  The multipole expansion of the polarization interaction between a charged
particle and an electrically charged particle has long been known to be
asymptotic in nature, i.e. the multiple expansion diverges at any finite
distance from the atom. However, it is shown that the multipole expansion of
the polarization potential of a confined hydrogen atom is absolutely convergent
at a distance outside the atoms confinement radius. It is likely that the
multipole expansion of the dispersion interaction of two confined atoms will
also be absolutely convergent provided the internuclear separation of the two
atoms is sufficiency large to exclude any overlap between the electron charge
clouds of the two atoms.
