  Random Phase Approximation (RPA) is the basic method for calculation of
excited states of nuclei over the Hartree-Fock ground state, suitable also for
energy density functionals (EDF or DFT). We developed a convenient formalism
for expressing densities and currents in a form of reduced matrix elements,
which allows fast calculation of spectra for spherical nuclei. All terms of
Skyrme functional were taken into account, so it is possible to calculate
electric, magnetic and vortical/toroidal/compression transitions and strength
functions of any multipolarity. Time-odd (spin) terms in Skyrme functional
become important for magnetic M1 and isovector toroidal E1 transitions. It was
also found that transition currents in pygmy region (low-lying part of E1
resonance) exhibit isoscalar toroidal flow, so the previously assumed picture
of neutron-skin vibration is not the only mechanism present in pygmy
transitions.
  RPA calculations with heavy axially-symmetric nuclei now become feasible on
ordinary PC. Detailed formulae for axial Skyrme RPA are given. Some numerical
results are shown in comparison with the approximate approach of separable RPA,
previously developed in our group for fast calculation of strength functions.
