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Theoretical description of reactions in general, and the theory for $(d,p)$reactions, in particular, needs to advance into the new century. Here deuteronstripping processes off a target nucleus consisting of ${A}$ nucleons aretreated within the framework of the few-body integral equations theory. Thegeneralized Faddeev equations in the AGS form, which take into account thetarget excitations, with realistic optical potentials provide the most advancedand complete description of the deuteron stripping. The main problem inpractical application of such equations is the screening of the Coulombpotential, which works only for light nuclei. In this paper we present a newformulation of the Faddeev equations in the AGS form taking into account thetarget excitations with explicit inclusion of the Coulomb interaction. Byprojecting the $(A+2)$-body operators onto target states, matrix three-bodyintegral equations are derived which allow for the incorporation of the excitedstates of the target nucleons. Using the explicit equations for the partialCoulomb scattering wave functions in the momentum space we present the AGSequations in the Coulomb distorted wave representation without screeningprocedure. We also use the explicit expression for the off-shell two-bodyCoulomb scattering $T$-matrix which is needed to calculate the effectivepotentials in the AGS equations. The integrals containing the off-shell CoulombT-matrix are regularized to make the obtained equations suitable forcalculations. For $NN$ and nucleon-target nuclear interactions we assume theseparable potentials what significantly simplifies solution of the AGSequations.

Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction