Chaoticity Parameter Lambda in Hanbury-Brown Twiss Interferometry

TL;DR

This paper investigates the chaoticity parameter lambda in Hanbury-Brown Twiss interferometry for boson gases, revealing its dependence on momentum and temperature, and challenging its use as a condensate indicator.

Contribution

It provides an exact analysis of lambda in a boson system within a harmonic trap, clarifying its relation to coherence and Bose-Einstein condensation.

Findings

Lambda varies with momentum and temperature, not solely indicating coherence.

High momentum can yield lambda=1 even with significant condensate.

Pion systems in heavy-ion collisions may contain large condensates.

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.