Beyond symmetry-projected quasi-particle mean fields

The solution of the Hartree-Fock-Bogoliubov problem with restoration of the broken symmetries before the variation, as it has been formulated within the VAMPIR and EXCITED VAMPIR approaches yields a description of each state of the nucleus by essentially one single symmetry-projected quasi-particle determinant. In the present paper we propose a procedure which allows to go beyond this mean-field approximation and to include the most important additional correlations in a systematic way. In this new approach each state is approximated by a linear combination of several symmetry-projected quasi-particle determinants, and the corresponding quasi-particle transformations are determined successively together with the configuration mixing via a chain of variational calculations. In this way the selection of the relevant configurations for each state is entirely left to the dynamics of the considered system. The method is applied to some selected examples within the 1s0d shell (the lowest three Iπ=1+ states in 20Ne and the 0+, 2+, 4+ members of the 28Si ground-state band). The results are compared to the exact as well as to the VAMPIR and EXCITED VAMPIR results. Considerable improvements with respect to the latter approaches are obtained. (orig.)