On the stability of a fluid toward solid formation

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Abstract
A traditional search for solidlike singlet densities in a system with a fluidlike pair distribution function is undertaken. The analysis is based upon a nonlinear integral equation relating the direct correlation function and the singlet density in contrast with previous analyses based upon similar relations between the singlet and pair number densities. An investigation is also made of the mechanical stability of such a system and it is found that a solidlike solution and mechanical instability appear simultaneously. Numerical analysis shows that the three-dimensional hard sphere system remains stable at all densities but that an additional attractive pair interaction produces a physically reasonable instability.