Integral–differential equations approach to atomic three-body systems

Three-charge-particle quantum systems with arbitrary masses are treated by a general formalism based on a coordinate-space integral–differential Faddeev–Hahn-type equation. 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 Schrödinger equation. After a proper angular momentum projection, a set of coupled integral–differential equations for the unknown expansion coefficients result, which are solved numerically by discretization for the calculation of both bound state and rearrangement scattering. In this work the formalism is employed to study atomic and muonic three-body systems like negative ion of positronium Ps−=(e+e−e−), positive ion of hydrogen molecule H2+, muonic molecules dtμ and ddμ, and also low-energy charge-transfer reaction for muonium production. Satisfactory results are obtained for all these cases. Comparison with results of other works and details of the numerical scheme are presented.