Thermal relaxation and coherence dynamics of spin 3/2. II. Strong radio‐frequency field

Abstract

ABSTRACT:The relaxation dynamics of the spin-3/2 density operator under strong, on-resonance radio-frequency (RF) irradiation and in the presence of fluctuating and static quadrupolar interactions is reviewed. The evolution under the lock is analyzed for any value of the static quadrupolar interaction, ranging from isotropic systems to systems exhibiting large splitting far exceeding the line widths. For isotropic systems, relaxation under offresonance spin-locking conditions and in the multiple-pulse quadrupolar echo (QE) experiment is reviewed also. Spin-lock pulse sequences optimized for the selective detection of nuclei involved in slow molecular motion and/or in anisotropic, liquid crystalline environment are discussed. In Part I, the classical relaxation dynamics of spin 3/2 was reviewed.

Multi-Quanta Spin-Locking Nuclear Magnetic Resonance Relaxation Measurements: An Analysis of the Long-Time Dynamical Properties of Ions and Water Molecules Confined within Dense Clay Sediments

“…Finally, a complete basis set of coherences is required to translate Equation (A14) into a matrix form [18,64,[78][79][80].…”

“…To simplify the derivations of these matrices, we selected symmetric and antisymmetric combinations of the coherences [78][79][80]; see Equation (A17). By using these coherences, the three spin operators, I x , I y and I z , become proportional to T 11 (a), T 11 (s) and T 10 , respectively, simplifying the formulation of the Hamiltonians describing the irradiation pulse and the heteronuclear dipolar coupling (see Equations (A7)-(A9)).…”

“…For spin I = 3/2 nuclei, the whole set of coherences splits again into two independent sub-sets [79,80] Figure A3. The eigenvalues ±iλ p with p ∈ {0, · · · , 6} describing their time evolution under the influence of the static quadrupolar Hamiltonian and irradiation pulse [64,79,80] By contrast, the corresponding eigenvectors must be calculated numerically [83].…”

“…The eigenvalues ±iλ p with p ∈ {0, · · · , 6} describing their time evolution under the influence of the static quadrupolar Hamiltonian and irradiation pulse [64,79,80] By contrast, the corresponding eigenvectors must be calculated numerically [83]. For spin I = 7/2 nuclei, no analytical solutions are available, and the eigenvalues and eigenvectors describing the time evolution of the 63 coherences must be solved numerically [55].…”

From NQR to NMR: The complete range of quadrupole interactions

“…In a truly spherically symmetrical field, any nucleus will have zero interaction. Nuclei with small moments, such as 6 Li, will have relatively small interactions, but 55 Mn may have cou-plings of hundreds of MHz (7,8 ). Note that we have not yet mentioned a magnetic field.…”