Generalized Sellmeier Models with Radiation Reaction for the Dielectric Function of Single Crystals and Retardation Effects in Atom-Surface Interactions

We present a generalized Sellmeier model that incorporates radiation reaction to describe the dielectric function of single crystals with greater accuracy. This model enables us to investigate the onset of retardation effects in atom-surface interactions. Our analysis reveals that the transition range from the van der Waals regime (1/z³) to the Casimir Polder regime (1/z⁴) depends critically on the atomic species and the dielectric function of the surface. The transition into the retarded regime proceeds at a surprisingly small distance of about 10 nm (200 Bohr radii) for simple “standard” atoms such as ground-state hydrogen and ground-state helium interacting with typical dielectric surfaces (e.g., intrinsic silicon) [Phys. Rev. A 109, 022808 (2024)]. This is significantly shorter than previous estimates based on the typical characteristic absorption wavelengths of the surface. Larger transition ranges are observed for atoms with an exceptionally large static polarizability such as metastable helium. We present a simple estimate for the critical distance of onset of retardation, z_cr = 137 √( α(0) / Z ) (in atomic units), where α(0) is the static polarizability and Z is the number of electrons in the atom.