Two-pion interferometry measurements are used to extract the Gaussian radii $R_{ { \rm out}}$, $R_{ { \rm side}}$, and $R_{ { \rm long}}$, of the pion emission sources produced in Cu$+$Cu and Au$+$Au collisions at several beam collision energies $\sqrt{ s_{ _{ NN}}}$ at PHENIX. The extracted radii, which are compared to recent STAR and ALICE data, show characteristic scaling patterns as a function of the initial transverse size $\bar{ R}$ of the collision systems and the transverse mass $m_T$ of the emitted pion pairs, consistent with hydrodynamiclike expansion. Specific combinations of the three-dimensional radii that are sensitive to the medium expansion velocity and lifetime, and the pion emission time duration show nonmonotonic $\sqrt{ s_{ _{ NN}}}$ dependencies. The nonmonotonic behaviors exhibited by these quantities point to a softening of the equation of state that may coincide with the critical end point in the phase diagram for nuclear matter.
Categories: nucl-ex