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We explore the formation and relaxation of so-called quasi-stationary states(QSS) for particle distributions in three dimensions interacting via anattractive radial pair potential $V(r \rightarrow \infty) \sim 1/r^\gamma$ with$\gamma > 0$, and either a soft-core or hard-core regularization at small $r$.In the first part of the paper we generalize, for any spatial dimension $d \geq2$, Chandrasekhar's approach for the case of gravity to obtain analyticestimates of the rate of collisional relaxation due to two body collisions. Theresultant relaxation rates indicate an essential qualitative differencedepending on the integrability of the pair force at large distances: for$\gamma >d-1$ the rate diverges in the large particle number $N$ (mean field)limit, unless a sufficiently large soft core is present; for $\gamma < d-1$, onthe other hand, the rate vanishes in the same limit even in the absence of anyregularization. In the second part of the paper we compare our analyticalpredictions with the results of extensive parallel numerical simulations in$d=3$, for a range of different exponents $\gamma$ and soft cores leading tothe formation of QSS. We find, just as for the previously well studied case ofgravity (which we also revisit), excellent agreement between the parametricdependence of the observed relaxation times and our analytic predictions.Further, as in the case of gravity, we find that the results indicate that,when large impact factors dominate, the appropriate cut-off is the size of thesystem (rather than, for example, the mean inter-particle distance). Ourresults provide strong evidence that the existence of QSS is robust only forlong-range interactions with a large distance behavior $\gamma < d-1$; for$\gamma \geq d-1$ the existence of such states will be conditioned strongly onthe short range properties of the interaction.

Formation and relaxation of quasi-stationary states in particle systems with power law interactions