  Spectroscopic amplitudes play an important role in nuclear capture reactions.
These amplitudes are shown to include both single-particle and polarization
effects: the former through their spatial dependence and the latter through
their normalization (the spectroscopic factors). Coupled-channels equations are
developed for the spectroscopic amplitudes. These equations serve as a
convenient starting point for the derivation of several approximations:
Hartree, Hartree-Fock and two different single-particle models. The
single-particle models include antisymmetry in different ways, but both miss
many-body effects. Therefore, cross sections calculated with either of these
models need to be multiplied by the spectroscopic factor.
