High-spin states in157,158Er and158,159Tm

High-spin states in ${}_{}{}^{157}{}_{}{}^{}$,158Er and ${}_{}{}^{158}{}_{}{}^{}$,159Tm have been studied via the ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$ ${(}^{40}$Ar,5,4n) and ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ ${(}^{22}$Ne,5,4n) reactions, respectively, using in-beam gamma-ray spectroscopy techniques which included γ-γ coincidence, angular correlation, angular distribution, excitation function, and multiplicity measurements. The favored (π=+, α=+(1/2)) $i_{13/2}$ neutron band in ${}_{}{}^{157}{}_{}{}^{}\mathrm{Er}$ has been established up to the ${\mathrm{}(53/2)\mathrm{}}^{+}$ level (ħω=0.417 MeV), and the favored (π=-, α=-(1/2)) and unfavored (π=-, α=+(1/2)) $h_{11/2}$ proton bands in ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tm}$, up to the ${\mathrm{}(59/2)\mathrm{}}^{\mathrm{-}}$ (ħω=0.454 MeV) and ${\mathrm{}(61/2)\mathrm{}}^{\mathrm{-}}$ (ħω=0.480 MeV) levels, respectively, i.e., well above the range of rotational frequency ħω where a second backbending has been observed in the neighboring even-even nuclei. In ${}_{}{}^{158}{}_{}{}^{}\mathrm{Er}$, the yrast levels have been observed up to ${38}^{+}$, and in ${}_{}{}^{158}{}_{}{}^{}\mathrm{Tm}$, up to ${25}^{\mathrm{-}}$. The favored $i_{13/2}$ band of the odd-N nucleus ${}_{}{}^{157}{}_{}{}^{}\mathrm{Er}$ displays a strong upbending at ħω=0.40 MeV, whereas, in the two branches of the $h_{11/2}$ yrast band of the odd-Z nucleus ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tm}$, no alignment effect has been observed between ħω=0.27 and 0.48 MeV. The experimental results have been analyzed in the framework of the cranked shell model. On the basis of blocking arguments and cranked shell model calculations, the obtained results show that the second backbending in the yrast band of even-even nuclei near A=158 is due to an $h_{11/2}$ proton alignment. The signature splitting of the intrinsic excitation energies (Routhians) and aligned angular momenta in ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tm}$ has been reproduced in cranked shell model calculations by introducing a triaxial deformation. The observed steep rise of the B(M1)/$Q_0^2$ values in the favored and unfavored bands of ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tm}$ are consistent with an increase of ‖$g_K$-$g_R$‖ at the first backbending due to the alignment of a neutron pair around ħω=0.27 MeV. The evolution of the kinematical and dynamical moments of inertia at very high rotational frequencies (ħω>0.50 MeV) yields information on the nuclear pairing correlations in this frequency range.