  The transverse nuclear magnetic resonance (NMR) decays of $^{129}$Xe in
polycrystalline xenon were recently shown to have a universal property: in the
long-time regime these decays all converge to the same sinusoidally modulated
exponential function irrespective of the initial transverse spin configuration
prepared by a sequence of one or more radio frequency pulses. The present work
constitutes a more comprehensive survey of this phenomenon. It examines
transverse decays for several different isotopic concentrations of $^{129}$Xe,
employs additional pulse sequences, and performs similar measurements in a
different material: $^{19}$F in single-crystal and polycrystalline CaF$_2$. We
additionally verified the polycrystalline nature of our frozen xenon samples by
X-ray diffraction measurements. With the possible exception of polycrystalline
CaF$_2$ where the observation of the long-time behavior is limited by the
experimental resolution, all these systems display the long-time universal
behavior characterized by particular values of the exponential decay
coefficient and beat frequency that were unique for each lattice. This behavior
has been theoretically predicted based on the notion of microscopic chaos.
