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

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.