Analytical treatment of singular equations in dissociative recombination

The Lippmann-Schwinger type singular integral equation, which arises in the multi-channel quantum defect theory of dissociative recombination process, is investigated. The singularity of its kernel is treated analytically by introducing an energy dependent quadrature. In many cases of physical inter est the energy-dependent coupling potential, which gives the integral kerne l of the equation, is quasi-separable in a way that allows to write down an analytical solution. The analytical treatment as well as the new solution are illustrated by taking the H-2(+) as an example. Our method is demonstra ted to be much better than the conventional ones, such as the first order p erturbation theory and the grid method. (C) 2000 Elsevier Science B.V. All rights reserved.