Chapter 8

Molecules in Magnetic Fields

Nuclear magnetic resonance (NMR) experiments subject a sample to a strong, static homogeneous magnetic field Image = (0,0, B) that splits the energy levels of degenerate nuclear spin states. Transitions between these “Zeeman levels” are induced with an oscillating field (radio frequencies around 10–4 cm–1).

8.1  Nuclear Spins

An atomic nucleus with spin angular momentum Image has magnetic moment Image, where γs = gsβN is the gyromagnetic ratio, i.e., the g-factor of the nucleus times the nuclear magneton Image; note that the electron charge is e and the proton charge is -e in our notation. This magnetic moment contributes to the magnetic vector potential, as discussed in problem 8.1. The total vector potential then becomes

Image

where Image. The total magnetic field is then not only the applied external field but also contains contributions from the nuclear magnetic moments, as ...

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