Quasiparticle random phase approximation with finite rank approximation for Skyrme interactions

A finite rank separable approximation for particle-hole random phase approximation (RPA) calculations with Skyrme interactions is extended to take into account the pairing. As an illustration of the method energies and transition probabilities for the quadrupole and octupole excitations in some O, Ar, Sn, and Pb isotopes are calculated. The values obtained within our approach are very close to those that were calculated within quasiparticle RPA (QRPA) with the full Skyrme interaction. They are in reasonable agreement with experimental data.