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Journal of Physics and Chemistry of Solids

Bound state of two 3He atoms confined in a narrow pore

Yoshitsugu Okaue, Dai S. Hirashima

Published Aug 1, 2005• 5 citations
Publisher
DOI
10.1016/j.jpcs.2005.05.048

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We consider the possibility of cooling 3He atoms in dilute solutions with liquid 4He by “filtering out” the hot atoms through a screen of small holes or channels. The proposed method is somewhat analogous to that employed to evaporatively cool trapped gases, and the specific heat of the 3He‐4He mixture makes it feasible to use in a device to refrigerate other samples. Three methods are considered: 1) Effusion through holes having diameters larger than a mean free path allowing atoms to pass through easily; 2) Particle waveguide‐like motion (also effusive) using very narrow channels that greatly restrict the quantum states of the atoms in them; and 3) Wall‐limited diffusion through channels of various widths, in which the wall scattering is disordered so that local density equilibrium is established within a channel. The methods studied all require sufficiently low temperatures and holes or channels with sufficiently small dimensions that temperature equilibrium between the escaping gas and the original gas is avoided; that is, we assume that channel dimensions are smaller than the mean free path for atom‐atom interactions. We find that the particle waveguide and the wall‐limited diffusion methods using channels on the order of the de Broglie wavelength give cooling. Recent advances in nano‐filters give these methods some hope of being practical.
We give a variational Monte Carlo description at T = 0 K of 4He filling a porous glass within the shadow wave function technique. The confining media is modeled by a smooth cylindrical pore, and we have considered two different pore radii: R = 13 A and R = 22.5 A. The radial density profiles show a strong layering of the 4He atoms. In the R = 13 A pore, as the density is increased, solidification takes place layer by layer, starting from the pore wall, and the radius is too small to allow a bulk‐like solid to nucleate in the small liquid region at the center of the pore. For the R = 22.5 A pore we find an hcp lattice accommodated in the central region surrounded by four layers which turn out to be solid at the density of the computation. Computing the one‐body density matrix (in the R = 13 A case) we are able to estimate the Bose‐Einstein condensate fraction, which is still non‐zero even when the whole system is in the solid phase.