Nuclear-Spin Exchange Interaction in Solid 3He

Abstract

Solid ³He has an unusually large nuclear spin‐spin exchange interaction, which is due to the large zero‐point motion of the atoms. This exchange can be described by a Hamiltonian of the form $\mathrm{\mathscr{H}\hspace{0.17em}=\hspace{0.17em}-ħJ\hspace{0.17em}}{\mathbf{I}}_1\mathrm{\hspace{0.17em}·\hspace{0.17em}}{\mathbf{I}}_2$ . The parameter $J$ is strongly dependent on the density, decreasing from ${\mathrm{ħJ/k}}_B{\text{\hspace{0.17em}=\hspace{0.17em}2×10}}^{\text{−3}}°\mathrm{K}$ at $\text{V\hspace{0.17em}=\hspace{0.17em}24.6\hspace{0.17em}}{\mathrm{cm}}^3/\mathrm{mole}$ to ${\mathrm{ħJ/k}}_B{\text{\hspace{0.17em}=\hspace{0.17em}4×10}}^{\text{−5}}\mathrm{\hspace{0.17em}°}\mathrm{K}$ at $\text{V\hspace{0.17em}=\hspace{0.17em}19.5\hspace{0.17em}}{\mathrm{cm}}^3/\mathrm{mole}$ in the bcc phase. Hence the exchange is large in comparison with the energy of dipolar interaction $E_{\mathrm{dip}}{\mathrm{/k}}_B{\text{\hspace{0.17em}=\hspace{0.17em}2×10}}^{\text{−8}}\mathrm{\hspace{0.17em}°}\mathrm{K}$ . There is some evidence that the exchange is antiferromagnetic. One can calculate that at the highest stable molar volume, the transition to the ordered state should occur at about ${\text{1.8×10}}^{\text{−3}}\mathrm{\hspace{0.17em}°}\mathrm{K}$ . In the still more dense hcp phase, the exchange continues to decrease with molar volume. The experimental evidence for this exchange comes from nuclear magnetic relaxation measurements taken in several laboratories. This paper presents a review of longitudinal and transverse relaxation data as well as diffusion data and their interpretation in terms of exchange. The consequences of exchange on some thermodynamic properties is then discussed.