Schematic plot of the radial density profile in an N-body cluster during the core collapse with four different values of the logarithmic density gradient, a_{I − I​V}. The dotted line has a slope equal to α and shows the asymptotic solution of Lynden-Bell & Eggleton (1980). The break radius r_I is identified with the core radius, r_III roughly corresponds to the half-mass radius, and r_k is the cluster radius. The notation is the same as in Eq. (15) that we used for the fitting of our numerical models.