Relativistic corrections to the partial wave expansion of two-electron atoms†

The asymptotic behavior of the partial wave expansion (or the CI expansion in terms of AOs with angular quantum number l) of the leading relativistic correction for two-electron atomic ions in a 1S state is studied analytically. In agreement with earlier numerical findings, the partial wave increments of the leading relativistic correction go as (l + 1/2)−2, whereas the nonrelativistic increments go as (l + 1/2)−4. The coefficient of the leading term is 2 α2 π2 ∫ | ψ(r,r,0)|2r3dr for the Dirac Coulomb operator, and surprisingly also the full Dirac-Breit operator, while the Gaunt term gives a contribution of −4α2π2∫|ψ(r,r,0)|2r3dr. The results obtained here rely entirely on the nonrelativistic correlation cusp, and do not require assumptions on a no-pair projection or a short-range regularization of the electron interaction. They do not give any information on what happens beyond the leading order of relativistic corrections. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

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