multipole expansion in the nucleus with general shape

[Art Willems]

Looking at it from a mathematical or computational perspective, it might be that the term Q X V is non-linear. This can give a lot of problems in the numerical analysis of nucleus-electron interaction. The multipole expansions certainly helps with this. Solving partial differential equations is normally an easy task, whereas solving something like a Wood-Saxon’s interaction (not-approximated) is a nightmare.

Looking at it from the physical side, the nucleus and the electron cloud consist out of many constituents that have their own interactions amongst themselves. Electrons interact with themselves and so do nucleons. As mentioned, doing a multipole expansion gives hierarchy and importance to an otherwise mush of interactions that are hard to oversee.

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