$ T $-matrix scattering elements for coulomb interaction systems

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.