Application of the complex scaling method in solving three-body Coulomb scattering problem

TL;DR

This paper demonstrates that the complex scaling method, combined with Faddeev-Merkuriev equations, effectively solves the three-body Coulomb scattering problem across a wide energy range, including near ionization thresholds.

Contribution

The work introduces a novel application of smooth complex scaling to three-body Coulomb scattering, extending its use beyond previous limitations and validating it against experimental data.

Findings

Successfully applied to electron scattering on Hydrogen and Positronium

Extended the method's applicability to energies beyond ionization thresholds

Achieved results consistent with experimental and theoretical data

Abstract

The three-body scattering problem in Coulombic systems is widespread, however yet unresolved problem by the mathematically rigorous methods. In this work this long term challenge has been undertaken by combining distorted waves and Faddeev-Merkuriev equation formalisms in conjunction with the complex scaling technique to overcome difficulties related with the boundary conditions. Unlike the common belief, it is demonstrated that the smooth complex scaling method can be applied to solve three-body Coulomb scattering problem in a wide energy region, including fully elastic domain and extending to the energies well beyond atom ionization threshold. Newly developed method is used to study electron scattering on ground states of Hydrogen and Positronium atoms as well as a $e^+$+H(n=1) $\rightleftarrows$ p+Ps(n=1) reaction. Where available, obtained results are compared with the experimental data and theoretical predictions, proving accuracy and efficiency of the newly developed method.