  An elegant formula for coordinates of carbon atoms in a unit cell of a
single-walled nanotube (SWNT) is presented and the potential of neon (Ne)
inside an infinitely long SWNT is analytically derived out under the condition
of the Lennard-Jones potential between Ne and carbon atoms.
  Specific heats of dilute Ne inside long (20, 20) SWNT are calculated at
different temperatures. It is found that Ne exhibits 3-dimensional (3D) gas
behavior at high temperature but behaves as 2D gas at low temperature.
Especially, at ultra low temperature, Ne inside (20, 20) nanotubes behaves as
lattice gas. A coarse method to determine the characteristic temperature
$\mathcal{T}_c$ for low density gas in a potential is put forward. If
$\mathcal{T}\gg \mathcal{T}_c$, we just need to use the classical statistical
mechanics without solving the Shr\"{o}dinger equation to consider the thermal
behavior of gas in the potential. But if $\mathcal{T}\sim \mathcal{T}_c$, we
must solve the Shr\"{o}dinger equation. For Ne in (20,20) nanotube, we obtain
$\mathcal{T}_c\approx 60$ K.
