Condition for Sudden Passage in the Earth’s-Field NMR Technique

The equation of motiondM/dt= γM × B is solved numerically in order to study the dynamic behavior of the magnetization during the cutoff of the polarizing field in the earth's-field NMR technique. It is assumed that the polarizing field is perpendicular to the earth's field and is reduced to zero linearly in a time short compared to all spin relaxation times. The numerical solution for arbitrary cutoff rates is obtained using the fourth-order Runge-Kutta algorithm and is found to be consistent with a power series solution. It is shown that the magnetization remains within a single octant, and that, for moderate to rapid cutoff, the cutoff rate is related to the cone angle of the subsequent free precession by[formula]Here θ^cis the complement of the cone angle in radians, γ is the proton gyromagnetic ratio, andB₀is the magnitude of the static field (normally, the earth's field) used to detect the free precession.