Sum rules and atomic correlations in classical liquids. III. Numerical estimates and an application

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Abstract
The expressions for the fourth and sixth frequency moments of current correlation functions are simplified by performing the angular integrations associated with the three-body contributions to these moments. The resultant expressions are applicable both in the long-wavelength limit as well as for any momentum transfer. These expressions are then numerically evaluated for a liquid-argon-like system near its triple point using the molecular dynamics data of Verlet for the static pair-correlation function. We have used Kirkwood superposition approximation for the triplet correlation function and a low-order decoupling approximation for the quadruplet correlation function. The Maxwell relaxation time for the longitudinal mode is calculated using our computed numbers for the fourth and sixth moments. The results for the relaxation time are compared with those of other authors as well as with the experimental observations. It is concluded that the approach of Machida and Murase is comparatively adequate and has to be modified in order to get a better wave-number dependence of the relaxation time.