  A luminosity-temperature relation for clusters of galaxies is derived. The
two models used, take into account the angular momentum acquisition by the
proto-structures during their expansion and collapse. The first one is a
modification of the self-similar model (SSM) while the second one is a
modification of the Punctuated Equilibria Model (Cavaliere et al. 1999). In
both models the mass-temperature relation (M-T) used is based on the
calculations of Del Popolo (2002b). We show that the above models lead, in
X-rays, to a luminosity-temperature relation that scales as L \propto T^5, at
scale of groups, flattening to L \propto T^3 for rich clusters and converging
to L \propto T^2 at higher temperatures. However a fundamental result of our
paper is that the non-similarity in the L-T relation, can be explained by a
simple model that takes into account the amount of the angular momentum of a
proto-structure. This result is in disagreement with the widely accepted idea
that the above non-similarity is due to non-gravitating processes as those of
heating/cooling.
