  The longstanding problem of characterization of the $0^+_2$ states in Gd
isotopes is revisited by adopting the Nilsson$+$BCS mean field and the
random-phase approximation. The interband electric quadrupole transition
strengths varying almost two orders of magnitude are nicely reproduced at the
same time as other observables. These results indicate that the $0^+_2$ states,
in particular, those in lighter isotopes are well described as $\beta$
vibrations excited on top of deformed ground states without recourse to the
shape-coexistence picture.
