Quasistationary states and the range of pair interactions

"Quasistationary'' states are approximately time independent out of equilibrium states which have been observed in a variety of systems of particles interacting by long-range interactions. We investigate here the conditions of their occurrence for a generic pair interaction V(r -> infinity) similar to 1/r(gamma) with gamma > 0, in d > 1 dimensions. We generalize analytic calculations known for gravity in d = 3 to determine the scaling parametric dependences of their relaxation rates due to two-body collisions, and report extensive numerical simulations testing their validity. Our results lead to the conclusion that, for gamma < d - 1, the existence of quasistationary states is ensured by the large distance behavior of the interaction alone, while for gamma > d - 1 it is conditioned on the short distance properties of the interaction, requiring the presence of a sufficiently large soft core in the interaction potential.