Hi Thibeau
Since the Hamiltonian consists out of the non-overlap term and the overlap term (or at least that was what I understood from it), it is safe to assume that there are always overlaps. However, I believe that there are ways to ditch the overlap, as I believe there are in nuclear physics as well.
The slides speak of ab initio models somewhere, in which we build up the nucleus from the ground up. In the study of Ab initio nuclei, one can always choose what type of interactions (if I can call it that) will contribute. This is expressed in orders, like leading order; two nucleons that are neighbors, next to leading order (NLO), next-to next-to leading order (NNO), etc. While not entirely an answer to your question, it seems that we can do something similar in our study of the multipole expansion here. To be entirely sure I would have to ask someone who has studied nuclear physics better.
Kind regards Art Willems