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 doesnt 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.
We prove that the amplitudes for the (d,p), (d,pn) and (e,ep) reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels are invariant under unitary correlation operators while the spectroscopic
factors are not. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and cannot provide a tool to determine the spectroscopic factors.
A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schrodinger equation. This method is well-known
for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $rtoinfty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}rm{N}$, the resonance $^{15}rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}rm{Be}$ and $^{11}rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{rm F}$
The 18O(p,alpha)15N reaction rate has been extracted by means of the Trojan-Horse method. For the first time the contribution of the 20-keV peak has been directly evaluated, giving a value about 35% larger than previously estimated. The present appro
ach has allowed to improve the accuracy of a factor 8.5, as it is based on the measured strength instead of educated guesses or spectroscopic measurements. The contribution of the 90-keV resonance has been determined as well, which turned out to be of negligible importance to astrophysics.
