# $ T $-matrix scattering elements for coulomb interaction systems

## TL;DR

This paper develops a new representation of two-particle T-matrix scattering elements for Coulomb interactions, facilitating solutions to three-body problems by simplifying integral equations without partial wave expansion.

## Contribution

It introduces a basis-based representation of T-matrix elements that simplifies the Faddeev equations for three-particle Coulomb systems, avoiding partial wave expansion.

## Key findings

- Representation simplifies Faddeev equations
- Applicable to small-particle Coulomb systems
- Reduces integral equations to a factored form

## Abstract

The paper derives the representation of the two-particle T-matrix scattering elements for the Coulomb interaction with respect to special bases without expansion in terms of partial waves. The results obtained are applicable to small-particle systems. The advantage of this expansion also arises in three-body problems when solving the Faddeev equation for three-particle systems. The main problem in solving the Faddeev equation is the approximate choice of approximation for the interaction potentials, at which the T-matrix scattering elements acquire a separable form. However, even in this case the solution to the Faddeev equation does not always become practical in view of the fact that the T-matrix elements themselves do not factor in the integral equations. Here we give the results with the T-matrix elements represented in the basis, for which there is an addition theorem and hence the integral Faddeev equations are reduced to a factored form.