Helium Drag in the Theory of Impurity Mobility in Liquid Helium

A "helium-drag" effect is calculated for the mobility of charged impurities in ${\mathrm{He}}^3$, and ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures. For low enough temperatures, the momentum imparted by the impurities to the helium may be partly trapped in the impurity-helium system, thereby raising the conductivity. This effect gives rise to a term in the mobility proportional to the concentration of impurities, and varying as $T^{-2\mathrm{}}$ for the lowest temperatures. It is estimated that the impurity concentration for this effect to be observed is easily within experimental reach for ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures, and possibly even for pure ${\mathrm{He}}^3$.