Analytical treatment of singular equations in dissociative recombination Original Research Article

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 interest the energy-dependent coupling potential, which gives the integral kernel 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 H2+ as an example. Our method is demonstrated to be much better than the conventional ones, such as the first order perturbation theory and the grid method.