent RHB triaxial energy maps of even-even Hs isotopes in the $\beta \text{−}\gamma$ plane ($0^{\circ }\le \gamma \le {60}^{\circ }$). For each nucleus energies are normalized with respect to the binding energy of the absolute minimum.

Figure 2

Lowest two-quasiparticle states in Rf (upper panel) and Sg (lower panel) isotopes with neutron number $N=160–166$. The 2qp states correspond to axially symmetric solutions obtained with the relativistic functional DD-PC1 and a pairing force separable in momentum space. The calculation includes time-reversal symmetry breaking.

Figure 3

Same as described in the caption to Fig. 2 but for the isotopes of Hs (upper panel) and Ds (lower panel).