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

摘要

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.