Zeeman Splitting

Lab Tricks

If one is ever unaware of the sign of $g_F$ in the equation

$g_F{\mu }_B{m}_F|B|$

you can figure it out if you are talking about stretched states. For instance if I am in the stretched state then I know $I$ and $J$ must be aligned with one another. Since the electron magnetic moment is anti parallel to $J$ if you know how is compares in direction to $-\mu \cdot B$ thus you can tell whether the energy is increasing or decreasing. Then you can use this to find the sign of $g_F$.

Since it came up in the lab, lets go through the logic required to know if you want ${\sigma }^{+}$ or ${\sigma }^{-}$ light in a decreasing field Zeeman slower. When an atom enters the slower its moving very fast. Thus the Doppler shift says the frequency of light seen by the atom is larger than what we would say. Thus we want a magnetic sub-level that increases with larger $B$. Now how can we tell whether that is $m_F=+F$ or $m_F=-F$? Well we care about cycling transitions in the slower because we want to cool the atoms. If we chose the $-F$ state this would mean $J$ is anti aligned with $B$ and thus the magnetic moment of the electron is aligned with $B$ so the energy gets lower because we have $-\mu B$ whereas for the $+F$ state the opposite is true and we get $\mu B$ so the energy rises, which we want to match the photon energy the atom sees.