  We present the first low-temperature thermodynamic investigation of the
controlled physisorption of He$^{4}$ gas in carbon single-wall nanotube (SWNT)
samples. The vibrational specific heat measured between 100 mK and 6 K
demonstrates an extreme sensitivity to outgassing conditions. For bundles with
a few number of NTs the extra contribution to the specific heat, C$_{ads}$,
originating from adsorbed He$^{4}$ at very low density displays 1D behavior,
typical for He atoms localized within linear channels as grooves and
interstitials, for the first time evidenced. For larger bundles, C$_{ads}$
recovers the 2D behaviour akin to the case of He$^{4}$ films on planar
substrates (grafoil).
