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-overlapped ranges is considered. Spherical functions basis expansion of the potential introduces partial amplitudes and corresponding radial functions. The approach is generalized to a 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 widens to distributions. Oscillations and rotations are incorporated into the scheme. The cross-sections for electron-vibrational transitions for H-2 are evaluated as an example. (C) 2003 Elsevier Science Ltd. All rights reserved.