Abstract
Dispersion-theory techniques, previously used to calculate the two-photon exchange potential ${V}_{2\ensuremath{\gamma}}(R)$ between two neutral systems, are used to study ${V}_{2\ensuremath{\gamma}}(R)$ acting between a neutral system $A$ and a charged system $B$. For the case when $A$ is an atom and $B$ an electron, general results are given for all corrections of order $\frac{{\ensuremath{\lambda}}_{e}}{R}$ or of order ${(\frac{{a}_{0}}{R})}^{2}$ relative to the leading ${R}^{\ensuremath{-}4}$ term.
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