Interactions between quasiparticles and phonons in odd-even nuclei in the region of 88Sr and 90Zr

Starting from a magic A-particle nucleus the neighbouring systems are investigated using the Green's functions method. For the A- and (A ± 2)-particle systems the well-known RPA equations are established, whereas for the (A ± 1)-particle systems one gets shift-equations, which describe the shift of the energies compared to the Hartree-Fock energies and the fracmentations of the single-particle strength between the quasiparticle states and states of more collective nature (quasiparticle x phonon). The mutual influence of the solutions of the RPA and the shift equations is discussed. Emphasis is put on the consistent inclusion of the particle-hole as well as the particle-particle RPA. As a concrete example the semi-magic nuclei 88Sr and 90Zr are considered. Calculations are performed with a Skyrme-III force. For the RPA and the shift calculations a Landau-Migdal force is used. The parameters are fixed from the consistency relations for nuclear matter and from comparison of the RPA results with empirical data. The shift calculations lead to an enhancement of the protonshell gap as compared to the Hartree-Fock calculations. (orig.)