Resonance line shapes for semi-integer spins in liquids

An effective Liouville equation which describes resonance line shapes and is accurate to first order in the nonsecular term is derived. The equation has a quasisecular form but includes T₁ contributions and the effect of the modulation of second order shifts by the molecular rotation. Simple explicit expressions for the linewidth and shift of the $\text{−1/2 → 1/2}$ transition are derived which are valid when the rotation is fast compared to the static second order shifts. The width has a maximum near the the T₁ minimum and a minimum. The line shape for slow motion is also discussed and results of numerical calculation are presented. It is shown that the equations can be interpreted as a modulation of the second order shifts.