Integraldifferential 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 integraldifferential FaddeevHahn-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 Schrdinger equation. After a proper angular momentum projection, a set of coupled integraldifferential 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 dt? and dd?, 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.
faddeevhahn-type equation few-body coulomb systems close-coupling-approximation