  Having first performed a Monte Carlo simulation to justify the analysis
technique to be used, we then analyze the Bose-Einstein correlation functions
from CERN experiment NA44 in the context of the core-halo model. Although
experimental resolution and error bar distribution prevents a direct
observation of the halo structure, the values for the core radius and the core
fraction of pions can be obtained in a straight-forward manner. These are found
to be independent of the structure of the correlation function at small
relative momenta of Q < 50 MeV. Hence, the omega meson decay products do not
distort the Gaussian shape of the Bose-Einstein correlation function in S + Pb
-> pi + pi + X reaction at CERN SPS. As we find that the "model-independent"
HBT radii yield results that are quantitatively as well as qualitatively
unreliable for systems with long-lived resonances, we present their corrected
form that applies for correlation functions with lambda(K) < 1.
