A mean-field nonlinear equation for the mean-square displacement, recently proposed by one of the present authors [M. Tokuyama, Phys. Rev. E 62, R5915 (2000); Physica A 289, 57 (2001)], for concentrated, equilibrium suspensions of hard spheres is extended to describe equilibrium atomic systems of hard spheres. The validity of two types of mean-field equations is investigated by two kinds of computer simulations; a Brownian-dynamics simulation on suspensions of hard spheres and a molecular-dynamics simulation on atomic systems of hard spheres. A good agreement between the mean-field equations and simulations is then shown for different volume fractions. The two types of model systems of hard spheres are thus shown to be identical to each other on the study of the liquid-solid transition. However, analyses suggest that a new interaction is indispensable to understand the mechanism for the liquid-glass transition in both systems.