Collisionless Sound in Classical Fluids

The dynamic form factor S(K,ω) for a classical fluid is calculated from the linearized Vlasov equation. Following Percus or Zwanzig, the effective interatomic potential is taken as -kTc(r), where $c(r)$ is the direct correlation function. The result for S(K,ω) is a simple closed expression with no free parameters except for the static structure factor $S(K)$. Using Ashcroft and Lekner's hard-sphere Percus-Yevick results for $S(K)$, we calculate the inelastic neutron scattering from liquid lead. The resulting scattering law shows a strong qualitative similarity with experiment. The narrow quasielastic peak observed experimentally is not, however, given by the calculation. The reasons for this discrepancy are discussed. An extension of the calculations to include a phenomenological collision term is also presented.