Extension of the integrated hydrokinetic model to nuclear collision energies relevant for the RHIC Beam-Energy Scan program and the research program at GSI-FAIR

The present work is devoted to developing the integrated hydrokinetic model (iHKM) for relativistic nucleus-nucleus collisions. While the previous cycle of works on this topic focused on ultrarelativistic collisions at the top RHIC and different LHC energies, the current work addresses relativistic collisions at the lower energies, specifically ranging from approximately 2 to 50 GeV per nucleon pair in the center-of-mass colliding system. In such collisions, the formation times for the initial state of dense matter can be up to three orders of magnitude longer than those in ultrarelativistic collisions. This difference reflects a fundamentally distinct nature and formation process, particularly regarding the possible stages of initial state evolution, including thermalization (which may be only partial at very low collision energies), subsequent hydrodynamic expansion, and the final transition of matter evolution into a hadronic cascade. These stages, which are fully realized in ultrarelativistic reactions, can also occur within the energy range of BES RHIC, albeit with distinct timescales. This publication not only advances the theoretical development of iHKM referred to, if necessary, as the version of integrated hydrokinetic model (iHKMe), but also provides examples of model applications for calculating observables. A systematic description across a wide range of experimental energies, which is preliminary yet quite satisfactory, for spectra, flow, and femtoscopy, will follow this study.