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.
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