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I am looking for the proper (clear cut) classification of terms into contributing to the fine or hyperfine structure of an atom and why e.g. the lamb shift does not fall into either of the classifications.

I have tried looking in books and on the Internet but am just getting informal statements such as that the fine structure is due to relativistic effects without any further clarification.

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  • $\begingroup$ What's wrong with the terms listed here en.m.wikipedia.org/wiki/Hyperfine_structure and the Lamb shift involves interaction between vacuum energy fluctuations and electrons, something which is not mentioned in the hyperfine description? I am probably naively incomplete, but I thought I would ask :) $\endgroup$ – user140606 Jan 21 '17 at 10:44
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    $\begingroup$ @Countto10 my question is more to do with why these terms are classed as the hyperfine structure (and likewise with the fine structure). $\endgroup$ – Quantum spaghettification Jan 21 '17 at 10:54
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    $\begingroup$ For future reference: Curtis, L.J., 2003. Atomic structure and lifetimes: a conceptual approach. Cambridge University Press. (p207) and ned.ipac.caltech.edu/level5/Glossary/Glossary_index.html#DC99 give definitions of these two two phenomenon. $\endgroup$ – Quantum spaghettification Feb 4 '17 at 19:48
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I think the choice of the terms themselves really is just historical baggage. Fine structure corrections to the atomic spectrum can only be observed at relatively high definitions, and hyperfine corrections require even higher definitions.

However, in modern usage the terms have significantly specialized. The fine structure correction to the (hydrogen-like) atomic Hamiltonian are the first order terms in the non-relativistic expansion of the Dirac equation. Even though they are often introduced as the relativistic correction to kinetic energy, the spin-orbit coupling, and the Darwin term, they really have a unified origin, the Dirac equation.

The hyperfine corrections result from the interaction of the nuclear multipole moments (excluding the electric monopole) with internally generated fields. The effects of nuclear spin are sometimes introduced as the next step of spin-related corrections after the spin-orbit term, but a more unified treatment would probably group them together with electric quadrupole effects and so on.

With these definitions, it is easy to see why Lamb shift is not included in either fine structure or hyperfine structure, as it results from vacuum fluctuation and cannot be described by the Dirac equation, or multipole interactions.

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While I agree with the other answer about the terms being historical baggage, I believe the origin of the terms is connected with the historical origin of the fine structure constant $\alpha$ itself. In particular, the fine structure of the Hydrogen atom (relativistic correction to kinetic energy, spin-orbit coupling) is of the order $\alpha^2 E_1$, the square of the fine structure constant times the energy of the ground state.

From what I can tell, all the higher order corrections are collectively referred to as hyperfine structure. For example, the nuclear spin is of order $\frac{m_e}{m_p} \alpha^2 E_1$, and the Lamb shift is of order $\alpha^3 E_1$, and I have heard it included in the hyperfine structure corrections (but I may be mistaken).

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