Condensation of helium in interstitial sites of carbon nanotubes bundles

Helium atoms are believed to be strongly bound within the interstitial channels in bundles of carbon nanotubes. In a recent paper [F. Ancilotto , Phys. Rev. B 70, 165422 (2004)] inhomogeneity in the size distribution of nanotube radii was shown to make a system of He-4 atoms in such an environment effectively a four-dimensional Bose gas, thus permitting a Bose-Einstein condensation (BEC) of the adsorbed atoms into the minimum energy state. This surprising result was obtained for a model of noninteracting atoms in a continuum distribution of (virtually) infinite interstitial channels. Here we investigate how the singular thermal properties of the ideal system and the occurrence of BEC are affected by a more realistic modeling of a bundle of nanotubes where (i) the number of nanotubes is finite and where (ii) He-4 atoms adsorbed within the same interstitial channel interact among themselves. Also in this case we observe an anomalous heat capacity close to the ideal condensation temperature, suggesting the persistence of the condensation transition for interacting He-4 atoms, which might be experimentally observed.