Zeeman shift ($\Delta E=g_F{m}_F{\mu }_{B}B$)

The change of an energy level in a magnetic field. The displayed weak-field form applies to a hyperfine level with magnetic projection $m_F$, when $g_F$ is the corresponding Landé g-factor. A transition shift is the difference of the two level shifts divided by Planck constant. A clock transition can have zero first-order transition shift even when its two individual level slopes are nonzero. For $m_F=0$ hyperfine levels, the linear level shift vanishes and quadratic terms remain.