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We develop a new framework of the deformed quasiparticle-random-phaseapproximation (QRPA) where the Skyrme density functional and thedensity-dependent pairing functional are consistently treated. Numericalapplications are carried out for the isovector dipole and the isoscalarquadrupole modes in the spherical $^{20}$O and in the deformed $^{26}$Nenuclei, and the effect of the momentum dependent terms of the Skyrme effectiveinteraction for the energy-weighted sum rule is discussed. As a furtherapplication, we present for the first time the moments of inertia of $^{34}$Mgand $^{36}$Mg using the Thouless-Valatin procedure based on the self-consistentdeformed QRPA, and show the applicability of our new calculation scheme notonly for the vibrational modes but also for the rotational modes inneutron-rich nuclei.

Deformed quasiparticle-random-phase approximation for neutron-rich nuclei using the Skyrme energy density functional