Is sodium doublet caused by Zeeman effect inside atom? My understanding is that electron and nucleus spin are interacting, creating a magnetic field which is causing Zeeman effect and essentially splitting optical lines emmited by sodium and these lines can be further split by introducing external magnetic field again causing Zeeman effect. Anyone willing to confirm/correct? Thanks!
 A: You're mostly correct.  The sodium doublet is part of the fine structure of the atomic spectrum.  This difference is caused by spin-orbit interaction, which says that the energy of an electron is affected by the alignment between its spin angular momentum $\vec{S}$ and its orbital angular momentum $\vec{L}$.  
Spin-orbit interaction can in some sense be thought of as an "internal Zeeman effect".  Classically, any electron moving in an electric field will "see" a magnetic field in its own rest frame.  Since the electron is orbiting the atom, it "sees" a magnetic field due to the nucleus in its own rest frame.  It is the interaction between this "rest frame magnetic field" and the electron's magnetic dipole moment (proportional to $\vec{S}$) that causes the energy splitting.  
However, you also say that

My understanding is that electron and nucleus spin are interacting, creating a magnetic field...

The interactions between the electron's magnetic field (both due to its motion and its spin) and the nucleus's magnetic dipole moment (also proportional to the nuclear spin) give rise to the hyperfine structure of the atomic spectrum.  As the name implies, these energy splittings are generally much, much smaller than the splittings of the fine structure.
