Azimuthal Distributions of K + Mesons in Heavy-Ion Collisions

Strange mesons are considered to be sensitive to in-medium modifications. Theory predicts a repulsive K ⁺ N potential and an attractive K ^? N potential in dense matter. A repulsive K ⁺ N potential would repel the K ⁺ mesons from the bulk of the nucleons and therefore cause a preferred out-of-plane emission of K ⁺ mesons at midrapidity and a directed flow opposite to the nucleons at target and projectile rapidity. One of observables to probe in-medium effects is the azimuthal emission pattern of K ⁺ mesons in heavy ion collisions. KaoS collaboration has measured the azimuthal distributions of K ⁺ mesons in Au + Au reactions at 1.5 A GeV and Ni + Ni reactions at 1.93 A GeV. Data show that K ⁺ mesons exhibit a pronounced enhancement at ${\phi = {90}^\circ}$ , i.e. perpendicular to the reaction plane. The data have also been fitted using the first two components of a Fourier series to get the directed flow v ₁ and elliptic flow v ₂. We used the quantum molecular dynamics model based on the covariant kaon dynamics to simulate the Au + Au collisions at 1.5 A GeV and the Ni + Ni collisions at 1.93 A GeV, to analyze the azimuthal distributions of K ⁺ mesons, and to calculate v ₁ and v ₂ of K ⁺ mesons. Calculated results with a repulsive in-medium K ⁺ N potential can reasonably describe the features of KaoS data. This indicates that the azimuthal distribution is one of sensitive probes to extract information on in-medium properties at high densities.     

Rotation-like behavior as a function of projectile energy and target mass

The azimuthal distributions produced in the intermediate energy⁴⁰Ar-induced reactions are calculated via the nuclear transport theory. The rotational collective motion is observed from the mid-rapidity particles emission. In addition to the investigation on particle emission in the coordinate space, the momentum distributions of emitted particles as a function of azimuthal angle are also discussed. The azimuthal distributions are fitted by performing Legendre polynomial expansion to second order. By incorporating the fluctuation between the estimated and true reaction plane into our calculations, quantitative agreements with the data are obtained for⁴⁰Ar+²⁷Al reactions below 85 MeV/nucleon. It is found that the rotation-like behavior becomes stronger with the increasing of the impact parameter and weaker with the increasing of the projectile energy. For⁴⁰Ar+²⁷Al system at about 85 MeV/nucleon the rotation-like behavior almost vanishes and the mid-rapidity azimuthal distribution tends to be isotropic. For 35 MeV/nucleon⁴⁰Ar-induced reactions the rotation-like behavior becomes weaker and the out-of-plane enhancement of particle emission appears with the increasing of target mass. The possible origins of these target mass dependent azimuthal distributions at mid-rapidity are discussed.     

Flow effects in 84Kr induced collisions in emulsion at 0.95 GeV per nucleon

Using emulsion detector the collective flow signals in inelastic interactions of ⁸⁴Kr nuclei with Ag(Br) at 950 MeV/nucleon are studied. A transverse momentum analysis is performed to determine the reaction plane. The bounce-off of spectator fragments is observed. In azimuthal distributions relative to the reaction plane squeeze-out and side-splash of participants are seen. Received: 27 September 1999     

Directed collective flow and azimuthal distributions in 36Ar + 27Al collisions from 55 to 95 MeV/u

A 4π charged particle detector array with a low velocity threshold has been used to detect the products from reactions induced by ³⁶Ar on ²⁷Al at energies ranging from 55 to 95 MeV/u. Well characterized events were selected and sorted as a function of the impact parameter. Two methods were used for sorting these events with respect to their impact parameters and three methods were compared to determine the reaction plane. The transverse momentum analysis has been found to be the best method to extract the direction of the reaction plane for this system and for the experimental set-up used here. The energy of vanishing flow for central collisions has been found to be around 90–95 MeV/u. The azimuthal distributions of mid-rapidity particles exhibit a preferential in-plane emission and no squeeze-out effect.     

