Femtoscopic parameters of pion emission sources in EPOS4 Au+Au collisions from 7.7 to 200 GeV

Three-dimensional femtoscopy probes the space-time structure of particle-emitting sources in relativistic heavy-ion collisions. The collision-energy dependence of Lévy source parameters may reveal the evolution of strongly interacting matter and possible signatures of the QCD phase diagram. We previously studied the excitation function of three-dimensional Lévy source parameters for pion pairs in Au+Au collisions with EPOS4, analyzing the pair-distance distribution $D(\rho )$ through one-dimensional projections. Here, we analyze the full three-dimensional source distribution and correlation function directly. We construct $D({\rho }_{\mathrm{o}\mathrm{u}\mathrm{t}},{\rho }_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}},{\rho }_{\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}})$ as a 3D histogram, transform it into $C(q_{\mathrm{o}\mathrm{u}\mathrm{t}},q_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}},q_{\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}})$ using a Fast Fourier Transform, and fit the correlation function with the analytic Lévy formula. This approach can reduce biases arising when one-dimensional projections are used to describe a non-elliptical source. We apply the method across the RHIC Beam Energy Scan range and compare the extracted energy dependence with results from the projection-based method and recent UrQMD calculations. We focus on the out-side observables $R_{\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{f}}^2=R_{\mathrm{o}\mathrm{u}\mathrm{t}}^2-R_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}^2$ and $R_{\mathrm{o}\mathrm{u}\mathrm{t}}\mathrm{/}{R}_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}$, whose different energy dependences in EPOS4 and UrQMD may illuminate the roles of emission duration and source dynamics. This work establishes a direct three-dimensional framework for comparison with future femtoscopic measurements and for exploring possible non-monotonic structures associated with the QCD phase diagram.