  We report a systematic study of xenon gas diffusion NMR in simple model
porous media: random packs of mono-sized glass beads, and focus on three
specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion
of spins on the order of the pore dimensions during the application of the
diffusion encoding gradient pulses in a PGSE experiment (breakdown of the
'narrow pulse approximation' and imperfect background gradient cancellation),
(ii) the ability to derive long-length scale structural information, and (iii)
effects of finite sample size. We find that the time-dependent diffusion
coefficient, D(t), of the imbibed xenon gas at short diffusion times in small
beads is significantly affected by the gas pressure. In particular, as
expected, we find smaller deviations between measured D(t) and theoretical
predictions as the gas pressure is increased, resulting from reduced diffusion
during the application of the gradient pulse. The deviations are then
completely removed when water D(t) is observed in the same samples. The use of
gas also allows us to probe D(t) over a wide range of length scales, and
observe the long-time asymptotic limit which is proportional to the inverse
tortuosity of the sample, as well as the diffusion distance where this limit
takes effect (~ 1 - 1.5 bead diameters). The Pade approximation can be used as
a reference for expected xenon D(t) data between the short and long time
limits, allowing us to explore deviations from the expected behaviour at
intermediate times as a result of finite sample size effects. Finally, the
application of the Pade interpolation between the long and short time
asymptotic limits yields a fitted length scale (the "Pade length"), which is
found to be ~ 0.13b for all bead packs, where b is the bead diameter.
