In a previous publication [Phys. Rev. Lett. 110, 112501 (2013)] we have proposed a generalization of the adiabatic model of $(d,p)$ reactions that allows the nonlocality of the nucleon optical potential to be included in a consistent way together with the deuteron breakup. In this model an effective local $d\text{−}A$ potential is constructed from local nucleon optical potentials taken at an energy shifted by $\sim 40$ MeV with respect to the widely used $E_d/2$ value, where $E_d$ is the deuteron incident energy. The effective $d\text{−}A$ potential is shallower than that traditionally used in the analysis of $(d,p)$ reactions within the adiabatic distorted wave approximation and this affects the calculated cross sections and the nuclear structure quantities obtained from their comparison with experimental data. In the present paper we give full derivation of the deuteron effective potential, consider its leading-order term within the local-energy approximation and discuss corrections to the leading-order term. The new method is applied to $(d,p)$ reactions on ${}^{16}$O, ${}^{36}$Ar, and ${}^{40}$Ca targets and the influence of the deviation from the $E_d/2$ rule on the calculated cross sections is quantified.

• Received 25 March 2013

DOI:https://doi.org/10.1103/PhysRevC.87.064610