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 \(D(ρ)\) through one-dimensional projections. Here, we analyze the full three-dimensional source distribution and correlation function directly. We construct \(D(ρ_{\rm out},ρ_{\rm side},ρ_{\rm long})\) as a 3D histogram, transform it into \(C(q_{\rm out},q_{\rm side},q_{\rm long})\) 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 \(R_{\rm diff}^{2}=R_{\rm out}^{2}-R_{\rm side}^{2}\) and \(R_{\rm out}/R_{\rm side}\), 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.