  Phase diagram of microcanonical ensembles of self-attracting particles is
studied for two types of short-range potential regularizations:
self-gravitating fermions and classical particles interacting via attractive
soft $-(r^2+r_0^2)^{-1/2}$ Coulomb potential. When the range of regularization
is sufficiently short, the self-attracting systems exhibit gravitational or
collapse-like transition. As the fermionic degeneracy or the softness radius
increases, the gravitational phase transition crosses over to a normal
first-order phase transition, becomes second-order at a critical point, and
finally disappears. Applicability of a commonly used saddle-point or mean-field
approximation and importance of metastable states is discussed.
