Abstract
Making use of the finite rank separable approach for the quasiparticle random phase approximation enables one to perform nuclear structure calculations in very large two-quasiparticle spaces. The approach is extended to take into account the residual particle-particle interaction. The calculations are performed by using Skyrme interactions in the particle-hole channel and density-dependent zero-range interactions in the particle-particle channel. To illustrate our approach, we study the properties of the lowest quadrupole states in the even-even nuclei $^{128}\mathrm{Pd}$, $^{130}\mathrm{Cd}$, $^{124\ensuremath{-}134}\mathrm{Sn}$, $^{128\ensuremath{-}136}\mathrm{Te}$, and $^{136}\mathrm{Xe}$.
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