  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 the
neutron-proton $(np)$ interaction model when the nucleon-nucleus optical
potential is nonlocal. The verification of this unusual finding using more
reliable methods is aimed for in the present work. A rigorous Faddeev-type
three-body scattering theory is applied to the study of $(d,p)$ transfer
reactions. The equations for transition operators are solved in the
momentum-space partial-wave framework. Differential cross sections for
$^{26}$Al$(d,p)^{27}$Al reactions are calculated using nonlocal nuclear optical
potentials and a number of realistic $np$ potentials. Only a weak dependence on
the $np$ force model is observed, typically one order of magnitude lower than
in the previous ADWA study. The shape of the angular distribution of the
experimental data is well reproduced. Cross sections of $(d,p)$ transfer
reactions calculated using a rigorous three-body method show little sensitivity
to the $np$ interaction model. This indicates a failure of the ADWA in the
context of nonlocal potentials. Some evident shortcomings of the ADWA are
pointed out.
