Generalized Faddeev equations in the Alt-Grassberger-Sandhas form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

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 N N and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.

Adiabatic model of(d,p)reactions with explicitly energy-dependent nonlocal potentials

“…[7,19]. It should be added that the approximate prescription proposed here is intended for use only in the calculation of the incident channel distorting potential in a particular expression for the A(d,p) [20][21][22].…”

Nonlocality in the adiabatic model ofA(d,p)Breactions

“…As the result, the ratio of the measured and calculated cross sections, which is traditionally used to give nuclear structure information in the form of spectroscopic factors and asymptotic normalization coefficients, cannot serve this purpose anymore. Reference [7] suggests a way that the missing many-body information can be included within the Faddeev framework by generalizing it to include couplings to excited target states and modifying the asymptotic conditions at small p-A and n-A distances to account for realistic values of coupling constants in two-body decay vertices. However, the result is a formalism that is too complicated for wide use by nuclear experimentalists and, in fact, no applications have been made so far.…”

Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach

“…Therefore, a new method for treating (d,p) reactions with the exact inclusion of the Coulomb force as well as target excitation was formulated in Ref. [16]. This new approach relies on a separable representation of the pairwise forces.…”