Posted by Steve Simon on January 24, 2013, 4:43 pm, in reply to "diverging interaction"
If the two positively charged nuclei are stuck right on top of each other, then you pay a huge Coulomb energy cost (this much I think should be easy).
But in fact, the potential between two atoms becomes extremely large even when the nuclei are not quite on top of each other. Really the potential starts becoming large when the "atomic cores start to overlap". We didn't treat this properly in the lecture at all (except to say that our crude approximations must break down at these distances). One thing that makes it clear that the energy must diverge is the Pauli exclusion principle. If you have an atom with many electrons in its core and you try to put more electrons in the same region of space, the Pauli principle prevents this. The new electrons must go into highly excited states since all the low energy states are already filled. This is what it means to say that when atomic cores overlap, the energy goes way up.
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