8 pages REVTEX, 4 eps figures, submitted to Phys. Rev. CMaking use of the finite rank separable approach for the quasiparticle random phase approximation enables one to perform nuclear structure calculations in very large two-quasiparticle spaces. The approach is extended to take into account the residual particle-particle interaction. The calculations are performed by using Skyrme interactions in the particle-hole channel and density-dependent zero-range interactions in the particle-particle channel. To illustrate our approach, we study the properties of the lowest quadrupole states in the even-even nuclei $^{128}$Pd, $^{130}$Cd, $^{124-134}$Sn, $^{128-136}$Te and $^{136}$Xe

A finite rank separable approximation for the particle-hole RPA calculations with Skyrme interactions is extended to take into account the pairing. As an illustration of the method energies and transition probabilities for the quadrupole and octupole excitations in some O, Ar, Sn and Pb isotopes are calculated. The values obtained within our approach are very close to those that were calculated within QRPA with the full Skyrme interaction. They are in reasonable agreement with experimental data.

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.

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one-and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.

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 propose an extension of the finite rank separable approximation for the case of charge-exchange nuclear modes. This approximation enables one to reduce considerably the dimensions of the matrices that must be diagonalized to perform QRPA calculations in very large configuration spaces. First, we check that the approximation reproduces reasonably well the full charge-exchange RPA results of the spindipole resonances in the nuclei 90 Zr and 132 Sn. The approach is then applied to the study of the Gamow-Teller and the spin-dipole resonances in the neutron-rich Cd isotopes, within the quasiparticle random phase approximation.Subject Index: 210, 213 §1. IntroductionThe study of spin-isospin excitations in neutron-rich nuclei is presently an important problem not only from the nuclear structure point of view but also because of the special role they play in many astrophysical processes. Many fundamental issues depend on our quantitative understanding of phenomena like beta decays of nuclei, nuclear electron capture or the r-process in nucleosynthesis. It is desirable to have theoretical models which can describe the data wherever they can be measured and which can predict the properties related to spin-isospin excitations in systems too short-lived to allow for experimental studies.Recent progress in measurements of charge-exchange modes have stimulated developments of the nuclear models. For example, the neutron skin thickness of nuclei could be in principle obtained from data on properties of spin-dipole (SD) excitations. 1)-3) If such neutron skin measurements could be done on 208 Pb one would have an independent and accurate check of the expected results from the ambitious PREX project at CEBAF 4), 5) and thus, a reliable determination of the density dependence of the nuclear symmetry energy.At the same time, the experimental studies using the multipole decomposition analysis (MDA) of the (n, p) and (p, n) reactions 2), 3), 6) have clarified the longstanding problem of the missing experimental Gamow-Teller (G-T) strength in nuclei, 7), 8) hence resolving the discrepancy between the random phase approximation (RPA) predictions and G-T measurements. Thus, the field of charge-exchange nuclear excitations is a cornerstone in the study of atomic nuclei, and it is our purpose here at University of Georgia on June 29, 2015 http://ptp.oxfordjournals.org/ Downloaded from 490 A. P. Severyukhin, V. V. Voronov and N. Van Giai to propose a method which can simplify the microscopic calculations of such excited states.The quasiparticle random phase approximation (QRPA) with the Skyrme interaction is a standard microscopic approach in nuclear structure theory. 9), 10) Many charge-exchange versions of it were developed during the last decade. 7), 8), 11)-16) Their common feature is that they allow to relate the properties of the ground states and excited states through the same energy density functional. On the other hand, it would be desirable to extend the description beyond the QRPA scheme i...

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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