Nuclear Matter Equation Of State Research Articles

Subthreshold kaon production and compression effects

With regard to the use of subthreshold kaons from relativistic heavy-ion collisions as a tool to gain information on the nuclear matter equation of state, we investigate the role of the elementary kaon production cross section. The uncertainties introduced because of the poor knowledge of the latter near threshold are largely eliminated by considering kaon yield ratios.

Pion production as a test of nuclear matter properties.

Nuclear matter equations of state are constructed which incorporate explicitly the pion and delta degrees of freedom. These are used in relativistic one-dimensional and three-dimensional hydrodynamical models of central nucleus-nucleus collisions to determine the influence of the compressional energy on the observed pion multiplicity. We find a modest dependence on the compressional energy but a significant difference between slab-slab and sphere-sphere collisions having to do with curved shock waves. Thus one-dimensional hydrodynamic models do not appear to be suitable for interpreting pion production at energies of 100 MeV--2 GeV.

Nuclear compression effects of pion production in nuclear collisions

We show that the method of analyzing the pion excitation function proposed by Stock et al. may determine only a part of the nuclear matter equation of state. With the addition of missing kinetic energy terms the implied high density nuclear equation of state would be much stiffer than expected from conventional theory. A stiff equation of state would also follow if shock dynamics with early chemical freeze out were valid.

Pion production as a probe of the nuclear matter equation of state

It is shown that thermal and chemical equilibrium are approached during the high density stage in central nucleus-nucleus collisions and that the yield of produced pions is determined at that time. A chemical model with Rankine-Hugoniot compression is used to extract a nuclear matter equation of state from the observed pion yield assuming a partition of the internal energy per nucleon into thermal and compressional energy fractions, with only the former part contributing to particle production.

Relativistic nucleus-nucleus collisions

Recent investigations of relativistic heavy ion collisions are reviewed. In particular, use of 4π detector systems. Streamer Chamber and Plastic Ball, has yielded insight into the mechanisms of thermal and chemical equilibrium establishment at Bevalac and Dubna energies, as required for the formation of compressed fireball matter. Hydrodynamical flow of high density matter, and the total pion yield are established as primordial probes of the high density stage. First information is discussed about the nuclear matter equation of state. Towards higher energies, the conditions for quark matter formation are examined. First observations, in cosmic ray reactions, of extremely high mean transverse momenta, agree with predictions concerning possible signatures of a phase transition.

Investigation of nuclear matter properties by means of high energy nucleus-nucleus collisions

We review recent advances towards an understanding of high density nuclear matter, as created in central collisions of nuclei at high energy. In particular, information obtained for the nuclear matter equation of state will be discussed. The lectures focus on the Bevalac energy domain of 0.4 to 2 GeV per projectile nucleon.

Deuteron and entropy production and the nuclear liquid-gas phase transition

The entropy of hot matter produced in medium energy nuclear collisions is inferred from recent data on light fragment cross sections. A previously suggested model is used to fit the abundances of both the deuterons, and the deuteronlike pairings contained in higher mass clusters, with a single parameter. The model takes into account finite density effects in six-dimensional phase space. The entropy rises monotonically with energy, as expected, but remains rather high even at the lower energies. Surprisingly the measured entropy always lies above the theoretically expected value (about 3.3) at the critical point of the liquid-gas phase transition which, it is argued, depends only upon the gross features of the nuclear matter equation of state.

Manifestation of nuclear compression in high multiplicity selected collisions of [formula omitted] and consequences for a study of the nuclear equation of state

On the basis of the nuclear fluid dynamical model a kinetic energy flow analysis of high multiplicity selected collisions of 93Nb (E lab = 0.4 ffGeV/n) + 93 Nb is performed. Finite particle number effects on the flow tensor are explicitely taken into account. Strong sidewards peaks in the distribution of event by event flow angles dN/dcos are in quantitative agreement with data from the new Plastic Ball electronic detection system. It is pointed out that systematic measurement of the flow tensor excitation function can yield clues to the nuclear matter equation of state.

Event-by-event analysis: Possible testing ground for the nuclear matter equation of state

Intranuclear cascade calculations and fluid dynamical predictions of the kinetic energy flow are compared for collisions of /sup 40/Ca+ /sup 40/Ca and /sup 238/U+ /sup 238/U. The aspect ratio, R/sub 13/, as obtained from the global analysis, is independent of the bombarding energy for the intranuclear cascade model. Fluid dynamics, on the other hand, predicts a dramatic increase of R/sub 13/ at medium energies E/sub lab/< or approx. =200 MeV/nucleon. In fact, R/sub 13/(E/sub lab/) directly reflects the incompressibility of the nuclear matter and can be used to extract the nuclear equation of state at high densities. Distortions of the flow tensor due to few nucleon scattering are analyzed. Possible procedures to remove this background from experimental data are discussed.

