  In this article an hierarchy of terms in the expansion of the multipolar
Hamiltonian for non relativistic moving atoms in QED is considered. The
particular case of neutral composite systems of 2,3 and 4 particles is
considered. The proposed hierarchy is based on a scaling analysis of the
multipolar Hamiltonian together with a multipolar expansion of the coupling
terms. We give explicit results up to the fourth order in the fine structure
constant.
