A simple method for the extraction of the times of maximal emission for kaons and pions using the combined fitting of their transverse momentum spectra and the longitudinal interferometry radii dependencies on the pair transverse mass $m_T$ is applied to Pb+Pb collisions at the LHC energy $sqrt{s_{NN}}=5.02$ TeV. The method is based on the analytical formulas, that were earlier successfully utilized in the studies of Pb+Pb collisions at $sqrt{s_{NN}}=2.76$ TeV. To test the method, the spectra, radii and particle radiation picture are calculated within the integrated hydrokinetic model (iHKM), that includes all the stages of the matter evolution in high-energy A+A collisions: the systems formation, its thermalization, viscous hydrodynamics evolution, particlization and subsequent hadronic cascade. The model describes and predicts well already published LHC data in soft physics? kinematic region. Thus, the fitting results for maximal emission times of kaons and pions are compared to the approximate maximal emission time values, estimated based on the emission function plots, obtained in iHKM. The developed simple method is intended for use in experimental analysis of femtoscopy data in relativistic A+A collisions.
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