Long-range forces between a charged and neutral system

Dispersion-theory techniques, previously used to calculate the two-photon exchange potential $V_{2\gamma }\mathrm{}\left(R\right)\mathrm{}$ between two neutral systems, are used to study $V_{2\gamma }\mathrm{}\left(R\right)\mathrm{}$ 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 $\frac{{\lambda }_e}{R}$ or of order ${\left(\frac{a_0}{R}\right)}^2$ relative to the leading $R^{-4\mathrm{}}$ term.