collective flow phenomena of protons and mesons...

COLLECTIVE FLOW PHENOMENAOF PROTONS AND MESONS

IN NUCLEUS-NUCLEUS COLLISIONSAT A MOMENTUM OF

4.2 ÷ 4.5 GeV/ PER NUCLEON

CCOOLLECTIVE FLOW PHENOMENALLECTIVE FLOW PHENOMENAOF PROTONS AND MESONS OF PROTONS AND MESONS

IN NUCLEUSIN NUCLEUS--NUCLEUS COLLISIONSNUCLEUS COLLISIONSAT A MOMENTUM OF AT A MOMENTUM OF

4.2 4.2 ÷÷ 4.5 4.5 GeVGeV/ PER NUCLEON/ PER NUCLEON

L.V.Chkhaidze , T.D.Djobava (IHEPI TSU Georgea)E.N.Kladnitskaya (JINR)

Relativistic Nuclear Physics2005

2E.Kladnitskaya et al. May 24 2005

IntroductionOne of the central goals of the experiments related with high energy heavy ion collisions is a study of nuclear matter under extreme conditions of high density and temperature vastly different from that in normal nuclei. The most impressive results of high energy heavy ion research so far are the new collective phenomena discovered in these reactions. Collective processes are well established both experimentally and theoretically, such as different collective flow patterns. A collective flow is a motion characterized by space-momentum correlations of dynamic origin. The collective effects lead to characteristic, azimuthally asymmetric sideward emission of the reaction products. The analysis of the main characteristics of the collective flow allows one to obtain the information about the fundamental properties of nuclear matter, connected particularly to the equation of state (EOS). (H.St cker et al., Phys. Rev. Lett. 44, 725 (1980); H.St cker et al., Phys. Rev. C 25, 1873 (1982))

Two different signatures of collective flow have been predicted:a) the directed flow of nucleons from the overlap region between the colliding nuclei (participants) in the reaction plane. b) the squeeze-out of the participant matter out of the reaction plane - the elliptic flow. The method proposed by Danielewicz and Odyniec (P.Danielewicz and G.Odyniec, Phys. Lett. B 157, 146 (1985)) turned out to be the most convenient and fruitful for the investigation of collective flow phenomena, which allows one to determine the reaction plane by using the transverse momenta of particles.

At present the collective flow effects are investigated in the wide range of energies from several hundreds of MeV up to hundreds of GeV.


Experimental dataWe present the experimental results of collective behavior of protons and mesons in He-C, C-C, C-Ne, C-Cu and C-Ta collisions at a momentum of 4.2 ÷ 4.5 GeV/ per nucleon registered in the SKM-200-GIBS set-up and 2 m Propane Bubble Chamber of JINR.

We have measured directed flow of protons and π- mesons and elliptic flow of protons.

A central trigger was used to select events with no charged projectile spectator fragments (withGeV/c ) within a cone of half angle = 2.4 or 2.9 The study of collective flow phenomenon needs"event-by-event" analysis, which requires the exclusive analysis of each individual collision. The data on He-C, C-C and C-Ta interactions have been obtained using 2 meter Propane BubbleChamber of JINR. The chamber was placed in a magnetic field of 1.5 T.

The experimental data contained 723 C-Ne, 663 C-Cu, 9737 He-C, 15962 C-C and 2469 unambiguouslyidentified C-Ta inelastic collisions. The sub-sample of ``semicentral'' events with the number of participant protons 3,4,6 respectively were selected for the analysis from the whole ensemble of He-C, C-C and C-Ta collisions. The target fragments ( p < 0.3 GeV/c ), projectile stripping ( p > 3 GeV/c and angle θ < 4 ) wereexcluded from participant protons. In consequence, the groups of semicentral 6400 He-C, 9500 C-C and 1620 C-Ta collisions wereseparated from inelastic collisions.


Transverse flow of protonsThe method of Danielewicz and Odyniec has been used for study of collective flow protons. This method is based on the summation of the transverse momenta of selected particles. The reaction plane is the plane containing the impact parameter and beam axis. Taking into account that the definition of experimentally is not possible, in the transverse momentum analysis method of Danielewiczand Odyniec the vector is replaced by . The reaction plane vector in each individual event is defined by the transverse vector:

where is a detected particle index and is a weight. In eq. (1) the vector is summing over all protons with stripping particles. =1 for y y , = -1 for y y and = 0 for . y is the rapidity of particle. For He-C and C-C interactions we take = 0.2, for C-Ne, C-Cu and C-Ta

interactions we take = 0.4. These values of remove particles from midrapidity.

To remove the autocorrelations, Danielewicz and Odyniec supposed to estimate the reaction plane for each particle , i.e., to project onto the summary vector of all other particles in the same event:

The transverse momentum of each particle, in the estimated reaction plane is calculated as


Transverse flow of protons

The dependence of the mean transverse momentum of each particle in the reaction plane on the rapidity is constructed. The average transverse momentum is obtained by averaging over all events in the corresponding intervals of rapidity. The component in the true reaction plane is systematically larger than the component in the estimated plane, hence:

where is the angle between the estimated and true planes.

