Highly accurate evaluation of atomic three-electron integrals of lowest orders

Relativistic corrections to the non-Born-Oppenheimer energies of the lowest singlet Rydberg states of He3 and He4

In this work the authors present an approach to calculate the leading-order relativistic corrections for ground and excited states of helium isotopomers. In the calculations they used variational wave functions expanded in terms of explicitly correlated Gaussians obtained without assuming the Born-Oppenheimer approximation.

Singular and nonsingular three-body integrals for exponential wave functions

Integrals which are individually singular, but which may be combined to yield convergent expressions, are needed for computations of relativistic effects and various properties of atomic and quasiatomic systems. As computations become more detailed and precise, more such integrals are required. This paper presents general formulas for the radial parts of the singular and nonsingular (regular) integrals that occur when three-body systems are described using wave functions that include exponentials in all three interparticle coordinates. Our results are compared with those found in the literature for some of the integrals, and are also shown to be consistent with previously reported results for Hylleraas functions (a limiting case in which one of the exponential parameters is set to zero).