  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.
