Spin Echoes*t

Intense radiofrequency power in the form of pulses is applied to an ensemble of spins in a liquid placed in a large static magnetic Geld H&. The frequency of the pulsed r-f power satisGes 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 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 Ho. 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 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 echoes, including the observed shifts in magnetic resonance frequency of spins due to magnetic shielding of nuclei contained in molecules. I. INTRODUCTIOH ' N nuclear magnetic resonance phenomena the nu~ - clear systems have relaxation times varying from a few microseconds to times greater than this by several orders of magnitude. Any continuous Larmor precession of the ensemble which takes place in a static magnetic field is finally interrupted by field perturbations due to neighbors in the lattice. The time for which this precession maintains phase memory has been called the spin-spin or total relaxation time, and is denoted by T~. Since T~ is in general large compared with the short response time of radiofrequency and pulse techniques, a new method for obtaining nuclear induction becomes possible. If, at the resonance condition, the ensemble at thermal equilibrium is subjected to an intense r-f pulse which is short compared to T2, the macroscopic magnetic moment due to the ensemble acquires a non-equilibrium orientation after the driving pulse is removed. On this basis Bloch' has pointed out that a transient nuclear induction signal should be observed immediately following the pulse as the macroscopic magnetic moment precesses freely in the applied static magnetic field. This effect has already been reported' and is closely related to another effect, given the name of spin echoes, which is under consideration in this investigation. These echoes refer to spontaneous nuclear induction signals which are observed to appear due to the constructive interference of precessing macroscopic moment vectors after more than one r-f pulse has been applied. It is the purpose of this paper to describe and analyze these eQ'ects due to free Larmor precession in order to show that they can be applied