Kernspins

Kernspins, or nuclear spins, are the intrinsic angular momentum carried by atomic nuclei. They arise from the quantum spins of protons and neutrons and are described by a nuclear spin quantum number I and a magnetic moment μ. The magnetic moment is proportional to the spin, with μ = γ I ħ, where γ is the gyromagnetic ratio. In an external magnetic field B0, nuclear spin levels split due to the Zeeman interaction, producing a Larmor precession at frequency ω0 = γ B0. The exact splitting depends on the nucleus, its environment, and molecular motion.

Nuclei have different spin values. For common nuclei used in spectroscopy, I can be 1/2 (as in 1H, 13C, 15N) or higher (for example, 14N with I = 1, 17O with I = 5/2). Nuclei with I > 1/2 possess a nuclear quadrupole moment, which interacts with electric field gradients in the surrounding lattice. This interaction often broadens or shifts resonances, particularly in solids or in non-symmetric environments.

Interactions and relaxation form the practical basis for measurements. Hyperfine coupling to electron spins can modify line positions and splittings. Nuclear spins exchange energy with their surroundings through relaxation processes: spin-lattice (T1) and spin-spin (T2) relaxation describe energy exchange with the lattice and loss of phase coherence, respectively. In liquids, rapid molecular motion averages out many anisotropic interactions, yielding sharp signals, while in solids lines tend to broaden.

Applications include nuclear magnetic resonance (NMR) spectroscopy, which probes molecular structure and dynamics through transitions with ΔmI = ±1, and magnetic resonance imaging (MRI), which primarily uses 1H signals. Other nuclei such as 13C, 15N, and 31P provide site-specific information. Techniques like dynamic nuclear polarization can enhance signal strength, expanding the range of detectable systems.