Configuration-constrained potential-energy-surface calculations are performed including ${\beta }_6$ deformation to investigate high-$K$ isomeric states in nuclei around ${}^{254}$No and ${}^{270}$Ds, the heaviest nuclei where there have been some observations of two-quasiparticle isomers, while data for four-quasiparticle isomers are scarce. We predict the prevalent occurrence of four-quasiparticle isomeric states in these nuclei, together with their favored configurations. The most notable examples, among others, are $K^{\pi }={20}^{+}$ states in ${}^{266,268}$Ds and ${}^{268,270}$Cn having very high $K$ value, relatively low excitation energy, and well-deformed axially symmetric shape. The predicted isomeric states, with hindered spontaneous fission and $\alpha$ decay, could play a significant role in the future study of superheavy nuclei.

• Received 19 February 2014

DOI:https://doi.org/10.1103/PhysRevC.89.044304