Correlated exponential-basis integrals with logarithmic integrands

Formulas are derived for three-body integrals containing all the interparticle coordinates as exponentials and with one coordinate also entering logarithmically. These integrals are relevant to the computation of relativistic and quantum electrodynamic effects in two-electron systems, and can contribute to an assessment of current approaches for the treatment of such effects. The present work is a generalization of earlier studies by others using Hylleraas wavefunctions (those in which only two of the three interparticle coordinates exhibit exponential dependence). Alternate formulations are developed to yield stability for all values of the parameters. The formulas have been checked by intercomparison of different methods, by agreement with three-dimensional numerical integration, and by their reduction to limiting cases corresponding to Hylleraas integrals. Representative integrals have been tabulated to illustrate the issues governing the choice of optimum formulas.