Abstract
Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in ^{158}Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes - as done in previous cranking calculations - two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation gamma. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment Q_{t} ~ 10.5 eb is close to the measured value of ~11 eb; hence, it is a candidate for the structure observed in experiment.