 Paschen-Back effect

In the Paschen-Back effect, the external magnetic field interaction becomes large compared with the spin-orbit interaction that holds $\mathbf{L}$ and $\mathbf{S}$ coupled. Then $J$ ceases to be a good approximate quantum number; $m_L,m_S$ become more useful, with leading electronic shifts $\Delta E\simeq {\mu }_{B}B(m_L+g_s{m}_S)$. In the ideal complete-decoupling limit an electric-dipole interaction preserves $m_S$, so its spin contribution cancels between the levels and orbital triplet spacing can reappear. Intermediate fields require mixing the coupled states. This is a change of coupling regime, distinct from the weak-field anomalous Zeeman effect; still larger fields require additional terms beyond this linear model.