What is "fine structure"

n. the presence of groups of closely spaced spectrum lines observed in the atomic spectrum of certain elements; "the fine structure results from slightly different energy levels"

In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation.

The gross structure of line spectra is the line spectra predicted by the quantum mechanics of non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy levels only depend on the principal quantum number n. However, a more accurate model takes into account relativistic and spin effects, which break the degeneracy of the energy levels and split the spectral lines. The scale of the fine structure splitting relative to the gross structure energies is on the order of (Zα), where Z is the atomic number and α is the fine-structure constant, a dimensionless number equal to approximately 1/137.

The fine structure energy corrections can be obtained by using perturbation theory. To do this one adds three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin-orbit coupling, and the Darwinian term. The full Hamiltonian is given by

where H is the Hamiltonian from the Coulomb interaction. These corrections can also be obtained from the non-relativistic limit of the Dirac equation, since Dirac's theory naturally incorporates relativity and spin interactions.