Long-range relativistic interactions in the Cowan-Griffin approximation and their QED retardation: Application to helium, calcium, and cadmium dimers

The theory of long-range relativistic interactions in the Cowan-Griffin approximation is formulated and the expression for the leading-order relativistic correction to the dispersion energy is derived. It is shown that the relativistic dispersion energy for closed-shell atoms behaves as C₆ʳᵉˡR^-6 with the interatomic distance R. The relativistic correction to the van der Waals constant δC₆ is expressed as a Casimir-Polder integral of the product of a nonrelativistic frequency-dependent linear-response function with two dipole operators and a frequency-dependent quadratic-response function, including in addition one relativistic operator. In the Cowan-Griffin approximation, there are two contributions, involving the mass-velocity and the one-electron Darwin operators. The QED retardation effect on the long-range relativistic dispersion energy is also considered, and applications to the helium, calcium, and cadmium dimers are presented.