Relaxation of N-body systems with additive r^-{\alpha} interparticle
  forces
  In Newtonian gravity the final states of cold dissipationless collapses are
characterized by several structural and dynamical properties remarkably similar
to those of observed elliptical galaxies. Are these properties a peculiarity of
the Newtonian force or a more general feature of long-range forces? We study
this problem by means of $N-$body simulations of dissipationless collapse of
systems of particles interacting via additive $r^{-\alpha}$ forces. We find
that most of the results holding in Newtonian gravity are also valid for
$\alpha\neq2$. In particular the end products are triaxial and never flatter
than an E7 system, their surface density profiles are well described by the
S\'ersic law, the global density slope-anisotropy inequality is obeyed, the
differential energy distribution is an exponential over a large range of
energies (for $\alpha\geq1$), and the pseudo phase-space density is a power law
of radius. In addition, we show that the process of virialization takes longer
(in units of the system's dynamical time) for decreasing values of $\alpha$,
and becomes infinite for $\alpha=-1$ (the harmonic oscillator). This is in
agreement with the results of deep-MOND collapses (qualitatively corresponding
to $\alpha=1$) and it is due to the fact the force becomes more and more
similar to the $\alpha=-1$ case, where as well known no relaxation can happen
and the system oscillates forever.
