Ground state correlations and structure of odd spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators one can take into account the Pauli principle corrections. Besides the ground state correlations due to the quasiparticle interaction in the ground state influence the single particle fragmentation as well. In this paper, we generalize the basic QPM equations to account for both mentioned effects. As an illustration of our approach, calculations on the structure of the low-lying states in $^{131}$Ba have been performed.