The three-dimensional pion and kaon emission source functions are extracted
from the HKM model simulations of the central Au+Au collisions at the top RHIC
energy $\sqrt{s_{NN}}=200$ GeV. The model describes well the experimental data,
previously obtained by the PHENIX and STAR collaborations using the imaging
technique. In particular, the HKM reproduces the non-Gaussian heavy tails of
the source function in the pair transverse momentum (out) and beam (long)
directions, observed in the pion case and practically absent for kaons. The
role of the rescatterings and long-lived resonances decays in forming of the
mentioned long range tails is investigated. The particle rescatterings
contribution to the out tail seems to be dominating. The model calculations
also show the substantial relative emission times between pions (with mean
value 14.5 fm/c in LCMS), including those coming from resonance decays and
rescatterings. The prediction is made for the source functions in the LHC Pb+Pb
collisions at $\sqrt{s_{NN}}=2.76$ TeV, which are still not extracted from the
measured correlation functions.Comment: 23 pages, 4 figure