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 ${x}_{3}\ensuremath{\ll}{10}^{\ensuremath{-}3}$ for the onset of mass-fluctuation-wave behavior.

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