# Virtual Resonant Emission and Oscillatory Long-Range Tails in van der Waals Interactions of Excited States: QED Treatment and Applications

## TL;DR

This paper provides a QED-based analysis of long-range van der Waals interactions involving excited atomic states, revealing resonant emission effects and large interaction coefficients for hydrogen atoms.

## Contribution

It introduces a comprehensive QED framework for excited-state van der Waals interactions, including resonant emission and symmetry effects, with detailed calculations for hydrogen.

## Key findings

- Identification of virtual resonant emission contributions to long-range tails.
- Large numerical coefficients in hydrogen nD-1S interactions.
- Analysis of symmetry-dependent mixing terms in identical excited atoms.

## Abstract

We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails which are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term which depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the ungerade state for close approach), and we include all nonresonant states in our rigorous QED treatment. In order to illustrate the findings, we analyze the fine-structure resolved van der Waals interaction for nD-1S hydrogen interactions with n=8,10,12 and find surprisingly large numerical coefficients.