J-matrix method for calculations of three-body Coulomb wave functions and cross sections of physical processes

摘要

The review is devoted to a widely known method of numerical solution to the three-body Coulomb problem, namely, the J-matrix method. Special attention is paid to ways of solving the Lippmann-Schwinger integral equation without attraction of pseudostates. Difficulties related to the formulation of the integral equation in spherical coordinates, leading to the divergence of its integral part if the wave function is calculated with two asymptotically free electrons, are demonstrated. In addition, the relation between exact and approximate solutions turns out to be unclear if the matrix of a residual potential is restricted to a finite number of basis functions, with the latter being increased. It is shown that, in principle, these problems can be avoided by reformulating a problem in parabolic coordinates.