A simple molecular statistical treatment of nematics

A slightly modified version of the Maier-Saupe model is presented. As a result of this modification, that relies on the introduction of a spherical constraint, the model can be easily solved analytically in the mean field approximation. Simple expressions result for the relevant thermodynamic quantities, e.g. the temperature dependence of the order parameter. Consequently the thermodynamic properties of the original model can be understood without any appreciable numerical effort. The method can be applied to other models as well. As an example we shortly deal with the Meyer-Lubensky model of the nematic to smectic A transition.