Chaoticity parameter λ in Hanbury-Brown–Twiss interferometry

Abstract

In Hanbury-Brown--Twiss interferometry measurements using identical bosons, the chaoticity parameter \ensuremath{\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 \ensuremath{\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 \ensuremath{\lambda} can then be evaluated from the momentum correlation function. We find that the $\ensuremath{\lambda}(p,T)$ parameter is a sensitive function of both the average pair momentum $p$ and the temperature $T$, and the occurrence of $\ensuremath{\lambda}=1$ is not a consistent measure of the absence of a coherent condensate fraction. In particular, for large values of $p$, the \ensuremath{\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.