The nature of E1 low-energy strength (LES), often denoted as a "pygmy dipole resonance", is analyzed within the random-phase approximation (RPA) in 208 Pb using Skyrme forces in a fully self-consistent manner. A first overview is given by the strength functions for the dipole, compressional, and toroidal operators. More detailed insight is gained by averaged transition densities and currents where the latter provide a very illustrative flow pattern. The analysis reveals clear isoscalar toroidal flow in the low-energy bin 6.0-8.8 MeV of the LES and a mixed isoscalar/isovector toroidal/compression flow in the higher bin 8.8-10.5 MeV. Thus the modes covered by LES embrace both vortical and irrotational motion. The simple collective picture of the LES as a "pygmy" mode (oscillations of the neutron excess against the nuclear core) is not confirmed.

The multipole vortical, toroidal, and compression modes are analyzed. Following the vorticity concept of Ravenhall and Wambach, the vortical operator is derived and related in a simple way to the toroidal and compression operators. The strength functions and velocity fields of the modes are analyzed in 208 Pb within the random-phase-approximation using the Skyrme force SLy6. Both convection and magnetization nuclear currents are taken into account. It is shown that the isoscalar (isovector) vortical and toroidal modes are dominated by the convection (magnetization) nuclear current while the compression mode is fully convective. The relation between the above concept of the vorticity to the hydrodynamical vorticity is briefly discussed.

A self-consistent factorization of the two-body residual interaction in random-phase approximation ͑RPA͒ is proposed for density-and current-dependent nuclear energy functionals. Following this procedure, a separable RPA ͑SRPA͒ method is constructed. SRPA provides a reliable approximation to exact RPA while considerably simplifying the calculations. The method is tested and exemplified for the Skyrme forces SkI3 and SkM*. 66 044307-1where J ␣ (r) is the static ground-state density andaccounts for the small change through the deformation. Inserting Eq. ͑43͒ into the mean-field Hamiltonian ͑42͒ and expanding the latter in orders of Ĝ , we get, in the first order, the response Hamiltonian ͓V res ,Ĝ ͔ ph in terms of the density functional SEPARABLE RANDOM PHASE APPROXIMATION FOR . . . PHYSICAL REVIEW C 66, 044307 ͑2002͒ 044307-5

We formulate the self-consistent separable random-phase-approximation (SRPA) method and specify it for Skyrme forces with pairing for the case of axially symmetric deformed nuclei. The factorization of the residual interaction allows to avoid diagonalization of high-rank RPA matrices, which dramatically reduces the computational expense. This advantage is crucial for the systems with a huge configuration space, first of all for deformed nuclei. SRPA takes self-consistently into account the contributions of both time-even and time-odd Skyrme terms as well as of the Coulomb force and pairing. The method is implemented to description of isovector E1 and isoscalar E2 giant resonances in a representative set of deformed nuclei: 154 Sm, 238 U, and 254 No. Four different Skyrme parameterizations (SkT6, SkM*, SLy6, and SkI3) are employed to explore dependence of the strength distributions on some basic characteristics of the Skyrme functional and nuclear matter. In particular, we discuss the role of isoscalar and isovector effective masses and their relation to time-odd contributions. High sensitivity of the right flank of E1 resonance to different Skyrme forces and the related artificial structure effects are analyzed.

The spin-flip M1 giant resonance is explored in the framework of the random-phase-approximation (RPA) on the basis of the Skyrme energy functional. A representative set of eight Skyrme parametrizations (SkT6, SkM*, SLy6, SG2, SkO, SkO', SkI4, and SV-bas) is used. Light and heavy, spherical and deformed nuclei ( 48 Ca, 158 Gd, 208 Pb, and 238 U) are considered. The calculations show that spin densities play a crucial role in forming the collective shift in the spectrum. The interplay of the collective shift and spin-orbit splitting determines the quality of the description. None of the considered Skyrme parametrizations is able to describe simultaneously the M1 strength distribution in closed-shell and open-shell nuclei. It is found that the problem lies in the relative positions of proton and neutron spin-orbit splitting. This calls for a better modeling of the tensor and isovector spin-orbit interaction.