# Van der Waals-London interaction of atoms with pseudo-relativistic kinetic energy

## TL;DR

This paper rigorously establishes the van der Waals-London law for atoms with pseudo-relativistic electrons, detailing the decay of interaction energy and precise energy expansion up to order |D|^{-9}.

## Contribution

It provides the first rigorous proof of van der Waals interactions for systems with pseudo-relativistic kinetic energy, including detailed energy expansion and decay estimates.

## Key findings

- Interaction energy decays as |D|^{-6}
- Computed energy terms up to |D|^{-9} with error of |D|^{-10}
- Proved exponential decay of eigenfunctions in this context

## Abstract

We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions. Particles interact via Coulomb potential and electrons have pseudo-relativistic kinetic energy. We prove the van der Waals-London law, which states that the interaction energy between neutral atoms decays as the sixth power of the distance $|D|$ between the atoms. We rigorously compute all the terms in the binding energy up to the order $|D|^{-9}$ with error term of order $\mathcal{O}(|D|^{-10})$ . As intermediate steps we prove exponential decay of eigenfunctions of multiparticle Schr\"odinger operators with permutation symmetry imposed by the Pauli principle and new estimates of the localization error.