  Theories of $(d,p)$ reactions frequently use a formalism based on a
transition amplitude that is dominated by the components of the total
three-body scattering wave function where the spatial separation between the
incoming neutron and proton is confined by the range of the $n$-$p$
interaction, $V_{np}$. By comparison with calculations based on the CDCC method
we show that the $(d,p)$ transition amplitude is dominated by the first term of
the expansion of the three-body wave function in a complete set of Weinberg
states. We use the \nuc{132}{Sn}(d,p)\nuc{133} {Sn} reaction at 30 and 100 MeV
as examples of contemporary interest. The generality of this observed dominance
and its implications for future theoretical developments are discussed.
