hyperfine structure

Fine structure splits atomic levels at the alpha^2 level; look even closer, with a very high-resolution instrument, and each of those levels is split again by a factor of a thousand smaller. That extra splitting is the hyperfine structure, and its cause sits at the very centre of the atom: the nucleus is not an inert point charge but has its own spin and magnetic moment, and the electrons feel it.

The dominant contribution is the magnetic-dipole interaction between the nuclear spin I and the electronic angular momentum J, of the form H_hf ∝ A I·J; for nuclei with I ≥ 1 an electric-quadrupole term adds on. The nuclear and electronic angular momenta combine into a new total F = I + J, taking values F = |I - J|, ..., I + J, and F, m_F become the good quantum numbers. Because the nuclear magnetic moment is smaller than the electron's by roughly the mass ratio m_e/m_p ~ 1/1836, the hyperfine energy scale is about three orders of magnitude below fine structure. In hydrogen's 1s ground state the two levels F = 1 and F = 0 are split by 1420 MHz — a photon of wavelength 21 cm.

Hyperfine structure gives us two of physics' most useful clocks and probes. The 21-cm line of neutral hydrogen maps the gas of the entire galaxy and the early universe; the 9,192,631,770 Hz hyperfine transition of caesium-133 defines the SI second. An honest note: the 21-cm transition is magnetic-dipole (M1) and strongly forbidden for electric-dipole radiation, so a single atom takes about ten million years to make it — it is astronomically important only because interstellar hydrogen is so vast. Hyperfine structure is also distinct from the isotope shift, which comes from finite nuclear mass and size rather than nuclear spin.