Variational Calculations for Solid and Liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ with a "Shadow" Wave Function

A new class of trial wave functions is introduced to compute variationally the ground-state energy of solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. This wave function is symmetric under particle exchange, translationally invariant, and does not require the a priori introduction of a crystal lattice. It gives a lower energy than and has properties comparable with those given by previous calculations in which atoms are explicitly localized. The same functional form of the wave function is used to investigate the liquid phase, where a lower energy than those given by a wave function of the Jastrow form is obtained as well.