Effective mass of helium atoms in one-dimensional microporous channels

Abstract

In microporous media characterized by a pore size in the range 5–15 Å, mass transport of He atoms at low temperatures is quantum mechanical in nature. By solving the one-particle Schrödinger equation, we investigate the effective mass ${\mathit{m}}^{\mathrm{*}}$/m of He atoms (bare mass m) moving inside one-dimensional tubular channels consisting of cylindrical cages connected by necks of different diameters and lengths. We find that m/${\mathit{m}}^{\mathrm{*}}$ is a highly nonlinear function of the geometrical parameters characterizing these channels. In certain cases, m/${\mathit{m}}^{\mathrm{*}}$ changes rapidly from 1 to zero indicating the possibility of transition from delocalized to localized state. We also find that in the presence of attractive potential produced by positive ions located on the channel wall, the atoms are trapped near the wall, resulting in a drastic reduction in m/${\mathit{m}}^{\mathrm{*}}$.