Self-consistent separable RPA approach for Skyrme forces: Axial nuclei

The self-consistent separable RPA (random phase approximation) method is formulated for Skyrme forces with pairing. The method is based on a general self-consistent procedure for factorization of the two-body interaction. It is relevant for various density- and current-dependent functionals. The contributions of the time-even and time-odd Skyrme terms as well as of the Coulomb and pairing terms to the residual interaction are taken self-consistently into account. Most of the expression have a transparent analytical form, which makes the method convenient for the treatment and analysis. The separable character of the residual interaction allows to avoid diagonalization of high-rank RPA matrices and thus to minimize the calculation effort. The previous studies have demonstrated high numerical accuracy and efficiency of the method for spherical nuclei. In this contribution, the method is specified for axial nuclei. We provide systematic and detailed presentation of formalism and discuss different aspects of the model