  In order to explore the nature of collective modes in weakly bound nuclei, we
have investigated deformation effects and surface flow patterns of isovector
dipole modes in a shape-coexisting nucleus $^{40}$Mg. The calculations were
done in a fully self-consistent continuum finite-amplitude Quasiparticle Random
Phase Approximation (QRPA) in a large deformed spatial mesh. An unexpected
result of pygmy and giant dipole modes having disproportionate deformation
splittings in strength functions was obtained. Furthermore, the transition
current densities demonstrate that the long-sought core-halo oscillation in
pygmy resonances is collective and compressional, corresponding to the lowest
excitation energy and the simplest quantum flow topology. Our calculations show
that surface flow patterns become more complicated as excitation energies
increase.
