Shadow wave function for liquid and solid He-3

The ideas of the shadow wave function are applied to construct a variational wave function to describe the liquid and the solid phase of a system that obeys Fermi statistics. The shadow variables are introduced in the symmetric correlating factor. The antisymmetric part is a standard determinant of plane waves modified by backflow effect. Variational Monte Carlo calculations for He-3 provide ground-state energies in the liquid phase at the level of the most elaborate trial function available in the literature. With this wave function, properties like translational invariance and antisymmetry under particle interchange are maintained even in the crystalline phase.