Fine-Structure Constant Connects the Polarizability of Atoms and Vacuum

TL;DR

This paper links atomic polarizability and van der Waals radius through the fine-structure constant, providing a new interpretation of fundamental constants and atomic scales based on vacuum and matter properties.

Contribution

It derives a formula connecting atomic polarizability, vdW radius, and the fine-structure constant, offering a novel physical interpretation of these quantities.

Findings

Derived a formula for the constant factor in the polarizability-vdW radius relation.

Confirmed the formula's validity through quantum-mechanical calculations.

Interpreted the fine-structure constant as a ratio of vacuum and matter polarizability densities.

Abstract

We examine the recently derived quantum-mechanical relation between atomic polarizabilities and equilibrium internuclear distances in van der Waals (vdW) bonded diatomic systems [Phys. Rev. Lett. {\bf 121}, 183401 (2018)]. For homonuclear dimers, this relation is described by the compact formula $\alpha_{\rm m}^{\rm q} = \Phi R_{\rm vdW}^7$, where the constant factor in front of the vdW radius was determined empirically. Here, we derive $\Phi = (4\pi\epsilon_0/a_0^4) \times \alpha^{4/3}$ expressed in terms of the vacuum electric permittivity $\epsilon_0$, the Bohr radius $a_0$, and the fine-structure constant $\alpha$. The validity of the obtained formula is confirmed by estimating the value of the fine-structure constant from non-relativistic quantum-mechanical calculations of atomic polarizabilities and equilibrium internuclear vdW distances. The presented derivation allows to interpret the fine-structure constant as the ratio between the polarizability densities of vacuum and matter, whereas the vdW radius becomes a geometrical length scale of atoms endowed by the vacuum field.