Is a quantum of energy such as that in transverse RF field produced by NMR probe absorbed instantaneously by a single nucleus? It would make sense - that way the photon would either exist or not and it would not have to be disappearing gradually like a Cheshire cat :).
If that were so, then how would you reconcile that notion with the gradual nutation picture for a single spin 1/2 nucleus shown in the NMR books, such as text by Dr. Levitt - e.g. Fig. 10.21 of "Spin Dynamics", second edition? - where an RF pulse such as 90 degree gradually transforms spin state
The other thing that's weird in this case - shouldn't it only take half the energy of the photon to convert
There's an elementary discussion of this in: The Magnetic Resonance Myth of Radio Waves. Hoult, D.I. Concepts in Magnetic Resonance 1989, 1, 1-5. And there's an extremely detailed discussion in this paper: The Origins and Present Status of the Radio Wave Controversy in NMR. Hoult, D.I. Concepts in Magnetic Resonance Part A, 2009, 34A(4), 193-216.
Hoult goes through everything theoretically and experimentally. The physics is way beyond me, but he concludes that NMR is a near-field phenomenon best described by Faraday's Law. He goes on to say that if we insist on a quantum explanation for the NMR signal, virtual photons (whatever they are) may provide a reasonable foundation, but that no one knows how such a Hamiltonian can be constructed. He also notes that it hasn't been proved that virtual photons are responsible for the FID, and that such a proof would be a major exercise in QED.
He seems to feel that the NMR phenomenon itself is best described as a classical phenomenon, and specifically that coherent spontaneous emission (radio waves) is not responsible for excitation of coherences or for the NMR signal. Of course, that doesn't extend to all the complications like J coupling and relaxation, which have to be treated quantum mechanically.