Two-electron coulomb integrals with minimal group theory. Direct analytic solution and computer program

A general closed-form analytic solution is developed for two-electron Coulomb integrals such as those that appear in perturbative treatments of multielectron atoms. In developing this solution, no recourse is necessary to group theory, Clebsch-Gordan coefficients, or specialized coordinate transformations: only familiar properties of hydrogenic wavefunctions and standard integrals are employed. One constraint from group theory is adopted for the purpose of establishing an upper limit on an index of summation for computational purposes. An accurate and efficient computer program for evaluating such integrals is made available.