Hadronic Matter Is Soft

The stiffness of the hadronic equation of state has been extracted from the production rate of K mesons in heavy-ion collisions around 1 AGeV incident energy. The data are best described with a compression modulus K around 200 MeV, a value which is usually called ''soft.'' This is concluded from a detailed comparison of the results of transport theories with the experimental data using two different procedures: (i) the energy dependence of the ratio of K from Au Au and C C collisions and (ii) the centrality dependence of the K multiplicities. It is demonstrated that input quantities of these transport theories which are not precisely known, such as the kaon-nucleon potential, the N ! NK cross section, or the lifetime of the in matter, do not modify this conclusion. DOI: 10.1103/PhysRevLett.96.012302 PACS numbers: 25.75.Dw, 21.65.+f For many years one of the most important challenges in nuclear physics has been to determine E=A; T, the energy/nucleon in nuclear matter in thermal equilibrium as a function of the density and the temperature T. Only at equilibrium density, 0 , do we know the energy per nucleon E=A 0 ; T 0 ÿ16 MeV by extrapolating the Weizsäcker mass formula to infinite matter. This quest has been dubbed ''search for the nuclear equation of state (EoS).'' Modeling of neutron stars or supernovae has not yet constrained the nuclear equation of state [1]; therefore, the most promising approach in extracting E=A; T is to use heavy-ion reactions in which the density of the colliding nuclei changes significantly. Three principal experimental observables have been suggested in the course of this quest which carry -according to theoretical calculations -information on the nuclear EoS: (i) the strength distribution of the giant isoscalar monopole resonances (i) The study of monopole vibrations has been very successful, but the variation in density is minute; therefore, giant monopole resonances are sensitive to the energy which is necessary to change the density of a cold nucleus close to the equilibrium point 0 . According to theory the vibration frequency depends directly on the force that counteracts any deviation from the equilibrium and therefore the potential energy. The careful analysis of the isoscalar monopole strength in nonrelativistic [2] and relativistic mean field models has recently converged which measures the curvature of E=A; T at the equilibrium point. is the compressibility. The values found are around K 240 MeV and therefore close to what has been dubbed a ''soft equation of state.'' (ii) If the overlap zone of projectile and target becomes considerably compressed in semicentral heavy-ion collisions, an in-plane flow is created due to the transverse pressure on the baryons outside of the interaction region with this flow being proportional to the transverse pressure. In order to obtain a noticeable compression, the beam energy has to be large compared to the Fermi energy of the nucleons inside the nuclei and hence a beam energy of at least 100 AMeV is necessary. Compression goes along with excitation and therefore the compressional energy of excited nuclear matter is encoded in the in-plane flow. It has recently been demonstrated [6] that transport theories do not agree quantitatively yet and therefore conclusions (iii) The third method is most promising for the study of nuclear matter at high densities and is the subject of this Letter. K mesons produced far below the NN threshold cannot be created in first-chance collisions between projectile and target nucleons. They do not provide sufficient energy even if one includes the Fermi motion. The effective energy for the production of a K meson in the NN center of mass system is 671 MeV as, in addition to the mass of the kaon, a nucleon has to be converted into a to conserve strangeness. Before nucleons can create a K at these subthreshold energies, they have to accumulate en-PRL 96

On the elliptical flow in asymmetric collisions and nuclear equation of state

We here present the results of elliptical flow for the collision of different asymmetric nuclei (10Ne20 +13 Al27, 18Ar40 +21 Sc45, 30Zn64 +28 Ni58, 36Kr86 +41 Nb93) by using the Quantum Molecular Dynamics (QMD) model. General features of elliptical flow are investigated with the help of theoretical simulations. The simulations are performed at different beam energies between 40 and 105 MeV/nucleon. A significant change can be seen from in-plane to out-of-plane elliptical flow of different fragments with incident energy. A comparison with experimental data is also made. Further, we predict, for the first time that, elliptical flow for different kind of fragments follow power law dependence ? C(Atot)? for asymmetric systems

An Improved Quantum Molecular Dynamics Model and its Applications to Fusion Reaction near Barrier

An improved Quantum Molecular Dynamics model is proposed. By using this model, the properties of ground state of nuclei from $^{6}$Li to $^{208}$Pb can be described very well with one set of parameters. The fusion reactions for $^{40}$Ca+$^{90}$Zr, $^{40}$Ca+$^{96}$Zr and $^{48}$Ca+$^{90}$Zr at energy near barrier are studied by this model. The experimental data of the fusion cross sections for $^{40}$Ca+$^{90,96}$Zr at the energy near barrier can be reproduced remarkably well without introducing any new parameters. The mechanism for the enhancement of fusion probability for fusion reactions with neutron-rich projectile or target is analyzed.Comment: 20 pages, 12 figures, 3 table

Dynamic study on fusion reactions for 40,48^{40,48}Ca+90,96^{90,96}Zr around Coulomb barrier

By using the updated improved Quantum Molecular Dynamics model in which a surface-symmetry potential term has been introduced for the first time, the excitation functions for fusion reactions of $^{40,48}$Ca+$^{90,96}$Zr at energies around the Coulomb barrier have been studied. The experimental data of the fusion cross sections for $^{40}$Ca+$^{90,96}$Zr have been reproduced remarkably well without introducing any new parameters. The fusion cross sections for the neutron-rich fusion reactions of $^{48}$Ca+$^{90,96}$Zr around the Coulomb barrier are predicted to be enhanced compared with a non-neutron-rich fusion reaction. In order to clarify the mechanism of the enhancement of the fusion cross sections for neutron-rich nuclear fusions, we pay a great attention to study the dynamic lowering of the Coulomb barrier during a neck formation. The isospin effect on the barrier lowering is investigated. It is interesting that the effect of the projectile and target nuclear structure on fusion dynamics can be revealed to a certain extent in our approach. The time evolution of the N/Z ratio at the neck region has been firstly illustrated. A large enhancement of the N/Z ratio at neck region for neutron-rich nuclear fusion reactions is found.Comment: 21 pages, 7 figures,3 table

