Coulomb Few-Body Systems in the Framework of a Set of Coupled Integral-Differential Equations: Application to e~-e~+e~-and p + (e~-e~+)

摘要

Three-charge-particle quantum systems with arbitrary masses are treated by a general formalism based on coordinate space integral-differential Faddeev-Hahn-type equations. To solve these equations we expand the wave function components in terms of bound states in initial and final channels and project these equations on these bound states as in the close coupling method used in the Schrodinger equation. After a proper angular momentum projection, a set of coupled integral-differential equations for the unknown expansion coefficients results,, which is solved numerically by discretization for the calculation of both bound state and rearrangement scattering. In this work, the formalism is employed to study atomic 3-body systems like negative ion of positronium Ps~-=(e~+e~-e~-) and H_2~+, as well as an anti-hydrogen production 3-body reaction, i.e. p + (e~-e~+) → (pe+) + e~-. Details of the applied numerical schemes are presented.