  The purpose of this paper is to develop an alternative theory of deuteron
stripping to resonance states based on the surface integral formalism of
Kadyrov et al. [Ann. Phys. 324, 1516 (2009)] and continuum-discretized coupled
channels (CDCC).
  First we demonstrate how the surface integral formalism works in the
three-body model and then we consider a more realistic problem in which a
composite structure of target nuclei is taken via optical potentials. We
explore different choices of channel wave functions and transition operators
and show that a conventional CDCC volume matrix element can be written in terms
of a surface-integral matrix element, which is peripheral, and an auxiliary
matrix element, which determines the contribution of the nuclear interior over
the variable $r_{nA}$. This auxiliary matrix element appears due to the
inconsistency in treating of the $n-A$ potential: this potential should be real
in the final state to support bound states or resonance scattering and complex
in the initial state to describe $n-A$ scattering. Our main result is
formulation of the theory of the stripping to resonance states using the prior
form of the surface integral formalism and CDCC method. It is demonstrated that
the conventional CDCC volume matrix element coincides with the surface matrix
element, which converges for the stripping to the resonance state. Also the
surface representation (over the variable $r_{nA}$ of the stripping matrix
element enhances the peripheral part of the amplitude although the internal
contribution doesn't disappear and increases with increase of the deuteron
energy. We present calculations corroborating our findings for both stripping
to the bound state and the resonance.
