NMR Relaxation by Redfield's equation in a spin system $I=7/2$

TL;DR

This paper analytically solves Redfield's master equation for a spin $I=7/2$ system, applying it to $^{133}$Cs nuclei in a liquid crystal, providing precise theoretical expressions for relaxation dynamics.

Contribution

It introduces an analytical solution to Redfield's equation for a high-spin system and demonstrates its application to experimental NMR data with high accuracy.

Findings

Analytical solutions match experimental relaxation data.

Method can be extended to other nuclei.

Provides precise mathematical expressions for relaxation dynamics.

Abstract

Redfield's master equation is solved analytically for a nuclear system with spin $I=7/2$. The solutions of each density matrix element are computed using the irreducible tensor operator basis. The $^{133}$Cs nuclei of the caesium-pentadecafluorooctanoate molecule in a lyotropic liquid crystal sample at the nematic phase and at room temperature was used as an experimental setup. Experimental longitudinal and transverse magnetization dynamics of the $^{133}$Cs nuclei signal were monitored and by numerical procedures the theoretical approach generates valuable mathematical expressions with the highest accuracy. The methodology introduced could be extended without major difficulties to other nuclei species.