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The pair-connectedness function and the average cluster size are determined for two different three-dimensional fluid systems using the Percus-Yevick (PY) approximation (1980). The permeable-sphere model of Blum and Stell (1980) provides a one-parameter bridge from the ideal gas (perfectly penetrable spheres) to the PY hard-sphere fluid. Two of such particles are considered to be 'bound' when their cores overlap. The percolation transition is located as a function of the interpenetrability of the particles, and is found to correspond to an average coordination number z=4. Baxter's adhesive-sphere model (1968) is also investigated in the PY approximation and it is found that at the percolation transition the average coordination number is 2. The boundary between percolating and non-percolating homogeneous thermodynamic states is determined.
Chiew et al. (Mon,) studied this question.