Three-body scattering at positive energies: Solving the problem of moving logarithmic singularities

Abstract

For three-body scattering at positive total energies, integral equations are obtained whose kernels have no logarithmic singularities on the contour of integration. The corresponding singularities that are present in original integral equations can be circumvented by shifting a part of the contour of integration from the real axis to the complex plane. This is done only for a special auxiliary solution appearing to be an analytic function in this region. The physical amplitude proper is found as one of the solutions to the resulting set of equations. In contrast to conventional techniques, an additional analysis is therefore not required here, so that numerical solutions can be obtained within standard computational schemes.