S. V. Akkelin

Coulomb corrections for interferometry analysis of expanding hadron systems

Abstract The problem of the Coulomb corrections to the two-boson correlation functions for the systems formed in ultra-relativistic heavy ion collisions is considered for large effective volumes predicted in the realistic evolution scenarios taking into account the collective flows. A simple modification of the standard zero-distance correction (so called Gamow or Coulomb factor) has been proposed for such a kind of systems. For π + π + and K + K + correlation functions this approximate analytical approach is compared with the exact numerical results and a good agreement is found for typical conditions at SPS, RHIC and even LHC energies.

Freeze-out problem in hydrokinetic approach to A + A collisions.

A new method for evaluating spectra and correlations in the hydrodynamic approach is proposed. It is based on an analysis of the Boltzmann equations (BE) in terms of probabilities for constituent particles to escape from the interacting system. The conditions of applicability of the Cooper-Frye freeze-out prescription are considered within the method. The results are illustrated with a nonrelativistic exact solution of BE for an expanding spherical fireball as well as with approximate solutions for ellipsoidally expanding ones.

The HBT interferometry of expanding sources

Abstract The structure of the bosonic correlation function for expanding thermalized systems is obtained using the conception of the systems lengths of homogeneity. The analysis of the p t -behavior of the long -, out - and side -interferometry radii is performed for radiating sources with relativistic transversal and longitudinal flows. Simple analytical formulas for all interferometry radii are obtained for typical classes of transversal flows.

Observables and initial conditions for self-similar ellipsoidal flows

Single-particle spectra and two-particle Bose-Einstein correlation functions are determined analytically utilizing a self-similar solution of nonrelativistic hydrodynamics for ellipsoidally symmetric, expanding fireballs, by assuming that the symmetry axes of the ellipsoids are tilted in the frame of the observation. The directed, elliptic, and third flows are calculated analytically. The mass dependences of the slope parameters in the principal directions of the expansion, together with the mass and angular dependences of the HBT radius parameters, reflect directly the ellipsoidal properties of the flow.

Simple solutions of fireball hydrodynamics for self-similar elliptic flows

A new family of simple, analytic solutions of self-similarly expanding fireballs is found for systems with ellipsoidal symmetry and a direction dependent, generalized Hubble flow. Gaussian, shell like or oscillating density profiles emerge for simple choices of an arbitrary scaling function. New, cylindrically or spherically symmetric as well as approximately one dimensional hydrodynamical solutions are obtained for various special choices of the initial conditions.

Hydro-kinetic approach to relativistic heavy ion collisions

We develop a combined hydro-kinetic approach which incorporates a hydrodynamical expansion of the systems formed in A+A collisions and their dynamical decoupling described by escape probabilities. The method corresponds to a generalized relaxation time ({tau}{sub rel}) approximation for the Boltzmann equation applied to inhomogeneous expanding systems; at small {tau}{sub rel} it also allows one to catch the viscous effects in hadronic component-hadron-resonance gas. We demonstrate how the approximation of sudden freeze-out can be obtained within this dynamical picture of continuous emission and find that hypersurfaces, corresponding to a sharp freeze-out limit, are momentum dependent. The pion m{sub T} spectra are computed in the developed hydro-kinetic model, and compared with those obtained from ideal hydrodynamics with the Cooper-Frye isothermal prescription. Our results indicate that there does not exist a universal freeze-out temperature for pions with different momenta, and support an earlier decoupling of higher p{sub T} particles. By performing numerical simulations for various initial conditions and equations of state we identify several characteristic features of the bulk QCD matter evolution preferred in view of the current analysis of heavy ion collisions at RHIC energies.

Correlation search for coherent pion emission in heavy ion collisions

The methods allowing to extract the coherent component of pion emission conditioned by the formation of a quasi-classical pion source in heavy ion collisions are suggested. They exploit a nontrivial modification of the quantum statistical and final state interaction effects on the correlation functions of like and unlike pions in the presence of the coherent radiation. The extraction of the coherent pion spectrum from pi+pi-, pi+pi+ and pi-pi- correlation functions and single--pion spectra is discussed in detail for large expanding systems produced in ultra-relativistic heavy ion collisions.

Matching of nonthermal initial conditions and hydrodynamic stage in ultrarelativistic heavy-ion collisions

A simple approach is proposed allowing actual calculations of the preequilibrium dynamics in ultrarelativistic heavy-ion collisions to be performed for a far-from-equilibrium initial state. The method is based on the phenomenological macroscopic equations that describe the relaxation dynamics of the energy-momentum tensor and are motivated by Boltzmann kinetics in the relaxation-time approximation. It gives the possibility to match smoothly a nonthermal initial state to the hydrodynamics of the quark gluon plasma. The model contains two parameters, the duration of the prehydrodynamic stage and the initial value of the relaxation-time parameter, and allows one to assess the energy-momentum tensor at a supposed time of initialization of the hydrodynamics.

On final conditions in high energy heavy ion collisions

Motivated by the recent experimental observations, we discuss the freeze-out properties of the fireball created in central heavy ion collisions. We find that the freeze-out conditions, like temperature, velocity gradient near center of the fireball, are similar for different colliding systems and beam energies. This means that the transverse flow is stronger in the collisions of heavy nuclei than that of the light ones. The system that created in relativistic heavy-ion collision can have both longitudinal and transverse expansion (see, e.g., [1]). In order to study the hadronic experimental data [2, 3], one needs a mathematical description of a final stage of collisions. At the region near mid-rapidity the boundary effect, due to the finite length of the hydrodynamic tube in longitudinal direction, can be neglected [4]. It is possible to use Bjorken’s model for longitudinal expansion: vl = xl/t. The same quasi-inertial flow is inherent to Landau model at freeze-out stage [5, 6]. In this approach, the parameter � was introduced to describe proper time of the expanding system. For the transverse expansion, we will use a rather general picture proposed in

Femtoscopic and Nonfemtoscopic Two-Particle Correlations in and Collisions at RHIC and LHC Energies

The theoretical review of the last femtoscopy results for the systems created in ultrarelativistic , , and collisions is presented. The basic model, allowing to describe the interferometry data at SPS, RHIC, and LHC, is the hydrokinetic model. The model allows one to avoid the principal problem of the particlization of the medium at nonspace-like sites of transition hypersurfaces and switch to hadronic cascade at a space-like hypersurface with nonequilibrated particle input. The results for pion and kaon interferometry scales in and collisions at LHC and RHIC are presented for different centralities. The new theoretical results as for the femtoscopy of small sources with sizes of 1-2 fm or less are discussed. The uncertainty principle destroys the standard approach of completely chaotic sources: the emitters in such sources cannot radiate independently and incoherently. As a result, the observed femtoscopy scales are reduced, and the Bose-Einstein correlation function is suppressed. The results are applied for the femtoscopy analysis of collisions at  TeV LHC energy and ones at  TeV. The behavior of the corresponding interferometry volumes on multiplicity is compared with what is happening for central collisions. In addition the nonfemtoscopic two-pion correlations in proton-proton collisions at the LHC energies are considered, and a simple model that takes into account correlations induced by the conservation laws and minijets is analyzed.