A microscopic calculation of the effective mass of one ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ impurity in homogeneous liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at zero temperature is performed for an extended Jastrow-Slater wave function, including two- and three-body dynamical correlations and also backflow correlations between the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom and the particles in the medium. The effective mass at equilibrium density, m〈main${\mathrm{〉}}_4^{\mathrm{*}}$/${\mathit{m}}_4$=1.21, is in very good agreement with the recent experimental determination by Edwards et al. The three-particle correlations appear to give a small contribution to the effective mass and different approximations for the three-particle distribution function give almost identical results for ${\mathit{m}}_4^{\mathrm{*}}$/${\mathit{m}}_4$.

DOI:https://doi.org/10.1103/PhysRevB.50.4248