Study of collective flow effects in CC collisions at a momentum of 4.2 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

Directed (in-plane) flows of protons, pions, and projectile light fragments (d, t, ³He, ⁴He) have been observed by investigating the dependence of the mean transverse momentum in the reaction plane 〈p _x 〉 on the rapidity y in the c.m. system for CC collisions at a momentum of 4.2 GeV/c per nucleon. The comparison of our in-plane-flow results of protons with flow data for various projectile/target configurations was made using the scaled flow F _s = F/(A _P ^1/3 + A _T ^1/3 ). F _s demonstrates a common scaling behavior for flow values from different systems. From azimuthal distributions of protons and π^? mesons, out-of-plane (squeeze-out) flow effects have been observed and the parameter a₂ (the measure of the anisotropic emission strength) has been extracted. The quark-gluon string model reproduces the experimental results quite well.     

Azimuthal anisotropy of photon and charged parti cle emissionin 208Pb + 208Pb collisions at 158 $\ cdot A$ GeV/ c

The azimuthal distributions of photons and charged particles with respect to the event plane are investigated as a function of centrality in ²⁰⁸Pb + ²⁰⁸Pb collisions at 158 GeV/c in the WA98 experiment at the CERN SPS. The anisotropy of the azimuthal distributions is characterized using a Fourier analysis. For both the photon and charged particle distributions the first two Fourier coefficients are observed to decrease with increasing centrality. The observed anisotropies of the photon distributions compare well with the expectations from the charged particle measurements for all centralities.Received: 22 May 2004, Revised: 14 April 2005, Published online: 4 May 2005PACS: 25.75.Dw     

Neutral strange particle correlations in 360 GeV/cpp interactions

Production properties and correlations forK _s ⁰ K _s ⁰ ,K _s ⁰ Λ,K _s ⁰ ¯Λ and Λ¯Λ systems in 360 GeV/cpp interactions are presented. All rapidity gap distributions are observed to peak at Δy=0 and the azimuthal angular distributions between the two particles are consistent with being flat. Experimental results are compared with the quark fusion and Lund models of particle production.     

Azimuthal pion fluctuation in ultra relativistic nuclear collisions and centrality dependence—a study with chaos based complex network analysis

Various works on multiplicity fluctuation have investigated the dynamics of particle production process and eventually have tried to reveal a signature of phase transition in ultra-relativistic nuclear collisions. Analysis of fluctuations of spatial patterns has been conducted in terms of conventional approach. However, analysis with fractal dynamics on the scaling behavior of the void has not been explored yet. In this work we have attempted to analyze pion fluctuation in terms of the scaling behavior of the void probability distribution in azimuthal space in ultra-relativistic nuclear collisions in the light of complex networks. A radically different and rigorous method viz. Visibility Graph was applied on the data of ³²S-Ag/Br interaction at an incident energy of 200 GeV per nucleon. The analysis reveals strong scaling behavior of void probability distributions in azimuthal space and a strong centrality dependence.     

Measurement of the azimuthal anisotropy coefficient <Emphasis Type="Italic">v</Emphasis><Subscript>2</Subscript> for the emission of α particles in nucleus-nucleus collisions at energies 1.88–10.6 GeV/nucleon

The azimuthal anisotropy of the emission of α particles in collisions of the ²²Ne, ²⁴Mg, ⁵⁶Fe, and ¹⁹⁷Au nuclei with photoemulsion nuclei has been measured at projectile energies E_pr = 1.88–10.6 GeV/nucleon. The results are compared with similar measurements for protons. It has been found that the ratio of the azimuthal anisotropy coefficients v₂ for α particles and protons is equal to 6 ± 2 at low energies E_pr ≈ 2 GeV/nucleon, whereas these coefficients coincide with each other for energies E_pr ≥ 4 GeV/nucleon. This difference may indicate that, at low projectile energies, α particles are formed predominantly at the early stage of a collective flow. Formation of α particles for E_pr ≥ 4 GeV/nucleon likely occurs at the stage of nuclear matter scattering.     

