Wave Number Dependence of the Relaxation Time for the Longitudinal Mode in Simple Liquid

From the study of the density response function of simple liquids in the dynamical region the microscopic expression for the relaxation time for the longitudinal mode is derived without using any adjustable parameters. The continued fraction representation of the generalized Langevin equation is used. Under two assumptions on the time correlation functions the correlation function of the first random force is approximated as the Maxwell type of relaxation, and the wave number dependence of the Maxwell relaxation time-r is obtained· from the molecular point of view. Numerical calculation of the wave number dependence of-r is carried out for the liquid Argon at T=84.25K, where many particle correlations are approximated by the products of the two-particle correlations. The results are compared with those of other authors. The wave number dependence differs from the results of Akcasu et al.S> especially for small wave numbers