Bose-Einstein Correlations for Expanding Finite Systems or from a Hot Fireball to a Snow-Flurry

Most boson emitting sources contain a core of finite dimensions surrounded by a large halo, due to long-lived resonances like $\omega,\eta,\eta',K^{0}$ etc. When the Bose-Einstein correlation (BEC) function of the core can be determined we show that its intercept ($\lambda$) measures, as a function of momentum, the square of the fraction of core particles produced. A simultaneos measurement of BEC and the single-particle distributions can thus determine the characteristics of the core. If the geometrical sizes of the core are sufficiently large the parameters of the BEC function obey the $m_{t}$-scaling observed in $SPb$ and $PbPb$ reactions at CERN. The model can describe the measurements of the single- and two-particle distributions in the central region of $SPb$ reactions. A fit to experimental data shows that the freeze-out of hadrons occurs at a larger volume and at a much lower temperature than that given by the measurement of the inverse slope of the $m_{t}$-spectrum and standard BEC analysis.