Single-particle motion in classical monatomic liquids

The scattering law Ss(k, omega ) observed in incoherent neutron scattering is studied in terms of the generalized Langevin equation of motion for its temporal Fourier transform. An approximate Ss(k, omega ) is obtained from a continued-fraction representation of the equation of motion which contains no arbitrary parameters, satisfies the first three moment relations, and has the correct small and large wavevector k dependence at zero energy transfer. It is shown to give a good description of the incoherent scattering from liquid argon measured by Skold, Rowe, Ostrowski and Randolph (1972). The corresponding velocity autocorrelation function is identical to that derived by Berne, Boone and Rice (1966).