Triplet and Higher Correlations in the Long Wavelength Limit

Abstract

The nth order structure function of a liquid, defined as the ensemble average of a product of n Fourier components of the atomic density, is studied in the limit of long wavelength for one or more Fourier components. It is shown by means of fluctuation theory that these limits are simply related to lower order structure functions and their derivatives with respect to pressure, and that they will be small in magnitude for normal liquids. This conclusion is important for the study of electronic properties of liquid metals because the screened ionic potential is always large in the long wavelength limit. Thus large spurious contributions may be obtained from the use of approximate structure functions that do not satisfy the correct long wavelength limits. In this respect the Kirkwood superposition approximation is very unsatisfactory.