  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.
