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

The asymptotic behavior of the partial wave expansion (or the Cl expansion in terms of AOs with angular quantum number 1) of the leading relativistic correction for two-electron atomic ions in a S-1 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 alpha(2)pi(2) integral(infinity)(0)vertical bar psi(r,r,0)vertical bar(2)r(2)dr for the Dirac Coulomb operator, and surprisingly also the full Dirac-Breit operator, while the Gaunt term gives a contribution of -4 alpha(2)pi(2) integral(infinity)(0) vertical bar psi(r,r,0)vertical bar(2)r(3)dr. 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. (c) 2008 Wiley Periodicals, Inc.