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The adiabatic distorted wave approximation (ADWA) is widely used by thenuclear community to analyse deuteron stripping ($d$,$p$) experiments. Itprovides a quick way to take into account an important property of the reactionmechanism: deuteron breakup. In this work we provide a numerical quantificationof a perturbative correction to this theory, recently proposed in [R.C.Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-onenucleon-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 againstcontinuum-discretized coupled channel predictions which treat deuteron breakupexactly.

Perturbative correction to the adiabatic approximation for $(d,p)$ reactions