Multiple Density Correlations in a Many-Particle System

A closed expression similar to the Ursell‐Mayer expansion is obtained for the static multiple density correlation function $I_n{\mathrm{=〈\rho }}_{{\mathbf{k}}_1}{\mathrm{\cdots \rho }}_{{\mathbf{k}}_n}〉$ of a many‐particle system. It is shown that I_n breaks into products of lower ones, if there exist partial momentum conservations among the k's. Using the convolution approximation for the n‐particle correlation function, we evaluate I_n in a closed form. The result is shown to be accurate in the small k region.