of the art in conventional variational theories. We introduce then the Shadow Wave
Function (SWF) in its original formulation, and its extension to Local Density Shadow
Wave Function (LD-SvVF), developed in order to describe inhomogeneous systems such
as liquid-solid coexistence. vVe will then present results on the spontaneous crystallization
of a superdense liquid sample using such formalism, on the study of the solid-liquid
coexistence and interface in 4He Finally preliminary results on the extension of SWF to
3He.
