Excitation function of femtoscopic L\'evy source parameters of pion pairs in EPOS4

Three-dimensional (3D) femtoscopic source parameters of pions provide a sensitive probe of the space-time structure of particle-emitting sources in high-energy heavy-ion collisions. Compared to one-dimensional measurements, three-dimensional femtoscopy not only provides a valuable cross-check but also offers a more complete characterization of the source geometry and its dynamical evolution. Particularly, differences between the out and side directions are sensitive to signals of a strong first-order phase transition, while the collision-energy dependence of L\'evy radii may reveal non-monotonic features related to the equation of state. In this work, we systematically investigate the transverse mass (mT) and collision-energy (sqrt(sNN)) dependence of the three-dimensional femtoscopic parameters of pion pairs with L\'evy-type sources in the STAR Beam Energy Scan (BES) range from sqrt(sNN) = 7.7 to 200 GeV using the EPOS4 model. The analyzed parameters include the L\'evy index alpha, the correlation strength lambda, and the three-dimensional radii Rout, Rside and Rlong, corresponding to the outward, sideward, and longitudinal (beam) directions. Derived quantities such as the out-side squared radius difference and the out/side ratio are also investigated. The results show that the extracted radii Rside and Rlong decrease with increasing transverse mass and increase gradually with collision energy, while Rout shows little energy dependence. The L\'evy index alpha exhibits only a mild dependence on mT and collision energy, whereas the correlation strength lambda shows a clear mT dependence and generally decreases with increasing collision energy. A comparison with EPOS3 results indicates general agreement within approximately 2sigma, with the notable exception of Rside, which is systematically smaller in EPOS4.