Streamer chamber experiments

The reactions 40Ar + KCl at eight energies from 0.36 to 1.8 GeV/u, 4He + KCl at 977 and 40Ar + Balg and 40Ar + Pb 3O 4 at 772 GeV/u measured in a Streamer Chamber experiment have been analyzed to determine the stopping power of nuclei, the degree of isotropy and thermalization achieved in central collisions, to search for collective expansion effects and to obtain compressional energies of bulk nuclear matter. Observables used were pion and proton exclusive final state measurements, ratios of total transverse to longitudinal momentum per event, momentum flux and Λ production. From the systematic discrepancy of the π − multiplicities produced in central collisions with respect to an intranuclear cascade model, compressional energies are extracted which fit a parabolic form of the nuclear matter equation of state with a compressibility constant of K = 240 MeV.

A saturating chiral field theory of nuclear matter

Catastrophe Theory analysis is used to construct a chiral theory of pions which leads to a saturating nuclear matter equation of state. This is achieved by introducing a vector meson field via the Higgs mechanism. The equation of state and the nuclear optical potential are computed. A metamorphosis of the nuclear force is suggested.

Softening Effects in the Equation of State and Influence of General Relativity on the Outcome of Stellar Collapse

AbstractHydrodynamical evolution of a collapsing stellar core is followed to test the influence of general relativity and of softening effects in the equation of state. The general relativistic treatment of the collapse does not show any spectacular deviation from the Newtonian treatment. In particular there is no indication within the standard scenario for potential barrier penetration and continued collapse to a black hole. In the case of strong electron capture during the collapse the nuclear matter equation of state is of importance. A softening according to a phase transition below the bounce density is found to reduce the shock strength, but the shock is strong enough to cause the usual blowing‐off.

Compression Effects in Relativistic Nucleus-Nucleus Collisions

The negative pion multiplicity is measured for inelastic and central collisions of 40Ar with KCl at eight energies from 0.36 to 1.8 GeV/nucleon and for 4He and 40Ar on BaI2 at 977 and 772 MeV/nucleon, respectively. A systematic discrepancy in central collision data with a cascade model calculation which fits proton- and pion-nucleus cross sections but omits potential energy effects is used to derive the energy going into bulk compression of the system. A value of the compressibility constant of K = 240 MeV is extracted in a parabolic form of the nuclear matter equation of state.

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the π NN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual N N loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.

Quasi-stationary nonlinear waves in nuclear matter close to pion condensation

The nuclear hydrodynamic model is extended to include the fluctuating spin-isospin density and its interaction with the nuclear matter density. Using the TDHF equations, it is shown that the dynamics of these densities interacting with the pion field can be expressed in terms of the generalized pressures derivable from the generalized nuclear matter equation of state. A phenomenological Skyrme interaction model is used to obtain these pressures. A theory of pion-like spin-isospin quasi-stationary nonlinear waves is formulated from the generalized hydroequations describing the dynamics of a coupled pion nuclear matter system. In the lowest order of nonlinearity, it is proved that the amplitude of the spin-isospin sound wave satisfies a nonlinear Schrodinger equation. The solution of these equations is the amplitude modulated pion-like solitary waves in nuclear matter. When this matter is near the pion condensate, the speed of these nonlinear waves is much smaller than that of the ordinary sound waves.

Current topics in relativistic nuclear collisions

First, we discuss current attempts to deduce the nuclear matter equation of state from inclusive data. Next, some puzzling projectile fragment properties found in emulsions are discussed. Finally, a new test of pion condensation is proposed and current pion data reviewed.

Spherical and linear fluid-dynamical models for relativistic central heavy ion collisions

Spherical hydrodynamical expansion and linear compression and expansion are calculated in viscous relativistic hydrodynamics. The break-up process subsequent to the hydrodynamical collective flow is also taken into account. The results lay the foundation of the blast-wave model and the comparison of the linear and spherical models with the experiment provides further evidence for the soft nuclear matter equation of state.

A mechanism for forming highly dense nuclear matter in relativistic nucleus-nucleus collisions

A reaction mechanism is outlined which, during the diving phase of the collision, provides the conditions for phase transitions with respect to the density. Within this relativistic dynamical model possible first- and second-order phase transitions are considered. On this basis and in connection with experimental alpha -particle data the second minimum of the nuclear matter equation of state is found to be located at rho / rho 0=3.5 with a bump width of about 1/2 rho 0.