Kinetic Theory of Collective Modes in Classical Liquids

By solving the linearized Vlasov-Boltzmann equation it is shown that zero sound can exist in classical liquids. The effective interatomic potential is shown to be expressed in terms of the direct correlation function. The real and imaginary parts of the frequency are expressed analytically for both small and large values of wave-vector k, but in general are obtained numerically. In our solution of the dispersion relation, first ( ordinary) sound and zero sound originate from the same pole; the former is the solution for. smaller k and the latter is that for larger k. We believe that the collective modes observed in classical liquids by neutron scattering experiments should be interpreted as zero sound. The imaginary part of the diffusion pole which contributes to the line width of the quasi-elastic peak, becomes small for the wave-vector. where the form factor S(k) has peaks. 1. Introduction Recently, the new collective modes in classical liquids are observed in the slow neutron inelastic scattering experiments. I ) T'he well-known collective modes in liquids are the ordinary (first) sound, which can be' described by hydrodynamical equation. The.se new modes observed in the neutron scattering experiments belong to the range of so large wave-vectork and frequency (j) that the hydrodynamical description cannot be applied and they have an origin different from first sound. These new collective modes provide an explicit indication of the "solid-like" phenomena in liquids; one, for example, is that the line-width of the quasi-elastic peak of the neutron scattering experiments is narrower than Dk2 (D; diffusion constant) and oscillates against wave-vector k (de Gennes narrowing 2 ) .