Statistical theory of crystallization in a system of hard spheres

The reasons for the contradictions between the results of different studies devoted to crystallization in terms of bifurcation of the solutions of nonlinear integral equations for the single-particle distribution function are elucidated. It is shown to be impossible to describe crystallization in a system of hard spheres in the framework of the standard approach based on an investigation into the instability of a liquid with respect to a continuous change in the density. An alternative formulation of the theory is proposed in which the fundamental role is played by the finite discontinuity of the density at the point of the transition from the liquid to the solid phase.