Fine-Structure Constant Connects the Polarizability of Atoms and Vacuum

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 ${\alpha }_{\mathrm{m}}^{\mathrm{q}}=\Phi R_{\mathrm{vdW}}^7$, 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.

5 pages

References in corpus (1)

• State of the art in the determination of the fine structure constant and the ratio $h/m_{\mathrm{u}}$

Cited by in corpus (3)

• Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems
• Quantum-Mechanical Force Balance Between Multipolar Dispersion and Pauli Repulsion in Atomic van der Waals Dimers
• Comprehensive Quantum Framework for Describing Retarded and Non-Retarded Molecular Interactions in External Electric Fields