Loophole toy models 0 and A

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    Brent Van Neste

    In the derivation of the first order monopole shift, we had two contributions (if we took overlap into account): a term dependent on the monopole field and a monopole shift term, which is zero if the nucleus is a point or the electrons do not enter the nucleus.
    In toy model 0, there are no electrons in the nucleus, so the monopole shift term would be zero. The only contribution would be of the monopole field, which is a negative contribution, so it would lower the energy (E_alpha).
    In toy model A, there are electrons in the nucleus, and as the nucleus is not a point (it’s a dumb-bell), the monopole shift term would not be zero. Therefore, to be consistent with the result from toy model A, the absolute value of the monopole field term should be higher than the monopole shift term.
    This explanation is probably not entirely correct, because I do not see how that would always have to be true.

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