Theory of SolidHe3. I. Comparative Study of Liquid and SolidHe3

The ground state of solid ${\mathrm{He}}^3$ is investigated using a new method. The procedure begins with a Gaussian-Jastrow trial wave function, and calculates the energy expectation value using a cluster development that takes into account the short-range two-particle correlations between all particles in each order of the expansion. This enables a wide range of correlation functions to be used and also permits a simultaneous treatment of the liquid and the solid phases. Numerical results are presented to illustrate this method and to demonstrate the above assertions. More precise numerical calculations, which will attest to the rapid convergence of the expansion and shed light on the phase transition, and the application of this method to the study of the lattice dynamics of correlated crystals will be given in later papers.