Fig. 1.

The angle θ_PH that we measure is the time average, over many nanosececonds, of the angle between the P-to-H vector and the director vector (perpendicular to the time average of the membrane surface). The rotation of the individual lipid molecule about the director makes the phosphorus see a ring of proton magnetization (indicated here by the shaded ring) at the lowest magnetic fields. It is easy to show from classical physics that the field on the axis of the ring is decreased by the factor S_L = (1/2)(3cos²θ_PH –1) when the protons are dynamically delocalized uniformly over the ring. This averaged field is the same as that which would be felt by the phosphorus spin if there were a fictitious proton spin the same distance away, on the director axis, with a magnetic moment equal to that of a proton but multiplied by S_L.