Spin Echoes

TLDR

Intense radiofrequency pulses are applied to spins in a liquid within a strong static magnetic field, satisfying NMR conditions and lasting shorter than the decay of the macroscopic magnetization. The study discusses the properties and underlying principles of spin echo signals using Bloch theory. After RF pulses, non‑equilibrium isochromatic moments precess, and due to inhomogeneity‑induced frequency distribution their constructive interference at specific times produces spontaneous nuclear induction signals, with Bloch theory describing the underlying principles and self‑diffusion effects on relaxation. Echo amplitudes enable direct and accurate measurement of relaxation times, and preliminary studies reveal frequency shifts caused by magnetic shielding of nuclei in molecules.

Abstract

Intense radiofrequency power in the form of pulses is applied to an ensemble of spins in a liquid placed in a large static magnetic field ${H}_{0}$. The frequency of the pulsed r-f power satisfies the condition for nuclear magnetic resonance, and the pulses last for times which are short compared with the time in which the nutating macroscopic magnetic moment of the entire spin ensemble can decay. After removal of the pulses a non-equilibrium configuration of isochromatic macroscopic moments remains in which the moment vectors precess freely. Each moment vector has a magnitude at a given precession frequency which is determined by the distribution of Larmor frequencies imposed upon the ensemble by inhomogeneities in ${H}_{0}$. At times determined by pulse sequences applied in the past the constructive interference of these moment vectors gives rise to observable spontaneous nuclear induction signals. The properties and underlying principles of these spin echo signals are discussed with use of the Bloch theory. Relaxation times are measured directly and accurately from the measurement of echo amplitudes. An analysis includes the effect on relaxation measurements of the self-diffusion of liquid molecules which contain resonant nuclei. Preliminary studies are made of several effects associated with spin echoes, including the observed shifts in magnetic resonance frequency of spins due to magnetic shielding of nuclei contained in molecules.