Trial shadow wave function for the ground state of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$

A trial shadow wave function is introduced to describe the ground state of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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 two-particle 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.