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We present a calculation of the properties of vibrational states in deformed,axially--symmetric even--even nuclei, within the framework of a fullyself--consistent Quasparticle Random Phase Approximation (QRPA). The sameSkyrme energy density and density-dependent pairing functionals are used tocalculate the mean field and the residual interaction in the particle-hole andparticle-particle channels. We have tested our software in the case ofspherical nuclei against fully self consistent calculations published in theliterature, finding excellent agreement. We investigate the consequences ofneglecting the spin-orbit and Coulomb residual interactions in QRPA.Furthermore we discuss the improvement obtained in the QRPA result associatedwith the removal of spurious modes. Isoscalar and isovector responses in thedeformed ${}^{24-26}$Mg, $^{34}$Mg isotopes are presented and compared toexperimental findings.

Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase-approximation