Theory of SolidHe3. II. The Quasicrystal Approximation

The double cluster expansion procedure first proposed in a previous paper (I) is used to compute expectation values with respect to correlated trial wave functions. A low-order application of this procedure to solid ${\mathrm{He}}^3$ results in the "quasicrystal approximation". An analysis of this approximation is given. Numerical results on the ground-state energy are consistent with calculations by other authors. This paper is complementary to I, and points out the fundamental difficulty common to all nonstochastic variational calculations on solid ${\mathrm{He}}^3$. It suggests that the next stage of progress will rely on a partial summation of the cluster expansion to all orders via the solution of integral equations derived for the solid distribution functions.