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Effects of high order deformation on superheavy high-$K$ isomers

Using, for the first time, configuration-constrained potential-energy-surface calculations with the inclusion of $β_6$ deformation, we find remarkable effects of the high order deformation on the high-$K$ isomers in $^{254}$No, the focus of recent spectroscopy experiments on superheavy nuclei. For shapes with multipolarity six, the isomers are more tightly bound and, microscopically, have enhanced deformed shell gaps at $N=152$ and $Z=100$. The inclusion of $β_6$ deformation significantly improves the description of the very heavy high-$K$ isomers.