Pressurized He-4 in cylindrical and in hexagonal pores

We give a variational Monte Carlo description at T = 0 K of He-4 filling under pressure a porous glass within the shadow wave function technique. We have considered as confining media two different smooth pores, one with a circular cross-section of radius R = 13 angstrom resembling a Gelsil pore, and the other with a hexagonal cross-section of side S = 14 angstrom resembling a FSM-16 pore. In all the studied cases the density profiles show a strong layering of the He-4 atoms. As the density is increased, solidification takes place layer by layer, starting from the pore wall. Computing the one-body density matrix 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.