Generalized Zero Range Potentials and Multi-Channel Electron-Molecule Scattering

A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges is considered. Spherical functions basis expansion of the potentials introduces partial amplitudes and corresponding radial functions. The approach is generalized to multi-channel case by a matrix formulation in which a state vector component is associated with a scattering channel. The zero-range potentials naturally enter the scheme when the class of operators of multiplication is widen to distributions. %Analog of multipolar expansion is treated. Spin variables, o Oscillations and rotations are incorporated into the scheme.