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

We develop a new formulation of the continuum quasiparticle random-phase approximation in which the velocity-dependent terms of the Skyrme effective interaction are explicitly treated except the spin-dependent and the Coulomb terms. Numerical analysis using the ${\mathrm{SkM}}^{*}$ parameter set is performed for the isovector dipole and the isovector/isoscalar quadrupole responses in $^{20}\mathrm{O}$ and $^{54}\mathrm{Ca}$. It is shown that the energy-weighted sum rule, including the enhancement factors for the isovector responses, is satisfied with good accuracy. We investigate also how the velocity-dependent terms influence the strength distribution and the transition densities of the low-lying surface modes and the giant resonances.