Fast and slow sound in a dense gas mixture of helium and neon

For a dense gas equilibrium mixture of 65 at.% He and 35 at.% Ne at T=39.3 K and p=114 bar, we determine from neutron scattering the total dynamic structure factor S(k,{ω}) as a function of frequency {ω} for wave numbers 4k28 nm^-1. For all k, S(k,{ω}) is a sum of four Lorentzians; two located at {ω}=±{}ωₛ⁽¹⁾(k) (directly visible for smaller k) and two located at {ω}=±{}ωₛ⁽²⁾(k) (not visible). ωₛ⁽¹⁾(k)>ck can be attributed to fast oscillations of the light He particles (fast sound) and ωₛ⁽²⁾(k)ck to slow oscillations of the heavy Ne particles (slow sound), where c is the hydrodynamic (k{→}0) sound velocity of the total mixture. ωₛ⁽¹⁾(k) is virtually indistinguishable from the (extended) sound dispersion measured in pure helium at T=39.3 K and p=114 bar. A kinetic model, consistent with our experiment, predicts that fast sound vanishes at k=0.7 nm^-1 and that slow sound merges into hydrodynamic sound then.