Zeeman Splitting Method

If the atoms and molecules are permeated by magnetic field $B$, in the normal Zeeman splitting, the transition splits into three lines

$$\nu_1 = \nu_0-\beta \vert B\vert,$$ (4.35)

$$\nu_2 = \nu_0,$$ (4.36)

$$\nu_3 = \nu_0+\beta \vert B\vert,$$ (4.37)

where $\beta=e \hbar /2 m_e=1.3996{\rm Hz \mu G^{-1}}$ is the Bohr magneton constant. This comes from the fact that the upper and lower levels are splited into $U_m=m_l\beta B$ using the magnetic quantum number $m_l$. HI $\lambda=21$cm, OH (maser emissions and thermally excited emissions), H$_2$O maser emissions are used to measure the magnetic field strength. Figure 4.4 represents the correlation between the magnetic field strength and gas density compiled by Fiebig & Guesten (1989), which indicates that $B$ is approximately proportional to $\rho^{1/2}$

Figure 4.4: