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Hey all
I was thinking about the “overlap” vs “no overlap” distinctions made in the last video. Is it true that the “no overlap” situation is merely an approximation to the “overlap” one? For the gravitational analogue, there is a clear distinction between the two, but I think this is a bit more tricky for the nucleus and electron cloud, since because of QM we cannot predict exactly where electrons would be present, while for mass distributions (in the classical case), it is very clear where the masses are and if they overlap or not. So is it true that in reality, there is always overlap, but in some cases it is a reasonable approximation to ignore the overlap?
I was also wondering if someone had examples or ideas about in which cases the overlap corrections would matter most. I mean, I can imagine that for some nuclei and electron clouds, the distributions of nucleus and electrons aren’t localised in each other’s neighbourhood (maybe the simple hydrogen atom), while for other cases, it may be that there is significant overlap between the distributions. I was thinking heavier atoms have a heavier nuclei and more protons and electrons, such that the two distributions would be closer to each other, since i) the nucleus is bigger and ii) the stronger Coulomb interaction gets the two charge distributions closer to each other (but the electrons repel each other, so maybe that alters the picture a bit).
What do you think?
Kind regards,
Thibeau WoutersArt WillemsParticipantHi Thibeau
Since the Hamiltonian consists out of the nonoverlap 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), nextto nextto 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

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