The ground state of solid He3 and the exchange interactions between nuclear spins of He3

Abstract

Of the published theories of solid ${He}^{3}$, that of Saunders has been shown to give an a priori prediction of the exchange interaction in fairly good agreement with the experimental results. In this paper, we improve that theory in three ways: (1) by using the correct ${He}^{3}\text{\ensuremath{-}}{He}^{3}$ pair wave function, which is quite different from that used by Saunders; (2) by computing explicitly the single-particle projection of the many-body wave function, rather than replacing it with a Gaussian of equal curvature at the lattice site; and (3) by calculating the exchange integral $J$ by numerical integration from the detailed wave function of (2), rather than by the use of a Gaussian. These changes do not make the agreement with observation significantly better, but, since the underlying theory has no very firm basis, these calculations should be regarded as an example of what is still required to calculate $J$ if one has a good theory of the solid. As for properties other than the exchange interaction, in the case of the bcc phase we have calculated the Debye temperature as $\mathrm{\ensuremath{\theta}}=\mathit{26.0}{(V/\mathit{20})}^{\text{\ensuremath{-}}2.265}$, to be compared with the experimental ${\mathrm{\ensuremath{\theta}}}_{\mathrm{exp}}=\mathit{28.5}{(V/\mathit{20})}^{\text{\ensuremath{-}}2.50}$.