Secular approximation for scalar-coupled spins ($H_{\mathrm{eff}}=({\omega }_{1}ZI+{\omega }_{2}IZ+JZZ)/2$)

The leading-order averaging of rapidly oscillating exchange terms in the interaction picture of two nuclear Zeeman energy terms. For $\Delta ={\omega }_1-{\omega }_2$,Their first-order time integrals are bounded by $2|J/\Delta |$, so they contribute little when $|\Delta |\gg |J|$, while the stationary Ising coupling $JZZ/2$ survives. Higher orders give frequency shifts of order $J^2/\Delta$. This approximation is controlled by the difference of resonance frequencies, not their common magnitude.