Matrix elements of singular potentials for singlet and triplet S(L = 0) states in two-electron atomic systems

The matrix elements arising for different singular potentials V(r) ∝ r-n(n ≥ 3) in the exponential basis set are considered for two-electron ions/atoms in their S(L = 0) states. The singular structure of such matrix elements is analysed. In general, each of these matrix elements contains a few singular three-body integrals and must be regularized before computations. A rigorous regularization procedure has been developed for the matrix elements which contain the Γ-n,1,1(a, b, c) singular three-body integrals. The closed analytical formulae and numerical results for the singular Araki-Sucher term (n = 3), polarization term (n = 4) and Wichmann-Kroll term (n = 5) are presented