Microscopic Models for Ultrarelativistic Heavy Ion Collisions

In this paper, the concepts of microscopic transport theory are introduced and the features and shortcomings of the most commonly used ansatzes are discussed. In particular, the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model is described in great detail. Based on the same principles as QMD and RQMD, it incorporates a vastly extended collision term with full baryon-antibaryon symmetry, 55 baryon and 32 meson species. Isospin is explicitly treated for all hadrons. The range of applicability stretches from $E_{lab} 200$ GeV/nucleon, allowing for a consistent calculation of excitation functions from the intermediate energy domain up to ultrarelativistic energies. The main physics topics under discussion are stopping, particle production and collective flow.Comment: 129 pages, pagestyle changed using US letter (8.5x11 in) format. The whole paper (13 Mb ps file) could also be obtained from ftp://ftp.th.physik.uni-frankfurt.de/pub/urqmd/ppnp2.ps.g

K^-/K^+ ratio at GSI in hot and dense matter

The $K^-/K^+$ ratio in heavy-ion collisions at GSI energies is studied including the properties of the participating hadrons in hot and dense matter. The determination of the temperature and chemical potential at freeze-out conditions compatible with the ratio $K^-/K^+$ is very delicate, and depends on the approach adopted for the antikaon self-energy. Three approaches for the $K^-$ self-energy are considered: non-interacting $K^-$, on-shell self-energy and single-particle spectral density. With respect to the on-shell approach, the use of an energy dependent $\bar{K}$ spectral density, including both s- and p-wave components of the $\bar{K}N$ interaction, lowers considerably the freeze-out temperature and gives rise to the "broad-band equilibration" advocated by Brown, Rho and Song.Comment: 8 pages, 5 figures, talk given at the Strange Quark Matter Conference, Atlantic Beach, North Carolina, March 12-17, 200

Transition from in-plane to out-of-plane azimuthal enhancement in Au+Au collisions

The incident energy at which the azimuthal distributions in semi-central heavy ion collisions change from in-plane to out-of-plane enhancement, E_tran, is studied as a function of mass of emitted particles, their transverse momentum and centrality for Au+Au collisions. The analysis is performed in a reference frame rotated with the sidewards flow angle, Theta_flow, relative to the beam axis. A systematic decrease of E_tran as function of mass of the reaction products, their transverse momentum and collision centrality is evidenced. The predictions of a microscopic transport model (IQMD) are compared with the experimental results.Comment: 32 pages, Latex, 22 eps figures, accepted for publication in Nucl. Phys.

Hadron Production in Heavy Ion Collisions

We review hadron production in heavy ion collisions with emphasis on pion and kaon production at energies below 2 AGeV and on partonic collectivity at RHIC energies.Comment: 31 pages, 26 figures, accepted for publication in Landolt-Boernstein Volume 1-23

Recent astrophysical and accelerator based results on the Hadronic Equation of State

In astrophysics as well as in hadron physics progress has recently been made on the determination of the hadronic equation of state (EOS) of compressed matter. The results are contradictory, however. Simulations of heavy ion reactions are now sufficiently robust to predict the stiffness of the (EOS) from (i) the energy dependence of the ratio of $K^+$ from Au+Au and C+C collisions and (ii) the centrality dependence of the $K^+$ multiplicities. The data are best described with a compressibility coefficient at normal nuclear matter density $\kappa$ around 200 MeV, a value which is usually called ``soft'' The recent observation of a neutron star with a mass of twice the solar mass is only compatible with theoretical predictions if the EOS is stiff. We review the present situation.Comment: invited talk Strange Quark Matter Conference SQM06 in Los Angele

Neutrons from multiplicity-selected La-La and Nb-Nb collisions at 400A MeV and La-La collisions at 250A MeV

Triple-differential cross sections for neutrons from high-multiplicity La-La collisions at 250 and 400 MeV per nucleon and Nb-Nb collisions at 400 MeV per nucleon were measured at several polar angles as a function of the azimuthal angle with respect to the reaction plane of the collision. The reaction plane was determined by a transverse-velocity method with the capability of identifying charged-particles with Z=1, Z=2, and Z > 2. The flow of neutrons was extracted from the slope at mid-rapidity of the curve of the average in-plane momentum vs the center-of-mass rapidity. The squeeze-out of the participant neutrons was observed in a direction normal to the reaction plane in the normalized momentum coordinates in the center-of-mass system. Experimental results of the neutron squeeze-out were compared with BUU calculations. The polar-angle dependence of the maximum azimuthal anisotropy ratio $r(\theta)$ was found to be insensitive to the mass of the colliding nuclei and the beam energy. Comparison of the observed polar-angle dependence of the maximum azimuthal anisotropy ratio $r(\theta)$ with BUU calculations for free neutrons revealed that $r(\theta)$ is insensitive also to the incompressibility modulus in the nuclear equation of state.Comment: ReVTeX, 16 pages, 17 figures. To be published in Physical Review