Analytical treatment of singular equations in dissociative recombination
The authors study a method of solving singular integral equations of Cauchy type which arise in the multi-channel quantum defect theory of the dissociative recombination process. To treat the singularity they introduce a method based on the use of Chebyshev polynomials which allows an analytical evaluation of all singular integrals that appear in the equations. Great emphasis is given to the case where the coupling potential is approximated by a product of functions of the variables. In this case it is possible to obtain an analytical solution. The methods developed in this paper are compared to conventional ones and shown to be very efficient.
singular integral equation of Cauchy type
scientific article; zbMATH DE number 1422862