Abstract. We have used the (α, 2n) and (α, 4n) reactions and the AFRODITE γ-ray spectrometer to make a comprehensive study of the nucleus 154 Gd below 20h. While the first excited 0 + 2 state at 681 keV is usually considered to be the head of a K π = 0 + β-vibrational band, we propose that the data are best described as two separate vacuum states, the ground state and the 681 keV level, each with its own γ and octupole vibrations, pairing and alignments. The implications of this finding, for understanding the structure of transitional rare-earth nuclei, are discussed.It has been a natural assumption since the early days of the collective model [1,2], that the first excited 0 + 2 state in deformed even-even nuclei is a β-vibration along the symmetry axis. Doubts about this assumption have been expressed [3][4][5][6][7][8][9][10][11][12] over the years and, more recently, a comprehensive review of the characteristic properties of such states was made by Garrett [13]. He found that the properties of most 0 + 2 states were not those of β-vibrations, e.g. in 166 Er [14], and he stressed the role pairing must play in the existence of the observed states.The rare-earth nuclei with neutron numbers N = 88 and 90 have particularly low-lying first excited 0 + 2 levels with excitation energies between 600 and 800 keV, well within the pairing gap of about 2.1 MeV. It has usually been assumed that these 0 + 2 levels are collective β-vibrations based on the ground state |0 + 1 vacuum in spite of the observation that they are very weakly excited in inelastic electron scattering [15,16], which is unusual for states with a collective nature. The N = 88 0 + 2 levels are strongly populated in (p,t) two-neutron pickup reactions [17][18][19][20][21] but are weakly populated in (t,p) two-neutron stripping reactions [22,23]. In contrast the N = 90 0 + 2 levels are weakly populated in the (p,t) reactions and strongly populated in the (t,p) reactions. If one assumes that the 0 + 2 levels correspond to collective β-vibrations it remains unclear why there would be a e-mail: jfss@tlabs.ac.za a substantial difference in the population patterns of these states. For nuclei with N ≥ 92 most of the two-neutron transfer strength is concentrated in the ground states [17][18][19][20][21][22]24], which is expected [25] for superfluid nuclei with a ground-state vacuum |0 + 1 well described by the BCS or Hartree-Fock-Bogolyubov theories [26].One should keep in mind that for the N = 88 and 90 nuclei even the most sophisticated models [2,4,27] fail to predict a β-vibration below about 1.5 MeV, adding further doubts about the interpretation of these states as β-vibrations. A totally different approach has been adopted by the Yale group [28] in which the 0 + 2 levels become s = 2 boson excitations [29][30][31] at a critical point X (5) symmetry.An alternative interpretation to β-vibrations for 0states was suggested for the actinide isotopes, where several 0 + 2 states that could not be described as a pairing or β-vibration had been observed by Maher et al...