- the experimental data, - QGSM generated data

QGSM − N.Amelin et al., Yad. Fiz. 51, 512 (1990)


Azimuthal anisotropic emission of protons

From the mean transverse momentum distributions one can extract the transverse flow , i.e., the slope of the momentum distribution at midrapidity (in the intersection point = 0):

is a measure of the amount of collective transverse momentum transfer in the reaction plane, i.e., intensity of nuclear interactions.

With the increase of , , the value of increases linearly from (MeV) for He-C up to (MeV) for C-Ta.


Azimuthal anisotropic emission of protonsThe preferential emission of partciles in the direction perpendicular to the reaction plane (i.e. "squeeze-out") is particularly interesting since it is the only way the nuclear matter might escape without being rescattered by spectator remnants of the projectile and the target, and is expected to provide direct information on the hot and dense participant region formed in high energy nucleus-nucleus interactions

The angle is the angle of the transverse momentum of each particle in an event with respect to the reaction plane ( ).

- the experimental data, - the QGSM data. The polynomial fits are shown .

The anisotropy factor is negative for out-of-plane enhancement (squeeze-out) and is the measure of the strength of the anisotropic emission.

A clear signature of an out-of-plane signal is evidenced.


Elliptic flow

The dependence of the Elliptic flow excitation function on energy E /A (GeV):

- FOPI,- MINIBALL,

- EOS, - E-895, - E-877,- NA49,- He-C, C-C, C-Ne, C-Cu and C-Ta

The scale of energy is slightly shifted for our results for better visual presentation of data.

The Fourier coefficient is related to via


Transverse flow of π--mesons

The dependence of on for mesons in He-C (a), C-C (b) and C-Ne (c) collisions in c.m.s. (He-C, C-C) and lab. (C-Ne) systems. - the experimental data, - QGSM generated data. The solid lines are the result of the linear approximation of experimental data in the interval of -0.9 0.9 for He-C; -0.75 0.75 for C-C; -0.15 1.20 for C-Ne. The solid curves for visual presentation of experimental events - results of approxomation by 4-th order polynomial.

Pions are copiously produced in relativistic heavy-ion collisions. Interesting information about the hot and dense hadronicmatter formed transiently during the reaction can be obtained by studying the pions. In view of the strong coupling between the nucleon and pion, it is interesting to know if pions also have a collective flow behaviour and how the pion flow is related to the nucleon flow.


Transverse flow of π--mesons

The dependence of on for mesons in C-Cu and C-Ta collisions in lab. system.

- the experimental data,- QGSM generated data.

The solid lines are the result of the linear approximation of experimental data in the interval of 0.15 1.60 for C-Cu; 0.0 1.25 for C-Ta. The solid curves for visual presentation of experimental events -results of approxomation by 4-th order polynomial.


Number of events, the correction factorand the flow for protons


The values of the parametersfor protons


ConclusionsThe collective properties of protons and π-mesons in He-C, C-C, C-Ne, C-Cu and C-Ta collisions at a momentum of 4.2 ÷

4.5GeV/c per nucleon (E=3.4 ÷ 3.7 GeV/nucleon) have been investigated.

1. The directed (in-plane) flow effects of protons and mesons have been investigated. The transverse momentum technique of Danielewicz and Odyniec was used for data analysis. Clear evidence of directed (in-plane) flow effectsfor protons and π-mesons has been obtained. From the transverse momentum distributions of protons and mesons with respect to the reaction plane, the flow F (the measure of the collective transverse momentum transfer in the reaction plane) has been extracted. The dependence of F on mass numbers of projectile Ap and target At was studied. The absolute value of F increases linearly with the increase of Ap , At , from F = 95 ± 8 (MeV) for He-C up to F = 178 ± 20 (MeV) for C-Ta for protons and from F = 17 ± 3 (MeV) for He-C up to F = -74 ± 6 (MeV) for C-Ta for π- mesons respectively.

2. A clear signature of elliptic flow (squeeze-out) has been obtained from the azimuthal distributions of protons with respect to the reaction plane in He-C, C-C, C-Ne, C-Cu and C-Ta collisions. Azimuthal distributions have been parametrized by a second order polynomial function, the parameter a2 of the anisotropy term a2cos2ϕ have been extracted. The second Fourier coefficient , which is related to a2 via and measures the elliptic flow, have been estimated both for all pairs of nuclei. The obtained results of the elliptic flow excitation function for protons in He-C, C-C, C-Ne, C-Cu and C-Ta collisions has been compared with the data in the available energy region of 0.2 ÷200.0 GeV/nucleon. The excitation function clearly shows an evolution from negative to positive elliptic flow within the region of GeV/nucleon and point to an apparent transition energy GeV/nucleon.

3. All experimental results have been compared with the predictions of the Quark Gluon String Model. The model reproduces experimental data quite well.

collective flow phenomena of protons and mesons...

Documents