  We introduce a new realistic expanding source model for invariant
one-particle multiplicity distributions and two-particle correlations in nearly
central relativistic heavy-ion collisions that contains nine adjustable
parameters, which are necessary and sufficient to properly characterize the
gross properties of the source during its freezeout from a hydrodynamical fluid
into a collection of noninteracting, free-streaming hadrons. These nine
physically relevant parameters fall into three categories of three parameters
each, with the first category corresponding to the source's longitudinal
motion, the second category corresponding to its transverse motion, and the
third category corresponding to its intrinsic properties. As an initial
application, we apply our model to the analysis of invariant pi^+, pi^-, K^+,
and K^- one-particle multiplicity distributions and pi^+ and K^+ two-particle
correlations for nearly central Si + Au collisions at p_lab/A = 14.6 GeV/c. In
a minimization with 1416 data points, the resulting chi-square is 1484.6, which
corresponds to an acceptable chi-square per degree of freedom of 1.055. We list
the values of the nine parameters determined this way plus several additional
calculated freezeout quantities of physical interest, along with their
uncertainties at 99% confidence limits.
