  This letter presents a remarkably simple approach to the first-principles
determination of the ergodic-non-ergodic transition in monodisperse colloidal
suspensions. It consists of an equation for the long-time asymptotic value
$\gamma$ of the mean squared displacement of the colloidal particles, whose
finite real solutions signal the non-ergodic state, and determines the
non-ergodic parameter $f(k)$. We illustrate its concrete application to three
simple model colloidal systems, namely, hard-spheres, hard-spheres plus
repulsive (screened Coulomb) Yukawa interaction, and hard-sphere plus
attractive Yukawa tail. The results indicate that this is quite a competitive
theory, similar in spirit to, but conceptually independent from, the well-known
mode coupling theory.
