Assessing continuum channel importance in continuum-discretized coupled-channels via dynamic polarization potential decomposition

A recurring question in continuum-discretized coupled-channels (CDCC) calculations is which continuum channels carry the breakup coupling, both to interpret the reaction and to decide which channels a model space can safely omit. The standard answer is bin deletion: remove a channel, re-solve the coupled equations, and read the change in the elastic $S$-matrix. We show that this cannot isolate an individual channel's contribution. Deleting a channel forces the surviving model space to reorganize, the neighboring bins rerouting through the off-diagonal Green's function, so the recorded change mixes the channel's own effect with the readjustment of all the others. Working instead from the channel-resolved Feshbach dynamic polarization potential (DPP), whose full-coupling Green's function is a fixed reference shared by every channel, we define an exclusion that removes one channel while holding that reference fixed, returning its contribution to the intact system. The two operations disagree on which continuum bins matter most, for $d$+$^{58}$Ni at 21.6~MeV even reversing their order of importance. The DPP further separates each channel's action into a direct path, virtual excitation and return, and a bridge path, relayed through neighboring bins, a split deletion cannot make; it shows the bins act on the elastic channel mainly as bridges, robustly across angular momentum, and that it is this bridge coupling that reorganizes under deletion. A deletion-based channel importance is therefore best read as the truncated calculation's sensitivity to a channel's removal, not as the channel's intrinsic coupling strength.