Exchange and Thermal Conductivity in bccHe3ContainingHe4Impurity

Using recent theory for solid ${\mathrm{He}}^3$, prediction of the large increase in exchange constant $J$ and thermal resistance $K^{-1\mathrm{}}$ due to ${\mathrm{He}}^4$ impurity is attempted. Using variational methods, a large change in the ${\mathrm{He}}^4$ function but little relaxation (∼0.75%) around the ${\mathrm{He}}^4$ or change in the neighboring ${\mathrm{He}}^3$ functions is found. An increase in $J$ by a factor of ∼1.6 only is directly predicted. If a large relaxation (∼5%) or ${\mathrm{He}}^3$ wave-function change is assumed, a large increase, but to positive $J$ only, occurs. Direct evaluation of the change in the self-consistent force constants around the ${\mathrm{He}}^4$ fails to predict the large defect resistance. It can be predicted using a continuum model, and calculating the local compressibility change which suggests that large relaxation around the ${\mathrm{He}}^4$ may not be needed to explain $K$.