I Particle field strength and sensitivity

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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?
 
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