Notation on energy level for atoms

[KFC]

Hi there,
I am reading an introduction for atomic physics. In one section, it introduces the energy levels for Rubidium and there are some labels like F=1, F=2 etc. shown next to the fine structure of a level . Also refer to http://www.sacher-laser.com/applications/overview/absorption_spectroscopy/rubidium_d2.html, I saw the same symbols. So what is that F=1, F=2 really means? It seems that so many books using the same letter 'F', is that any significance for that? Also, as shown in the reference, for different states $5S_{1/2}$ and $5P_{3/2}$, there will be F=1 and F=2 for each of them, is that any relation between F=1 for $5S_{1/2}$ and F=1 for $5P_{3/2}$?

 

[Simon Bridge]

You are aware of how you get J=L+S in spin-orbit coupling?
Well, there is similar motivation for F=I+S where I is the nuclear magnetic moment operator.
I suspect that is what you are seeing.

http://www.tcm.phy.cam.ac.uk/~bds10/aqp/lec12-14_compressed.pdf