Shape Co-Existence in the Transitional Nuclide ¹⁵⁷Yb

High-spin states in ¹⁵⁷Yb have been populated in the ¹⁴⁴Sm(¹⁶O, 3n)¹⁵⁷Yb fusion-evaporation reaction at a beam energy of 85 MeV, and two rotational bands have been established for the first time. Within the framework of the triaxial particle-rotor model, the energy spectra and single-particle configurations of ¹⁵⁷Yb are investigated. The calculated energy spectra agree well with the experimental data. The newly observed νf7/2 band, and the previously known νi13/2 band in ¹⁵⁷Yb, are also discussed by means of Total-Routhian-Surface methods. The structural characters observed in ¹⁵⁷Yb provide evidence for the shape coexistence of three distinct shapes: prolate, triaxial and oblate. At higher spins, both the νf7/2 band and the νi13/2 band in ¹⁵⁷Yb undergo a shape evolution with sizable alignments occurring.