Hard-sphere gas

A formal series solution to the Kirkwood-Salsburg equation and its radius of convergence are derived. This solution leads naturally to the establishment of an approximate hierarchy of equations for the distribution functions which needs no closure. The asymptotic behavior of the solutions to this approximate hierarchy is studied as well as the behavior of the derivatives of the pair function with respect to the interparticle distance.

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Solution of a truncated Kirkwood-Salsburg equation for the hard-sphere gas

Swendsen

Klein

1976

Phys. Rev. A

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A truncated form of the Kirkwood-Salsburg equation for the hard-sphere gas is solved. An exact algebraic recurrence relation is obtained for the coefficients of an expansion of the twoparticle correlation function in powers of the activity, z, in the neighborhood of z =0. The methods of series analysis and Pade approxim~rits allow this solution to be extended to all z~[-1, 11. 6048l. An equation of state is obtained which reproduces the first three virial coefficients exactly and shows a phase transition at z =11. 6048, which appears to be weakly second order. It is demonstrated that~nor modifications of the integral equation could substantially alter the~r1~&ytiC StruCture Of the SOlutiOn.

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Hard-sphere gas

Cited by 6 publications

References 26 publications

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Classical hard discs at high density

Perturbation solution of the Kirkwood-Salsburg equation

Solution of a truncated Kirkwood-Salsburg equation for the hard-sphere gas

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