The short-range reaction matrix in MQDT treatment of dissociative recombination and related processes

We discuss the Lippmann-Schwinger equation which governs the short-range reaction matrix (K-matrix) in the two-step multichannel quantum defect theory (MQDT) of dissociative recombination and related processes. We show that, if the energy dependence of the electronic coupling between the dissociative state and the ionization continua can be neglected, the convergence of the Born expansion of the Lippmann-Schwinger equation is achieved at second order. For the case of energy-dependent interaction, higher order effects are tested using a non-perturbative method for solving the Lippmann-Schwinger equation. Numerical examples are given for the dissociative recombination and vibrational de-excitation of the H2+ molecular ion. (authors)