K+ versus Λ flow in relativistic heavy-ion collisions

We study K⁺ and Λ flow in heavy-ion collisions at beam energies of about 2 AGeV. We present our results in both the “traditional” (i.e., in terms of the average transverse momentum in the reaction plane) as well as “modern” (i.e., in terms of coefficients of the Fourier analysis of azimuthal distributions) methods of flow analysis. We find significant differences between the K⁺ and the Λ flow: while the Λ flow is basically similar to that of nucleons, the K⁺ flow almost disappears. This difference is attributed chiefly to their different mean field potentials in dense matter. The comparisons with the experimental data, as well as theoretical results from independent calculations, indicate clearly the pivotal roles of both K⁺ and Λ medium effects. We emphasize that similar experimental data from independent collaborations are essential for the eventual verification of these medium effects.     

Angular distributions of H2 desorbed from the (100), (110), and (111) faces of copper crystals

The angular distributions of hydrogen molecules desorbed from copper have been measured for single-crystal surfaces of three different orientations: (100), (110), and (111). The surfaces were cleaned to the degree that the impurities were below the level of detection by Auger electron spectroscopy. The angular distributions were all significantly more peaked at the surface normal than the distribution corresponding to diffuse emission, i.e., where the molecular flux is proportional to cos θ, where θ is the angle measured from the surface normal. We have characterized the observed angular distributions by fitting the emperical expression cos^dθ to the data, where d is an adjustable parameter. The results are: d ≈ 5 for (100); d ≈ 2.5 for (110); d ≈ 6 for (111). The distributions are nearly symmetric about the azimuthal angle between the plane of detection and the principal axes of the surface lattice. Possible models are considered.     

Multiparticle azimuthal correlations of negative pions in nucleus-nucleus collisions

Multiparticle azimuthal correlations of ?? ^? mesons have been studied in dC, HeC, CC, CNe, MgMg, (d, He)Ta, CCu, CTa, and OPb collisions at momentum of 4.2, 4.5 GeV/c per nucleon within the standard transverse momentum analysis method of P. Danielewicz and G. Odyniec. The data were obtained by SKM-200-GIBS and Propane Bubble Chamber Collaborations of JINR. The axis has been selected in the phase space and with respect to this axis ?? ^? meson correlations were observed. The values of the coefficient of the correlations linearly depend on the mass numbers of projectile (A _P ) and target (A _T ) nuclei. The Quark-Gluon String Model satisfactorily describes the experimental results.     

Angular Dependence of Two Particle Correlation in 400GeV/c pp Collisions

The angular dependence of the particle-Particle comeladon (PPC) and its asytiumeby (PPCA) have been calculated by using the experimental data of multiplicity production for pp collisions at 400GeV/ c. The results are different stmngly from the overall behavior of e⁺e^－ data,but agree with the results obtained by NA22 collaboration quite well. The leading particles influence stingily the PPCA disribibudons for hadronic collisions data. The calculated results for the distributions of the azimuthal difference between two pardcles mean that the azimuthal correlation has been observed.     

Intermediate mechanisms in fission-like fragmentation in the 32S + 59Co and 32S + 63Cu reactions

The fission-like fragmentation of the ³²S + ⁵⁹Co and ³²S + ⁶³Cu composite systems has been studied at incident energies E/A ≈ (4–5) MeV/nucleon. Mass, energy and angular distributions of the fission-like fragments were obtained from time-of-flight measurements. The mean total kinetic energies of the fragments are found to be fully relaxed, whereas a strong angular dependence is observed in the mass distributions. The data are interpreted in terms of a dynamical model based on the transport theory.     

Strange mesons in dense nuclear matter

Experimental data on the production of kaons and antikaons in heavy-ion collisions at relativistic energies are presented and discussed with respect to in-medium effects. The K ^?/K⁺ ratios measured in nucleus-nucleus collisions are 1–2 orders of magnitude larger than in proton-proton collisions. The azimuthal angle distributions of K ⁺ mesons indicate a repulsive kaon-nucleon potential. Microscopic transport calculations consistently explain both the yields and the emission patterns of kaons and antikaons when assuming that their properties are modified in dense nuclear matter. The K ⁺ production excitation functions measured in light and heavy collision systems provide evidence for a soft nuclear equation-of-state.     

