Bose-Einstein correlations for Levy stable source distributions

The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability 0 < alpha <= 2, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of alpha = 2. We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and we check the model against two-particle correlation data.