  Exploration of the rich structure of the QCD phase diagram is an important
topic in the RHIC heavy ion program. One of the ultimate goals of this program
is to search for the critical endpoint. Investigation of the space-time
structure of hadron emissions at various phase transition points using
Bose-Einstein correlations of identical bosons may provide insight on the
location of the critical endpoint. PHENIX has performed comprehensive
measurements of the Bose-Einstein correlation in Au+Au collisions at sqrt(sNN)
= 15, 19, 27, 39, 62.4, and 200 GeV, where we incorporated Levy-type source
functions to describe the measured correlation functions. We put particular
focus on one of the parameters of the Levy-type source functions, the index of
stability alpha, which is related to one of the critical exponents (the
so-called correlation exponent eta). We have measured its collision energy and
centrality dependence. We have also extended our analysis from two-particle to
three-particle correlations to characterize the nature of the hadron emission
source. The three particle correlations confirmed the findings of the
two-particle correlations, and also provide insight on the pion production
mechanism beyond the core-halo model.
