Simulation of the Three-Particle Distribution Function in a Long-Range Oscillatory Potential Liquid

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Abstract
The three-particle distribution function, g(3) (r12, r23, r31) is calculated by means of the molecular-dynamics method in a dense classical liquid with the LRO-II potential proposed by Paskin and Rahman as the pair-interaction, which is taken for a model of liquid sodium just above the melting point (377.01 °K, 0.927 g·cm-3). The distribution of the symmetric triplets, g(3) (r, r, r), is tabulated up to r=11.0 Å and that of the isosceles triplets, g(3) (r, s, s), is up to s=11.0 Å with r's fixed to the positions of the first, the second maxima and of the first minimum of the pair-distribution function, g(r), and up to 9 Å with the four r's of succeeding maxima and minima. The structure of g(3) (r, r, r) and g(3) (r, s, s) is compared with Kirkwood's superposition approximation (SA) and also with the so-called closure approximations proposed by Abe and others. Comparison shows that (i) SA overestimates significantly the occurrence of equilateral triplets of sides smaller than the position of the first maximum, and of those comparable to that of the first minimum of g(r), (ii) SA is quite unreliable for the distribution of linear or nearly triplets of smaller size in which the net three-particle correlation work for the stability of triplets oppositely to the SA predictions, (iii) SA is better than 10% for larger triplets, i.e., for values of r and/or s larger than, say, the position of the second maximum of g(r), and (iv) the closure approximations seem insufficient to predict, even qualitatively, the fine structure in g(3) (r, s, t) in dense liquids shown as in (i) and (ii).

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