8 - Comments on electromagnetic form factors of the nucleon

Summary

These comments are intended to provide some historical background to a point that Robert Hofstadter touched on in Chapter 7. The point concerns the remark following his equation (7.4), to the effect that the nonrelativistic physical interpretation of the form factors as a Fourier transform of the charge density “could not hold at the short distances within the proton.” One of us (R.G.S.) took an interest in this specific problem after hearing Hofstadter raise the same issue in a presentation of his work many years ago. At that time he called for some valid physical interpretation of the form factors in the relativistic region, corresponding to this nonrelativistic interpretation. As Hofstadter has often suggested, it is useful to have a physical insight into the meaning of the form factors in order to further their interpretation in terms of the structure of the nucleon.

After the static magnetic moments, the electron–nucleon (e–N) interaction in the limit of q² = 0 (q is the momentum transfer) was the first measurement that gave information about the extended structure of the nucleon. Leslie L. Foldy made the interesting observation that this e–N interaction could be attributed to the anomalous magnetic moment of the neutron. His calculation was based on a relativistic Hamiltonian, which he then extended by assuming that a complete effective relativistic Hamiltonian could be written as a power series in the d'Alembertian operator.