Fine structure

Fine structure is the splitting of atomic energy levels into closely spaced sublevels, caused mainly by relativistic corrections and interactions involving electron spin.

Spin–orbit interaction: An interaction between a particle’s spin and its orbital angular momentum. It couples electron spin to orbital motion and produces a major fine-structure contribution.
Atomic orbital: A quantum state describing an electron’s spatial distribution in an atom. Orbital angular momentum helps determine which fine-structure sublevels occur.
Hydrogen spectral series: Groups of hydrogen spectral lines whose wavelengths follow regular patterns. Their resolved lines reveal the small energy corrections predicted by fine-structure theory.
Hyperfine structure: Small atomic energy-level splittings caused by interactions between nuclear and electronic magnetic moments. It arises chiefly from nuclear properties, unlike fine structure’s relativistic and electron-spin contributions.
Relativistic kinetic energy correction: The leading correction to nonrelativistic kinetic energy from special relativity. It shifts levels because bound electrons do not obey purely nonrelativistic dynamics.
Electron spin: An intrinsic form of angular momentum carried by electrons. Its coupling to orbital angular momentum distinguishes fine-structure states.
Balmer series: The set of hydrogen spectral lines produced by transitions ending at principal quantum number two. Its visible lines include fine-structure components that can be resolved with sufficient precision.
Zeeman effect: The splitting of atomic energy levels by an external magnetic field. It also splits spectral lines, but requires an applied magnetic field.
Darwin term: A relativistic quantum correction to the energy of an electron in an electric potential. It contributes to fine structure, especially for states with orbital angular momentum zero.
Orbital angular momentum: The angular momentum associated with a particle’s motion through space. It combines with electron spin to set the total angular momentum of each level.

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