Journal ArticleRetardation effects in atom-wall interactionsDas, T.; Ullrich, C. A.; Jentschura, U. D.The onset of retardation effects in atom-wall interactions is studied. It is shown that the transition range from the $1/z^3$ short-range (van der Waals) interaction to the $1/z^4$ long-range (Casimir) retarded interaction critically depends on the atomic properties and on the dielectric function of the material. For simple non-alkali atoms (e.g., ground-state hydrogen and ground-state helium) interacting with typical dielectric materials such as intrinsic silicon, the transition to the retarded regime is shown to proceed at a distance of about 10 nm (200 Bohr radii). This is much shorter than typical characteristic absorption wavelengths of solids. Larger transition regimes are obtained for atoms with a large static polarizability such as metastable helium. We present a simple estimate, $z_{crit} = 137 \, \sqrt{\alpha(0)/Z}$ atomic units, where $\alpha(0)$ is the static polarizability (expressed in atomic units) and Z is the number of electrons of the atom.American Physical Society2024-02-0110491382Physical Review A10920228082469-9926https://doi.org/10.1103/PhysRevA.109.0228082149082National Science Foundation