The Three‐Body Coulomb System

This chapter contains sections titled: Appropriate coordinate systems Separation of internal and external coordinates Spherical polar coordinates Hyperspherical coordinates Relative coordinates Elliptic coordinates Coordinate systems for continuum problems Jacobi coordinates Parabolic coordinates Parabolic-relative coordinates Parabolic-hyperspherical coordinates Approximate three-body states and the parabolic-relative coordinates Asymptotic properties of the three-body wave equation Dynamical screening in few-body systems Two electrons in the field of a positive ion Dynamical screening via complex effective wave vectors Threshold behaviour Kato cusp conditions Compatibility with the Fock expansion Parabolic-hyperspherical approach Parabolic-hyperspherical Schrödinger equation Parabolic-hyperspherical adiabatic expansion Three-body wave functions with mixed boundary conditions Asymptotic states of two bound electrons. Partial-wave decomposition of three-body wave functions Expansion of Coulomb wave functions in spherical harmonics Partial wave expansion of approximate three-body wave functions Three-body S states Partial-wave expansion of two-center Coulomb functions