Propagators in Quantum Chemistry, 2nd Edition

Chapter 8

Molecules in Magnetic Fields

Nuclear magnetic resonance (NMR) experiments subject a sample to a strong, static homogeneous magnetic field = (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 has magnetic moment , where γ_s = g_sβ_N is the gyromagnetic ratio, i.e., the g-factor of the nucleus times the nuclear magneton ; 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

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