  The adiabatic distorted wave approximation (ADWA) is widely used by the
nuclear community to analyse deuteron stripping ($d$,$p$) experiments. It
provides a quick way to take into account an important property of the reaction
mechanism: deuteron breakup. In this work we provide a numerical quantification
of a perturbative correction to this theory, recently proposed in [R.C.
Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-one
nucleon-proton potentials. The correction involves an additional, nonlocal,
term in the effective deuteron-target ADWA potential in the entrance channel.
We test the calculations with perturbative corrections against
continuum-discretized coupled channel predictions which treat deuteron breakup
exactly.
