Exchange Energy in bccHe3

Values of the exchange energy $J$ for bcc ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been obtained from the exchange contribution to the pressure in measurements extending to 13 mK. The relation between the exchange energy and the pressure is developed. A brief outline of the experimental arrangement including a description of a simple procedure for obtaining ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ of fairly high purity is given. The data analysis and uncertainty in $J$ are discussed. Values of $\mathrm{}\left|J\right|\mathrm{}$ are given and compared with other determinations. It is found for the solid near melting ($V=24.1\mathrm{}$ ${\mathrm{cm}}^3$/mole), that $\frac{\mathrm{}\left|J\right|\mathrm{}}{k}=0.72\mathrm{}$ mK, with a strong volume dependence $\frac{\partial \ln \mathrm{}\left|J\right|\mathrm{}}{\partial \ln V}\approx 18$. Assuming antiferromagnetic ordering, the Néel temperature for the solid near melting would be $T_N=2.0\mathrm{}$ mK. The specific heat, entropy, and thermal expansion of the solid are considered. A brief comment concerning ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ impurities is made.