Solid 4He in Narrow Porous Media

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 Å and R = 22.5 Å. The radial density profiles show a strong layering of the 4He atoms. In the R = 13 Å 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 Å 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 Å 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.