Self-consistent separable random-phase approximation for Skyrme forces: Giant resonances in axial nuclei

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 diagonalization of high-ranking RPA matrices to be avoided, 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 self-consistently takes 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 describe isovector E1 and isoscalar E2 giant resonances in a representative set of deformed nuclei: $^{154}\mathrm{Sm}$, $^{238}\mathrm{U}$, and $^{254}\mathrm{No}$. Four different Skyrme parameterizations (SkT6, SkM${}^{*}$, SLy6, and SkI3) are employed to explore the 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. The high sensitivity of the right flank of E1 resonance to different Skyrme forces and the related artificial structure effects are analyzed.