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

• Published in: International journal of quantum chemistry Vol. 108; no. 12; pp. 2280 - 2290
• Main Author: Kutzelnigg, Werner
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 2008
• Subjects: correlation cusp; partial-wave expansion; relative many-electron theory
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.21747

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 ∫ 0∞ | 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∫ 0∞|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