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.
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