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A trial shadow wave function is introduced to describe the ground state of He in the solid and liquid phases. We have used Monte Carlo integration to optimize the parameters of this function, and have carried out a thorough analysis of the shadow description of the system. This shows improved pair correlations, an improved condensate fraction, substantially reduced variational energies, and a good equation of state. We have explored the melting and freezing transition, and find the transition densities to be in good agreement with the exact results of Green's function Monte Carlo (GFMC) calculations.We introduce a second shadow wave function in which a basis set expansion is used to optimize the twoparticle correlations. This shadow wave function yields pair-correlation functions in excellent agreement with GFMC, as well as a substantial reduction in the variational energies at all densities.

A new class of variational wave functions for boson systems, shadow wave functions, is used to investigate the properties of solid and liquid He. The wave function is translationally invariant and symmetric under particle interchange. In principle, the calculations for the crystalline phase do not require the use of any auxiliary lattice. Using the Metropolis Monte Carlo algorithm, we show that the additional variational degrees of freedom in the wave function lower the energy significantly. This wave function also allows the crystalization of an equilibrated liquid phase when a crystalline seed is used. The pair correlation function and structure factor S(k) are determined in the liquid phase. The condensate fraction is calculated as well. Results are given for the single-particle distribution function around the lattice positions in the solid phase.