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

TL;DR

This paper develops a new formulation of the generalized Faddeev equations in the AGS form for deuteron stripping reactions, explicitly including target excitations and Coulomb interactions without screening, enhancing the theoretical modeling of such nuclear processes.

Contribution

The paper introduces a novel formulation of the AGS equations that explicitly incorporates target excitations and Coulomb interactions without the need for screening, advancing the theoretical framework for deuteron stripping reactions.

Findings

Derived matrix three-body integral equations with target excitations

Presented Coulomb distorted wave representation without screening

Regularized off-shell Coulomb T-matrix for practical calculations

Abstract

Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of ${A}$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the AGS form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a new formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the $(A+2)$-body operators onto target states, matrix three-body integral equations are derived which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering $T$-matrix which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb T-matrix are regularized to make the obtained equations suitable for calculations. For $NN$ and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.