Concentration Dependence of the Effective Mass of ${}^3\mathrm{He}$ Atoms in ${}^3\mathrm{He}{-}^4\mathrm{He}$ Mixtures

Recent measurements by Yorozu et al. [S. Yorozu, H. Fukuyama, and H. Ishimoto, Phys. Rev. B 48, 9660 (1993)] as well as by Simons and Mueller [R. Simons and R. M. Mueller, Czech. J. Phys. Suppl. 46, 201 (1996)] have determined the effective mass of ${}^3\mathrm{He}$ atoms in a ${}^3\mathrm{He}{-}^4\mathrm{He}$ mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the ${}^3\mathrm{He}$ concentration. Using correlated basis function perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.