Abstract
We present a zero-temperature quantum Monte Carlo calculation of liquid $^4$He immersed in an array of confining potentials. These external potentials are centered in the lattice sites of a fcc solid geometry and, by modifying their well depth and range, the system evolves from a liquid phase towards a progressively localized system which mimics a solid phase. The superfluid density decreases with increasing order, reaching a value $ \rho_{\rm s}/\rho = 0.079(16)$ when the Lindemann's ratio of the model equals the experimental value for solid $^4$He.
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