Computation of two-electron screened Coulomb potential integrals in Hylleraas basis sets

The Gegenbauer expansion and Taylor expansion methods are developed to accurately and efficiently calculate the two-electron screened Coulomb potential integrals in Hylleraas basis sets. The combination of these two methods covers the entire parameter space of the integrals, including arbitrary total angular momenta, two-electron configurations, powers of inter-electronic coordinate, and complex screening parameters. Numerical examples are given and comparisons with other computational methods in some restricted situations are made. The present methods can be easily applied to calculate the bound and resonant states of two-electron atoms or exotic three-body systems embedded in the screening environment by using the Hylleraas or Hylleraas-CI basis functions.