Stable Bose-Einstein correlations

The shape of Bose-Einstein (or HBT) correlation functions is determined for the case when particles are emitted from a stable source, obtained after convolutions of large number of elementary random processes. The two-particle correlation function is shown to have a stretched exponential shape, characterized by the Lévy index of stability 0 < alfa less-than or equal to 2 and the scale parameter R. The normal, Gaussian shape corresponds to a particular case, when alfa = 2 is selected. The asymmetry parameter of the stable source, beta is shown to be proportional to the angle, measured by the normalized three-particle cumulant correlations.