Upper bound to the collision diameter from HNC and PY effective pair potentials

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Abstract
Extensions of the HNC and PY theories to take account of three‐body forces lead to formulas for the effective pair potential in terms of the true pair potential. Molecular dynamics calculations with an effective (12, 6) potential agree well with recent neutron diffraction measurements in liquid Ar near the triple point. It is shown that the slow‐collision diameter σ* of the effective pair potential is an upper bound for the slow‐collision diameter σ of the true pair potential, and that in the case of the Ar–Ar interaction σ < 3.405 Å. We also observe that the PY and HNC equations with the (12, 6) potential lead to radial distribution functions g(r) at the triple point of Ar that are in good agreement with molecular dynamics and neutron diffraction g(r) data except for a discrepancy in the depth of the first minimum.