There are three effects in the fine structure of atoms: the spin-orbit interaction, the relativistic kinetic energy, and the Darwin term.
However, for atoms heavier than hydrogen, fine structure and spin-orbit interaction seem to be used almost synonymously. Why are the other two terms always neglected?
For example, in the book Atomic Physics by Chris Foot, the other two terms are mentioned for the case of hydrogen, but for all other atoms only the spin-orbit interaction is ever considered.
All three terms originate as the lowest order relativistic corrections, when reducing the Dirac equation to non-relativistic limit, e. g., to the Schrödinger equation, see Wikipedia for the overview, as well as many quantum mechanics textbooks for the derivations (e.g., the Schiff's book). The corrections to the kinetic and the potential energy (the Darwin term) are small quantitative corrections to the terms that are themselves finite. On the other hand, the spin-orbit interaction results in splitting of the spectral lines in the Zeeman effect, corresponding to different combinations of orbital and spin momentum, but having the same total angular momentum. This fine structure of the spectrum is actually the source of the term. Books dealing with atoms and atomic spectra are usually limited to non-relativistic theory, but cannot ignore the effect essential for observations. This is somewhat similar to the ad-hoc inclusion of spin and the Zeeman terms in the non-relativistic QM.
