same for both beams and will not affect the hyperfine interval, similar to how the interval is insensitive to any detuning of the probe from resonance.

2.  [*Effect of stray magnetic fields.*]{} The primary effect of a magnetic field is to split the Zeeman sublevels and broaden the line without affecting the line center. However, line shifts can occur if there is asymmetric optical pumping into Zeeman sublevels. For a transition $\ket{F,m_F}
        \rightarrow \ket{F',m_{F'}}$, the systematic shift of the line center is $\mu_B(g_{F'}m_{F'} -
        g_Fm_F)B$, where $\mu_B=1.4$ MHz/G is the Bohr magneton, $g$’s denote the Landé $g$ factors of the two levels, and $B$ is the magnetic field. The selection rule for dipole transitions is $\Delta m
        = 0,\pm 1$, depending on the direction of the magnetic field and the polarization of the light. Thus, if the beams are linearly polarized, there will be no asymmetric driving and the line center will not be shifted. We therefore minimize this error in two ways. First, we use polarizing cubes to ensure that the beams have near-perfect linear polarization. Second, we use a magnetic shield around the cell to minimize the field.

The experiment is repeated by reversing the scan direction to 