Undergrad Exploring the Lamb Shift: G-Factor & Angular Momentum

[Riverplatense]

Good day dear forum, greetings from Argentina. I am studying the Lamb Shift, which says that in the atomic orbitals, an upward energy shift occurs due to an interaction of the electron with itself. This means that a level s can have an energy slightly greater than a level p. So far so good, but there is something I do not understand and it is the following. This discovery also allowed us to estimate that the known factor g had a value slightly greater than 2 and not exactly 2 as previously thought. In the words of the book Rohlf Modern Physics from alpha to Z p.248: "There is a slight difference between the levels 2S (with j = 1/2) and 2P (with j = 1/2) since in the first case the j comes from the intrinsic angular momentum while in the second, the value of j comes from the unit of the orbital angular moment minus a half of the intrinsic angular momentum.If g is exactly equal to 2, then the z component of the angular momentum of the electron due to the intrinsic angular momentum is exactly equal to the z component of the magnetic moment due to a unit of orbital angular momentum. For g = 2, the energies of the n-fixed states depend only on the total angular momentum j and not on the sum of l and s that produce j, so since g is slightly greater than 2, the state P with j = 1/2 is less in energy than S with j = 1/2 ". I do not understand what g = 2 has to do with the z components of the moments being equal and why if g is greater than 2, the state P is smaller than that of S. I think I do not understand anything about that paragraph, any idea?

 

[PeterDonis]

the Lamb Shift, which says that in the atomic orbitals, an upward energy shift occurs due to an interaction of the electron with itself.

Actually, it's due to the effects of vacuum fluctuations in the quantum electromagnetic field. There is no "interaction of the electron with itself" in QED; the only interaction term in the QED Lagrangian is between electrons and photons.