# Long-Range Tails in van der Waals Interactions of Excited-State and Ground-State Atoms

## TL;DR

This paper investigates the long-range behavior of van der Waals interactions between excited and ground-state atoms, revealing a dominant pole contribution that modifies the interaction's functional form at large distances.

## Contribution

It provides a quantum electrodynamic framework that captures the long-range tails of atom-atom interactions, highlighting the importance of pole terms and deriving general expressions for arbitrary atomic states.

## Key findings

- Pole term dominates at long range, changing interaction from 1/R^7 to a cosinusoidal 1/R^2 tail.
- Interaction energy includes a long-range tail proportional to cos[2 (E_m-E_n) R/(hbar c)]/R^2.
- Correct treatment of pole terms is crucial for accurate interaction calculations.

## Abstract

A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term, and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded 1/R^7 Casimir-Polder form to a long-range tail-provided by the Wick-rotated term-proportional to cos[2 (E_m-E_n) R/(hbar c)]/R^2, where E_m < E_n is the energy of a virtual state, lower than the reference state energy E_n, and R is the interatomic separation. General expressions are obtained which can be applied to atomic reference states of arbitrary angular symmetry. Careful treatment of the pole terms in the Feynman prescription for the atomic polarizability is found to be crucial in obtaining correct results.