van der Waals force between positronium and hydrogenic atoms: Finite-mass corrections

The Feshbach projection-operator formalism is used to derive the asymptotic effective interaction potential between two atoms. Beyond the usual van der Waals potential, falling like ${\mathrm{x}}^{\mathrm{-}6}$, three ${\mathrm{x}}^{\mathrm{-}8}$ terms are also obtained: an attractive dipole-quadrupole term (absent in the positronium-positronium case because of symmetry), a repulsive energy-dependent term, and a repulsive mass-dependent but energy-independent one. This last term was not obtained by Manson and Ritchie using an independent method.