Towards a Faddeev-AGS description of $(d,p)$ reactions with heavy nuclei: Regularizing integrals with Coulomb functions

TL;DR

This paper develops an improved regularization scheme to evaluate Coulomb distorted form factors in three-body $(d,p)$ reactions involving heavy nuclei, addressing the singular behavior of Coulomb functions in momentum space calculations.

Contribution

It introduces a novel regularization method for Coulomb distorted form factors within the Faddeev-AGS framework, enabling more accurate descriptions of reactions with highly charged nuclei.

Findings

Regularization scheme effectively handles Coulomb singularities.

Enhances the accuracy of $(d,p)$ reaction modeling for heavy nuclei.

Facilitates Coulomb basis calculations without screening.

Abstract

The repulsive Coulomb force poses severe challenges when describing $(d, p)$ reactions for highly charged nuclei as a three-body problem. Casting Faddeev-AGS equations in a Coulomb basis avoids introducing screening of the Coulomb force. However, momentum space partial-wave $t$-matrix elements need to be evaluated in this basis. When those $t$-matrices are separable, the evaluation requires the folding of a form factor, depending on one momentum variable, with a momentum space partial-wave Coulomb function, which has a singular behavior at the external momentum $q$. We developed an improved regularization scheme to calculate Coulomb distorted form factors as the integral over the Coulomb function and complex nuclear form factors.