Interferometry Radii at RHIC BES Energies within the integrated HydroKinetic Model
The work is devoted to research of pion femtoscopic correlations in relativistic heavy-ion collisions across the RHIC Beam Energy Scan range using the extended integrated HydroKinetic Model (iHKMe). The model provides a comprehensive description of the system's dynamical evolution, starting from the initial collision state of colliding nuclei, passing through a possible thermalization process and hydrodynamic expansion to the hadron interacting cascade and formation of the observed particle spectra. The model smoothly couples all these stages of the matter evolution, ensuring a smooth transition between the stages. A primary focus of the current work, in contrast to the similar investigation within iHKM for high energies, concentrated in the energy region where extended nuclear overlap times and incomplete thermalization significantly influence the system's expansion comparing with very high energies. We extract the three-dimensional interferometry radii ($R_{out}$, $R_{side}$, $R_{long}$) in the region from 7.7 to 39 GeV per nucleon pair and evaluate their sensitivity to the features of the equation of state (EoS), specifically comparing crossover and first-order phase transition scenarios. The model demonstrates good agreement with experimental measurements in the crossover case. As for the first-order phase transition scenario, the $R_{long}$ component, at the optimal model parameters for particle spectra, is noticeably higher than the experimental data, and the difference is more pronounced with the growth of collision energy. Such a behavior is caused by the increased system's lifetime during the mixed-phase stage. The corresponding analysis within iHKMe below $\sqrt{s_{NN}} = 7.7$ GeV will be presented within a separate investigation.