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Adiabatic distorted-wave approximation (ADWA) study of three-body $(d,p)$transfer reactions [G.W. Bailey, N.K. Timofeyuk, and J.A. Tostevin, Phys. Rev.Lett. 117, 162502 (2016)] reported strong sensitivity of cross sections to theneutron-proton $(np)$ interaction model when the nucleon-nucleus opticalpotential is nonlocal. The verification of this unusual finding using morereliable methods is aimed for in the present work. A rigorous Faddeev-typethree-body scattering theory is applied to the study of $(d,p)$ transferreactions. The equations for transition operators are solved in themomentum-space partial-wave framework. Differential cross sections for$^{26}$Al$(d,p)^{27}$Al reactions are calculated using nonlocal nuclear opticalpotentials and a number of realistic $np$ potentials. Only a weak dependence onthe $np$ force model is observed, typically one order of magnitude lower thanin the previous ADWA study. The shape of the angular distribution of theexperimental data is well reproduced. Cross sections of $(d,p)$ transferreactions calculated using a rigorous three-body method show little sensitivityto the $np$ interaction model. This indicates a failure of the ADWA in thecontext of nonlocal potentials. Some evident shortcomings of the ADWA arepointed out.

Weak sensitivity of three-body ($d,p$) reactions to $np$ force models