Multiphonon γ -vibrational bands in the γ -soft nucleus 138 Nd

The low spin states of ${}^{138}$Nd have been reinvestigated via the ${}^{124}$Te(${}^{19}$F,$4n1p$) reaction at a beam energy of 103 MeV. The quasi-one-phonon $\ensuremath{\gamma}$-vibrational band based on the 1013.7 keV level has been expanded and the quasi-two-phonon $\ensuremath{\gamma}$-vibrational band built on the 1842.7 keV level has been proposed. A systematic comparison supports our assignments for multiphonon $\ensuremath{\gamma}$-vibrational bands in ${}^{138}$Nd. The characteristics of $\ensuremath{\gamma}$ softness in ${}^{138}$Nd have been discussed. Triaxial projected shell model calculations can well describe the rotational feature of the bands, but they fail to reproduce simultaneously the bandhead energies of the two $\ensuremath{\gamma}$-vibrational bands if a fixed triaxial deformation is assumed.