Abstract
In Hanbury-Brown-Twiss interferometry measurements using identical bosons, the chaoticity parameter {\lambda} has been introduced phenomenologically to represent the momentum correlation function at zero relative momentum. It is useful to study an exactly solvable problem in which the {\lambda} parameter and its dependence on the coherence properties of the boson system can be worked out in great detail. We are therefore motivated to study the state of a gas of noninteracting identical bosons at various temperatures held together in a harmonic oscillator potential that arises either externally or from bosons' own mean fields. We determine the degree of Bose-Einstein condensation and its momentum correlation function as a function of the attributes of the boson environment. The parameter {\lambda} can then be evaluated from the momentum correlation function. We find that the {\lambda(p,T)} parameter is a sensitive function of both the average pair momentum p and the temperature T, and the occurrence of {\lambda =1} is not a consistent measure of the absence of a coherent condensate fraction. In particular, for large values of p, the {\lambda} parameter attains the value of unity even for significantly coherent systems with large condensate fractions. We find that if a pion system maintains a static equilibrium within its mean field, and if it contains a root-mean-squared radius, a pion number, and a temperature typical of those in high-energy heavy-ion collisions, then it will contain a large fraction of the Bose-Einstein pion condensate.
