Cowan-Griffin approximation

Moszynski R, Lach G, Jaszunski M, Bussery-Honvault B (2003) Longrange relativistic interactions in the Cowan-Griffin approximation and their QED retardation Application to helium, calcium, and cadmium dimers. Phys Rev A 68 052706... 

The Pauli Hamiltonian is ideally suited for carrying out relativistic corrections as a first-order perturbation to a non-relativistic Hamiltonian. However, the Pauli terms have been used with considerable success in variational self-consistent field (SCF) calculations. Wadt and Hay (1985) used the above Hamiltonian within the Cowan-Griffin approximation to include relativistic effects for heavy atoms except that they typically do not include the spin-orbit effect variationally in the molecular calculations. 

Spin-free relativistic effects are readily incorporated into the ab initio model potential approximation by using a one-component spin-free relativistic method for the atom, such as the Cowan-Griffin method" or the Douglas-Kroll-Hess method. 

The AREP has the advantage that it may be used in standard molecular calculations that are based on A-S coupling. The AREP may be interpreted as containing the relativistic effects included in the Dirac Hamiltonian, with the exception of spin-orbit coupling. This form is the same as that presented by Kahn et al. (33) which is based on the relativistic treatment of Cowan and Griffin (34). The Hamiltonian employed by Cowan and Griffin is based on the Pauli approximation to the Dirac Hamiltonian with the omission of the spin-orbit term. 

Cowan RD, Griffin DC. Approximate relativistic corrections to atomic radial wave functions. J Opt Soc Am 1976 66 1010-1014. 

Crosswhite (23) has used the correlated multiconfiguration Hartree-Fock scheme of Froese-Fisher and Saxena (24) with the approximate relativistic corrections of Cowan and Griffin (25) to calculate the Slater, spin-orbit, and Marvin radial integrals for all of the actinide ions. A comparison of the calculated and effective parameters is shown in Table II. The relatively large differences between calculation and experiment are due to the fact that configuration interaction effects have not been properly included in the calculation. In spite of this fact, the differences vary smoothly and often monotonically across the series. Because the Marvin radial integral M agrees with the experimental value, the calculated ratios M3(HRF)/M (HRF) =0.56 and M4 (HRF)/M° (HRF) =0.38 for all tripositive actinide ions, are used to fix M and M4 in the experimental scheme. 

---