Heat capacities of helium in one- and three-dimensional channels at low temperatures

Abstract

The heat capacities of ⁴He and ³He atoms adsorbed in porous high-silica zeolites having channels about 5.5 AA in diameter have been measured below 6 K. In neither atom is the expected quantum degeneracy detected. In one-dimensional channels, in which the direct positional exchange of atoms is prohibited, the heat capacity depends linearly on temperature, T, as C=AT. This result can be understood by the tunnelling two-level system model for glasses or amorphous solids at very low temperatures. The large zero-point motion of the helium atom is reflected in the enormous value of the coefficient A, and in the wider temperature range of the linear term than in glasses. In three-dimensional channels, the heat capacity of helium atoms shows a shoulder around 2 K for lower atomic concentrations. The result below 2 K is reproduced by a consideration of discrete energy levels enhanced in the crossing space of channels. For higher concentrations the heat capacity shows a linear temperature dependence, which can be understood using the same picture as in the case of the one-dimensional system.