Journal of Statistical Physics, Vol. 42, Nos. 3/4, 1986. p. 493-508.
Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.