✍ Scribed by Freeman, Ray
No coin nor oath required. For personal study only.
A pictorial physical model is proposed to describe the characteristic properties of homonuclear multiple-quantum coherence. Double-quantum coherence is prepared by a pulse sequence that aligns two individual spins within a given molecule in a transverse parallel configuration, either r or s. The ensemble average over the entire sample is represented by two pairs of diametrically opposed macroscopic magnetization vectors. For the duration of the evolution interval, spin ᎐ spin splitting is suspended, locking these vectors in opposition, thus accounting for the ''invisibility'' of double-quantum coherence. At the end of the evolution interval, a 90Њ pulse reinstates the normal spin ᎐ spin splitting, allowing differential precession of these vectors and the buildup of a detectable nuclear magnetic resonance response in the receiver. By focusing attention on the evolution of individual spins within a given molecule, we calculate the probability that at the end of the evolution period they are simultaneously aligned parallel or antiparallel to a particular transverse axis, thus obtaining expressions for the modulation of the final observed signal. Fourier transformation as a function of the evolution time t gives a spectrum consisting of 1 the multiple-quantum frequencies, determined by sums and differences of chemical shifts. Calculations for weakly coupled homonuclear two-spin and three-spin systems give results in good agreement with those predicted by the product operator treatment. For the heteronuclear multiple-quantum correlation technique, a purely macroscopic vector picture appears to explain the experimental observations.
📜 SIMILAR VOLUMES
Let us consider a particle trapped in an infinite square well, that is, confined in the interval 0 < x < πa, and also in the Pöschl-Teller family (9.1) viewed as regularizations of such an infinite potential.