Multi-Boson Correlations Using Wave-Packets

Abstract

Brooding over bosons, wave packets and Bose - Einstein correlations, we present a generic quantum mechanical system that contains arbitrary number of bosons characterized by wave-packets and that can undergo a Bose-Einstein condensation either by cooling, or increasing the number density of bosons, or by increasing the overlap of the multi-boson wave-packet states, achieved by changing the size of the single-particle wave-packets. We show that the n-particle correlations may mimic coherent or chaotic behaviour for certain limiting wave-packet sizes. Effects of complete n-particle symmetrization are included. The resulting weights which fluctuate between 1 and n! are summed up with the help of a formal analogy between the considered wave-packet system and an already explored multi-boson plane-wave system. We solve the model analytically in the highly condensed and in the rare gas limiting cases, numerically in the intermediate cases. The relevance of the model to multi-pion production in high energy heavy ion physics as well as to the Bose-Einstein condensation of atomic vapours is discussed. As a by-product, a new class of probability distribution functions is obtained, event-by-event fluctuations of single-particle momentum distributions are predicted and the critical density for the onset of pion-lasing in high energy heavy ion collisions is derived.