Spin–orbit interaction

Spin–orbit interaction couples a particle’s intrinsic spin angular momentum to its orbital angular momentum. In nuclei, it splits single-particle energy levels and helps produce the observed shell structure.

Nuclear shell model: A model of the nucleus in which protons and neutrons occupy quantized single-particle states. Spin–orbit splitting is the ingredient that makes this model reproduce the observed magic numbers.
Maria Goeppert Mayer: A physicist who developed the nuclear shell model and shared the 1963 Nobel Prize in Physics. Her shell-model work established the nuclear setting in which strong spin–orbit splitting explained shell closures.
Quantum angular momentum: The quantized rotational quantity governing angular momentum states and their addition in quantum systems. The interaction follows the quantum rules for combining orbital and intrinsic angular momentum.
Nuclear magnetic moment: A nucleus’s magnetic dipole moment, arising from the magnetic moments and motion of its nucleons. Single-particle spin and orbital contributions shaped by shell levels inform magnetic-moment predictions.
Nuclear pairing: The tendency of identical nucleons to form correlated pairs, producing pairing gaps in nuclear spectra. Pairing changes nuclear level occupancy and gaps, but does not produce the spin-dependent single-particle splitting.
Spin angular momentum: Intrinsic angular momentum carried by quantum particles, independent of their motion through space. Its coupling to orbital angular momentum creates the level shifts.
J. Hans D. Jensen: A German physicist who developed the nuclear shell model and shared the 1963 Nobel Prize in Physics. He independently developed the shell-model account that relied on strong spin–orbit coupling.
Quantum number: A discrete value that labels a measurable property or state of a quantum system. Angular-momentum quantum numbers distinguish the nuclear states whose energies are shifted.
Nuclear deformation: A departure of a nucleus’s shape from spherical symmetry. Spin–orbit splitting affects shell gaps and can influence which nuclear shapes are energetically favored.
Centrifugal barrier: An effective energy barrier associated with nonzero orbital angular momentum in a central potential. It depends on orbital angular momentum but is distinct from coupling orbital motion to spin.

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