Out-of-plane emission of nuclear matter in Au+Au collisions between 100 and 800 AMeV

We present new experimental results concerning the azimuthal distributions of proton-likes, light and intermediate mass fragments at midrapidity for Au(100–800 A MeV) +Au collisions measured with the FOPI phase-I detector at GSI in Darmstadt. The azimuthal distributions are investigated as a function of the collision centrality, the incident energy, the fragment charge and transverse momentum. The azimuthal anisotropy is maximum for impact parameters around 7 fm. Intermediate mass fragments present a stronger out-of-plane emission signal than light fragments and a saturation is reached for Z ⩾ 4. The azimuthal anisotropy increases with the fragment transverse momentum and decreases as the incident energy increases. The azimuthal anisotropy of Z = 2 particles investigated as a function of the scaled fragment transverse momentum follows an universal curve for bombarding energies between 250–800 A MeV. A signature for a transition from in-plane to out-of-plane emission is evidenced at the lowest beam energies.     

Measurement of the azimuthal distribution of molecular orbital K X-rays emitted in 90 MeV Ni + Ni collisions

The azimuthal distribution of molecular orbital K X-rays emitted in 90 MeVNi + Ni collisions has been measured as a function of impact parameter using the particle—X-ray coincidence technique. A weak azimuthal anisotropy of less than 20% has been observed.     

Study of multiparticle azimuthal correlations in central CNE, MgMg, CCu, and OPb interactions at energy of 3.7 GeV per nucleon

Azimuthal correlations between protons and between pions have been investigated in central CNe, MgMg, CCu, and OPb collisions at an energy of 3.7 GeV/nucleon. Negative (back-to-back) correlations have been observed for protons in CNe, CCu, and for π ^? mesons in CNe and MgMg collisions. For π^? mesons, positive (side-by-side) azimuthal correlations have been observed for heavy systems of CCu and OPb. The Quark-Gluon String Model satisfactorily describes the experimental results both for protons and π^? mesons.     

Elliptic flow of ν ands <Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> mesons in heavy-ion collisions at 2 <Emphasis Type="Italic">A</Emphasis> GeVmesons in heavy-ion collisions at 2 <Emphasis Type="Italic">A</Emphasis> GeV

Elliptic flow of ν and π ⁰ mesons emitted at midrapidity are studied in collisions of 1.9 A GeV ⁵⁸Ni+⁵⁸Ni and 2 A GeV ⁴⁰Ca+^natCa. The observed anisotropy corresponds to a negative elliptic flow signal for ν mesons, indicating a preferred emission perpendicular to the reaction plane. In contrast, only small azimuthal anisotropies are observed for π ⁰ mesons. This may indicate that ν mesons freeze out earlier from the central interaction region than pions.     

Oxygen adsorption on Cu(110): Determination of atom positions with low energy ion scattering

The position of adsorbed oxygen on Cu($\text{1}$10) surfaces was determined with Low Energy Ion Scattering (LEIS). The experiments were performed by bombarding the copper surface at small angles of incidence with low energy Ne⁺ ions (3–5 keV). Measurements of the Ne⁺ ions scattered by adsorbed oxygen showed regular peaks in the azimuthal distribution of the scattered ions due to a shadowing effect. From the symmetry of the azimuthal distributions it follows that the centre of an adsorbed oxygen atom on the Cu(1&#x0304;10) surface lies about 0.6 Å below the midpoint between two neighbouring Cu atoms in a 〈001〉 row. A comparison of the azimuthal distributions of Ne⁺ ions scattered from clean Cu surfaces and oxygen-covered Cu surfaces showed that hardly any surface reconstruction had occurred in the oxygen-covered surfaces. The applied method seems to be an appropriate one for locating adsorbed atoms because it uses only simple qualitative considerations about azimuthal distributions of scattered ions.