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Rotational bands in $^{158}$Er at ultra-high spin have been studied in theframework of relativistic and non-relativistic nuclear density functionaltheories. Consistent results are obtained across the theoretical models usedbut some puzzles remain when confronted with experiment. Namely, the many-bodyconfigurations which provide good description of experimental transitionquadrupole moments and dynamic moments of inertia require substantial increaseof the spins of observed bands as compared with experimental estimates, whichare still subject to large uncertainties. If, however, the theoretical spinsassignments turned out to be correct, the experimental band 1 in $^{158}$Erwould be the highest-spin structure ever observed.

Description of 158Er at ultrahigh spin in nuclear density functional theory