Nonexistence of Kirkwood's instability in a uniform fluid

Kirkwood's instability in the theory of fluid-solid transitions is proved to be impossible. Fluctuation of the one-particle distribution function in the first equation of the BGY hierarchy is investigated beyond Kunkin and Frisch's treatment. The second equation of the BGY hierarchy is utilized to eliminate the three-particle distribution function left in the Kunkin-Frisch result. The final expression for the first-order fluctuation of the one-particle distribution function under the presence of an external field is written in a form including only the pair correlation function and agrees identically with the one obtained from the direct expansion of the oneparticle distribution function in terms of the external field.