# 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*_{s}β_{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 ...