Quantum-crystal alloys I: Mass-fluctuation waves

The mass fluctuations in a quantum-crystal alloy lead to a long-range interaction between the particles. For low ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ concentrations in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, this interaction requires a modification of the simple picture of mass-fluctuation waves. We determine the effect of this interaction on the motion of a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particle through ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and give an alternate explanation of the data that is assumed to show the existence of these excitations. We set a limit at $x_3\ll {10}^{-3\mathrm{}}$ for the onset of mass-fluctuation-wave behavior.