I Particle field strength and sensitivity

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The magnetic moment of an electron is significantly larger than that of a proton, with the electron's moment being approximately 700 times greater. In a magnetic field, the energy of an unpaired electron is also about 700 times higher than that of an unpaired proton. The magnetic moments of most nuclei are smaller than that of the proton, with some like Fe-57 and Au-197 being around 1.5% of the proton's moment. In a protium atom, the energy difference between the unpaired proton and electron is split by 1420 MHz, while proton-proton interactions in molecules exhibit much weaker coupling, typically around 6-8 Hz. The discussion raises questions about why the electron-proton interaction energy is 108 times greater than the proton-proton interaction energy, suggesting a complex relationship between magnetic fields and particle interactions.
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The magnetic moment of an electron is about 700 times bigger than that of a proton. Both have spin 1/2, but in equal external magnetic field, the energy of an unpaired electron is about 700 times bigger than the energy of an unpaired proton.
(All nuclei other than the triton have magnetic momenta smaller than the proton. The weakest magnetic moments, like Fe-57, Au-197 and IIRC some Ir are in the region of 1,5% of proton magnetic moment).
But how are magnetic particles affected by magnetic fields of each other?
In protium atom, of one unpaired proton and one unpaired electron, the relative orientations are split by 1420 MHz.
In molecules, the energy of a proton in the magnetic field of a nearby proton - that is, the J-J coupling of NMR - is typically in the order of magnitude of 6...8 Hz. Sometimes slightly more.
That is 108 times less than the energy of the proton in the field of an electron.
Why is the electron-proton interaction energy 108 times bigger than proton-proton interaction energy, rather than just 103 times bigger like the electron-external field interaction energy?
 
We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following; https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/66a6a6005101a2ffa86cdd48/original/a-derivation-of-maxwell-s-equations-from-first-principles.pdf 'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s...