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??)?1/r? with ?0, in d1 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 ?d-1, the existence of quasistationary states is ensured by the large distance behavior of the interaction alone, while for ?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.