  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.
