Quadrupole collective models from the Hartree-Fock standpoint

The assumptions underlying several quadrupole collective models are tested by a comparison with results of self-consistent Hartree-Fock plus BCS calculations using the Skyrme SIII interaction. We analyze the deformed states of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$ in terms of condensates of fermion pairs which have been introduced in the interacting boson model and in the quadrupole phonon model, and in terms of multipole components of the density suggested by the Bohr and Mottelson model. We compare the deformation energy curves obtained by using (i) several multipole truncations of the Hartree-Fock plus BCS pairs, (ii) pairs obtained by a variation after truncation, and (iii) truncated series of multipole correlation energies. The influence of the core and vacuum polarization effects on the structure of the fermion pairs is found to be fairly strong.