  We propose a self-consistent quasi-particle random phase approximation (QRPA)
plus quasi-particle-vibration coupling (QPVC) model with Skyrme interactions to
describe the width and the line shape of giant resonances in open-shell nuclei,
in which the effect of superfluidity should be taken into account in both the
ground state and the excited states. We apply the new model to the Gamow-Teller
resonance in the superfluid nucleus $^{120}$Sn, including both the isoscalar
spin-triplet and the isovector spin-singlet pairing interactions. The strength
distribution in $^{120}$Sn is well reproduced and the underlying microscopic
mechanisms, related to QPVC and also to isoscalar pairing, are analyzed in
detail.
