Posted by Steve Simon on June 16, 2014, 12:30 am, in reply to "Derivation of paramagnetic susceptibility"
This is a really good question, and actually I'm not positive I know the answer, but I think the following: The correction term you propose will be order B^2, so it will not make any difference in any of the paramagnetic calculations. However, addition of this term could then end up modifying the diamagnetic term, which is order B^2. In the diamag calculation, we first start by declaring that for J=0 atoms, there is no paramagnetism so we can ignore the paramagnetic term in the Hamiltonian and only treat the diamag term. The question is, once we apply B, is it correct to neglect this paramag term  particularly if we worry about the minimal coupling term. The answer is certainly that we cannot fully neglect it  but the corrections are of the form written in the footnote on page 218, and are therefore fairly weak. I'm not 100% positive about the last part of this answer, but I will try to find out more and post a reply (won't happen before tomorrow though)! Good luck on the exam! 
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