Calculation of NMR Free Induction Signals for Nuclei of Molecules in a Highly Viscous Medium or a Solid–Liquid System

Abstract

A general solution of the isotropic rotational diffusion equation applied to NMR transverse magnetization of molecules containing two identical spin‐one‐half nuclei is used to obtain the spin–echo amplitudes in one, two, and multiple 90° pulse sequences. Numerical calculations using the rotational correlation times (or rotational diffusion coefficients) appropriate to a highly viscous medium are used to evaluate the observable NMR decay parameters ($T_2*$ and $T_3*$ ). For rapid motion this general calculation gives the well‐known results for secular contributions to transverse relaxation. In the limit of slow motion, the shape parameter ${\mathrm{(BT}}_3\mathrm{*)}$ of the spin–echo amplitude at $2_{\tau }$ is found to depend on the cube root of the product of the splitting constant $\mathrm{(B)}$ and the rotational correlation time ${\mathrm{(\tau }}_c)$ . The relevance of this formalism to solid–liquid systems is also demonstrated.