Coulomb problem in momentum space without screening

Abstract

Background: The repulsive Coulomb force poses severe challenges when solving the three-body problem for ($d,p$) reactions on intermediate mass and heavy nuclei. Recently, a new approach based on the Coulomb-distorted basis in momentum space was proposed.Purpose: In this work, we demonstrate the feasibility of using the Coulomb-distorted basis in momentum space for calculating matrix elements expected in a wide range of nuclear reactions.Method: We discuss the analytic forms of the Coulomb wave function in momentum space. We analyze the singularities in the Coulomb-distorted form factors and the required regularization techniques. Employing a separable interaction derived from a realistic nucleon-nucleus optical potential, we compute and study the Coulomb-distorted form factors for a wide range of cases, including charge, angular momentum, and energy dependence. We also investigate in detail the precision of our calculations.Results: The Coulomb-distorted form factors differ significantly from the nuclear form factors except for the very highest momenta. Typically, the structure of the form factor is shifted away from zero momentum due to the Coulomb interaction. Unlike the Yamaguchi forms typically used in three-body methods, our realistic form factors have a short high-momentum tail, which allows for a safe and efficient truncation of the momentum grid.Conclusions: Our results show that the Coulomb-distorted basis can be effectively implemented.