Interferometry Analysis For The Hydrodynamic Evolution Sources In Heavy Ion Collisions At Different Energies

Two-pion interferometry analysis for the hydrodynamic evolving sources in (2+1) dimen-sion at HIRFL-CSR energy are performed. The particle emission models of chemical freeze-out (CFO), partial chemical equilibrium (PCE), and thermal freeze-out (TFO) are considered. We find that there is a much difference between the transverse and longitudinal velocities in TFO case. The two-pion correlation functions are fitted with the Bertsh-Pratt parameterized formu-la with a cross-term of Rol. The fitted results indicate that the cross-term has a great impact on the longitudinal HBT radius, R1. We also fit the correlation functions with Yano-Koonin-Podgoretskii parameterized formula in LCMS and PCMS frames. In LCMS, the lifetime of source is large if the initial source radius is large. In PCMS, the dynamic correlation for PCE particle emission is stronger than that for CFO at large pair rapidity. For the three particle e-mission models, both the source imaging radii and HBT radii decrease with the increase of transverse momentum of pion pair. The imaging radius for CFO is smallest, and the radius for TFO is largest. In longitudinal direction, both the imaging radius and HBT radius are related to the longitudinal initial source radius z0.We examine the HBT interferometry for the hydrodynamic evolution sources in cylinder geometry at GSI-FAIR energy. Two systems for nB/s=0.6and0.8are considered. For nb/s=0.06, the systems are initially located in QGP phase and at the soft point of mixed phase. For nb,/s=0.08, the systems are initially located at the soft point and hadronization point. In LCMS, the HBT correlation functions are fitted with the Bertsh-Pratt parameterized formula with the cross-term of Rol. For kaon, the effect of the cross-term on the HBT radii is great for the system with nb/s=0.06. For pion, the effect of the cross-term is more significant for the system initially at the soft point. We also fit the HBT correlation functions with Yano-Koonin-Podgoretskii parameterized formula. In LCMS, both the transverse and longitudinal radii R⊥and R‖decrease with the transverse momentum of the particle pair. The transverse radius R⊥is not sensitive to the rapidity of the particle pair, Yππ (or YKk).However, the longitudinal radius R‖and lifetime R0of source decrease with the rapidity. The systems reach their maximal lifetimes when they are initially located at soft points.In PCMS, the HBT radii are independent of the pair rapidity Yππ (or YKK). The lifetime and HBT radii for kaon sources are smaller than those for pion sources. The characteristic radii of the distributions of imaging source functions are almost as the same functions of pair transverse momentum as those for the HBT radii. The imaging source functions are much different from Gaussian distribution in out and long directions.We investigate the transverse momentum spectra and HBT interferometry of pion in ul-trarelativistic heavy ion collisions in the granular source model of quark-gluon plasma droplets. The QGP droplets evolve hydrodynamically. We find that the results of the QGP granular source model agree well with the data of pion transverse momentum spectra and HBT radii in the cen-tral collisions of (?)=200GeV at RHIC and (?)=2.76TeV at LHC. Because the systems produced in the collisions at LHC energy have a longer breakup time than that for RHIC colli-sions, the granular sources for LHC have wider transverse and longitudinal droplet distributions in space. It leads to larger HBT radii for the collisions at LHC energy. By the imaging analysis for the granular sources at LHC energy, we find that the characteristic radii of the distributions of imaging source functions are consistent with the HBT radii obtained by correlation function fit. The imaging source function in side direction is closed to a Gaussian distribution. However, there are long tails in the imaging source functions in out and long directions.