  The phase transition of nuclei to increasing angular momentum (or spin) and
excitation energy is one of the most fundamental topics of nuclear structure
research. The odd-N nuclei with A equal 160 are widely considered belonging to
the well-deformed region, and their excitation spectra are energetically
favored to exhibit the rotational characteristics. In the present work,
however, there is evidence indicating that the nuclei can evolve from rotation
to vibration along the yrast lines while increasing spin. The simple method,
named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the
evolution from rotational to vibrational structure in nuclei as a function of
spin. In addition, in order to get the insight into the rotational-like
properties of nuclei, theoretical calculations have been performed for the
yrast bands of the odd-A rare-earth nuclei using the total Routhian surfaces
(TRS) model. The TRS plots indicate that the 165Yb and 157Dy isotopes have
stable prolate shapes at low spin states. At higher rotational frequency
(larger than 0.50 MeV), a distinct decrease in the quadrupole deformation is
predicted by the calculations, and the isotopes becomes rigid in the gamma
deformation.
