Standing-wave rearrangement scattering formalism for multiarrangement quantum-defect theory

Nonrelativistic time-independent quantum scattering theory for collisions with rearrangements is investigated for standing-wave solutions, principal-value Green’s operators, and related reaction operators. The solutions corresponding to different arrangement configurations are obtained directly from the properties of the noninvertible Green’s operators, without having recourse to arguments based on unitarity. By casting multichannel quantum defect theory (MQDT) as a particular case of standing-wave scattering, a formalism for multiarrangement MQDT is presented and methods for calculating the wave functions and reaction matrices are proposed. The formalism is illustrated in connection with current work on ionization and dissociation in ${\mathrm{H}}_2.$