New variational treatment of the ground state of solid helium

Abstract

We use a new variational method recently proposed for treating the ground state of quantum crystals to calculate properties of solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. Key improvements over previous variational calculations include avoiding a low-order cluster expansion in determining the density distribution function, and using a quite general and correctly symmetrized single-particle wave function. The variational calculation, which is unrestricted, predicts the correct solidification density within 10%, but the binding energy is about 0.5°K too low possibly because of a superposition approximation. The pressure is in good agreement with experiment. The density distribution function has a Lindemann ratio of 0.24 in accordance with expectations, but the corresponding single-particle wave function is much more spread out. The important implications this result has for the possible existence of Bose-Einstein condensation in solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and also for the size of the exchange integral in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, are briefly discussed.