The effects of the phonon-phonon coupling on the β-decay rates of neutron-rich nuclei are studied in a microscopic model based on Skyrme-type interactions. The approach uses a finite-rank separable approximation (FRSA) of the Skyrme-type particle-hole (p-h) residual interaction. Very large twoquasiparticle spaces can thus be treated. A redistribution of the Gamow-Teller (G-T) strength is found due to the tensor correlations and the 2p − 2h fragmentation of G-T states. As a result, the β − -decay half-lives are decreased significantly. Using the Skyrme interaction SGII together with a volume-type pairing interaction we illustrate this reduction effect by comparing with available experimental data for the Ni isotopes and neutron-rich N = 50 isotones. We give predictions for 76 Fe and 80 Ni in comparison with the case of the doubly-magic nucleus 78 Ni which is an important waiting point in the r-process.

An influence of the phonon-phonon coupling (PPC) on the β-decay half-lives and multi-neutron emission probabilities is analysed within the microscopic model based on the Skyrme interaction with tensor components included. The finite-rank separable approximation is used in order to handle large two-quasiparticle spaces. The even-even nuclei near the r-process pathes at N = 82 are studied. The characteristics of ground states, 2 + excitations and β-decay strength of the neutron-rich Cd isotopes are treated in detail. It is shown that a strong redistribution of the Gamow-Teller strength due to the PPC is mostly sensitive to the multi-neutron emission probability of the Cd isotopes.

Starting from a Skyrme interaction we study the properties of the low-energy spectrum of quadrupole excitations in 90,92 Zr, 92,94 Mo. The coupling between one-and two-phonon terms in the wave functions of excited states are taken into account. We use the finite-rank separable approximation which enables one to perform the QRPA calculations in very large two-quasiparticle spaces. Our results from the SGII Skyrme interaction in connection with the volume pairing interaction are in reasonable agreement with experimental data. In particular, we present the successful description of the M 1 transition between low-energy quadrupole excitations.

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