  Multi-step effects between bound, resonant, and non-resonant states have been
investigated by the continuum-discretized coupled-channels method (CDCC). In
the CDCC, a resonant state is treated as multiple states fragmented in a
resonance energy region, although it is described as a single state in usual
coupled-channel calculations. For such the fragmented resonant states, one-step
and multi-step contributions to the cross sections should be carefully
discussed because the cross sections obtained by the one-step calculation
depend on the number of those states, which corresponds to the size of the
model space. To clarify the role of the multi-step effects, we propose the
one-step calculation without model-space dependence for the fragmented resonant
states. Furthermore, we also discuss the multi-step effects between the ground,
$2^{+}_{1}$ resonant, and non-resonant states in $^6$He for proton inelastic
scattering.
