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 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 -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.