The variable-phase method in multichannel electron-atom or electron-ion scattering

Abstract

The variable-phase method is used to transform the system of second-order linear differential equations occurring in the outer region of electron-atom scattering problems (r>r_a, where all exchange potentials can be neglected) into a system of first-order non-linear differential equations. The problem reduces to the direct outwards integration of the desired reactance K matrix, from its value given at r=r_a by application of the R-matrix method in the inner region. The method is tested on various multichannel scattering processes (C+e^-, C³⁺+e^-, N⁺+e^-,...) in the resonant or non-resonant region, when all channels are open or some of them are closed, and with up to 17 channels.