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We develop a new formulation of the continuum quasiparticle random phaseapproximation (QRPA) in which the residual interaction is derived directly fromthe Skyrme energy functional, keeping all the velocity dependent terms of theSkyrme effective interaction. Numerical analysis using the SkM$^*$ parameterset is performed for the isovector dipole and the isovector/isoscalarquadrupole responses in $^{20}$O and $^{54}$Ca. It is shown that theenergy-weighted sum rule including the enhancement factors for the isovectorresponses is satisfied with good accuracy. We investigate also how the velocitydependent terms influence the strength distribution and the transitiondensities of the low-lying surface modes and the giant resonances.

Continuum quasiparticle linear response theory using the Skyrme functional for multipole responses of exotic nuclei