Critique of the Saunders Theory of SolidHe3at 0°K

Abstract

An examination is made of the theory of the ground state of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ proposed by Saunders (EMS) and modified by Garwin and Landesman (GL). We find the theory is inconsistent or wrong in the following respects: Unphysical single-particle functions result from a misapplication of the Pluvinage method of generating a wave function; the heuristic derivation of an expression for the exchange integral $J$ is inconsistent with this wave function; a correct solution for the integral equation for the single-particle probability density has not been given; the heuristic expression used for the cohesive energy is inconsistent with the Pluvinage method. The use of the Pluvinage method and the single-particle probability density in the theory are analyzed in detail. The numerical results given in EMS and Gl, such as for the exchange integral, are shown to be in doubt because of the errors. We discuss a possible modification of the method, which is not subject to these criticisms, and which gives results similar to those of Nosanow's cluster-expansion theory.