Shape vibration and quasiparticle excitations in the lowest 0+ excited state in erbium isotopes

The ground and first excited 0⁺ states of the ^-172Er156 isotopes are analyzed in the framework of the generator coordinate method. The shape parameter β is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E 2 transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited 0⁺ states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between, both degrees of freedom are necessary.