Microscopic substructure effects in potential-model descriptions of the $^7$Be$(p,\gamma)^8$B reaction

The spectroscopic factor arises from short-range effects in the nuclear wave function. On the other hand, cross sections for external capture reactions, such as $^7$Be$(p,\gamma)^8$B at low energies, depend primarily on the asymptotic normalization of the bound-state wave function -- a long-range property. We investigate the relationship between potential models and the full many-body problem to illustrate how microscopic substructure effects arise naturally in the relevant transition matrix element and can be (in part) accounted for by a spectroscopic factor.