J. Aichelin

'Quantum' molecular dynamics: A Dynamical microscopic n body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions

Abstract The quantum molecular dynamics approach, an n-body theory to describe heavy ion reactions between 100 MeV/n and 2 GeV/n is reviewed. We start out with a survey of the present status of nuclear matter calculations and of kinetic theories as far as they are of importance for our approach. We then present a detailed derivation of the quantum molecular dynamics equation, discuss the various approximations necessary to derive this equation and to make actual calculations feasible. The calculations presented aim at the solution of two of the most interesting questions of contemporary heavy ion physics: What causes a nucleus to fragment into many heavy pieces, and can we determine the nuclear equation of state from heavy ion reactions? We first make detailed comparisons with a multitude of experimental data, which yield unexpectedly good agreement. We then proceed to detailed investigations of these questions. We find that fragmentation at these energies is triggered by the density wave caused by the projectile while travelling through the target. We reproduce the “squeeze out” and the “bounce off” predicted by hydrodynamical calculations and recently seen in experiment. Thus there is hope that the nuclear equation of state can be extracted from heavy ion experiments. However, very careful multiparameter experiments are necessary before one can achieve this goal.

Quantum molecular dynamics — A novel approach to N-body correlations in heavy ion collisions

Abstract We introduce a novel N-body approach to describe heavy ion collisions. The nucleons are represented as gaussian wave packets in configuration and momentum space. They interact via a combination of a Skyrme type potential and a Uehling-Uhlenbeck two-body scattering mechanism. This theory keeps track of the correlations and therefore allows for a selfconsistent theoretical description of the entire complex dynamics of heavy ion collisions, from the initial non-equilibrium penetration stage via the high density phase to the final formation of complex — stable and unstable — fragments. The cluster formation is caused by correlations and density fluctuations. We find that global equilibrium is not established in the course of the reaction. The form of the mass yield curve agrees with experimental findings. We also study the recently observed collective flow effects and find a strong dependence on the nuclear equation of state.

Fragmentation reactions on nuclei: Condensation of vapour or shattering of glass?

Abstract We analyse charge yield curves d σ /d Z from inclusive fragmentation reactions of the type A P + A T → Z + X where a high energy projectile A P (p,C) collides with a target A T (U, Ag, Xe, Kr) and a fragment of charge Z is observed. The principle of minimal information together with charge conservation leads to an expression for the shape of d σ /d Z which describes the experiments without free parameter.

Intermediate-energy heavy ion collisions with G matrix potentials and cross-sections

Abstract We present the first quantum molecular dynamics calculations of heavy-ion collisions in which the effective nucleon-nucleon potential and the nucleon-nucleon cross sections in a medium are consistently calculated in the Brueckner theory from the basic Reid soft-core potential. The strong momentum dependence of the Brueckner G -matrix yields a quite different time evolution of heavy-ion collisions as compared with that obtained via Skyrme potentials adjusted to nuclear matter properties and the optical potential. In the calculation of Nb+Nb collisions at 400 MeV/u, we find that the transverse momentum transfer is much larger than that obtained with the hard Skyrme potential, although the compressibility ( K = 182MeV) is even lower than that of the soft Skyrme potential ( K = 200MeV). This raises questions about the possibility of uniquely determining the parameters of the nuclear equation of state from heavy-ion collisions at intermediate energies. The momentum transfer has two physically quite different reasons: the strong momentum dependence of the G -matrix potential causes a strong transverse momentum very early in the time evolution of the reaction, i.e. before the system is compressed. Additional transverse momentum is transferred in the compression phase, similar to observations for Skyrme-like potentials. The momentum transfer in the second process is about that of the soft Skyrme potential, which is not unexpected because the compressibilities are similar and in both calculations about the same density is reached.

Emission temperatures in 40Ar+197Au reactions in the limiting fragmentation regime

Abstract Apparent emission temperatures of 4 He and 5 Li fragments were deduced for the reaction 40 Ar+ 197 Au at E / A =200 MeV from the relative population of excited states. Compared to previous measurements at E / A =60 MeV, the average emission temperatures increases by less than 2 MeV to a value of about 6 MeV. QMD calculations indicate that the momentum distribution of the nucleons forming a fragment is determined at a point where the system is still close to normal nuclear density and that they do not reflect the local momentum distribution of the surrounding nucleons. The simulations suggest that the observed low emission temperatures are a consequence of the dynamics of the fragment formation process.

QMD versus BUU/VUU. Same results from different theories☆

Abstract We demonstrate that the predictions of the n -body quantum molecular dynamics (QMD) approach to heavy-io n collisions does indeed agree with those of the well-established one-body VUU/BUU theory, as far as single-particle observables are concerned. We find in particular good agreement of the longitudinal and transverse momentum transfer, the particle multiplicities and the double differential cross section in the two approaches. These predictions could be checked experimentally via exclusive 4π measurements. Omitting collisions, QMD results agree with that of TDHF and of the Vlasov equation. Thus neither the details of the TDHF wave function (which are not reproduced in Vlasov and QMD) nor the parametrization of the single-particle Wigner densities as gaussians with a constant width (which is employed in QMD) do play a decisive role for intermediate-energy heavy-ion collisions.

Multiplicity distributions of particles from string fragmentation calculated in a phase space model

Abstract The multiplicity distributions of particles from string fragmentation are calculated in a phase space model, using the grand canonical approximation. The variation of the multiplicity distribution with the size of the rapidity interval as observed in e + e − annihilation and deep inelastic μp scattering is well reproduced in our model. We discuss its relation to a negative binomial distribution and calculate the k -parameter. The effects from the violation of energy conservation on the multiplicity distributions are investigated and found to be sizable at low energies and in the full rapidity interval.

Beam energy independence of the target fragmentation above Ekin = 1 GeV/N

Abstract Above a beam energy of 1 GeV/N the distributions of protons and fragments in the target rapidity regime become independent of the beam energy. The reaction scenario is close to that expected from the simple geometrical participant-spectator model. The difference between the rapidity distributions of baryons reported for the reaction of Ne (2.1 GeV/N) + Au and O (200 GeV/ N) + Au is caused by a different experimental acceptance. The slope of the measured transverse energy spectra of protons at 200 GeV/N (〈Et〉 = 75 MeV) is very close to that calculated at 2.1 GeV/N (〈Et〉 = 86 MeV). Thus spectator matter does not act as a “detector” for particles created at high beam energies as hoped. This is the result of the “quantum” molecular dynamics (QMD) calculations employed for these asymmetric systems.

Three heavy fragments observed in simulations of medium energy heavy ion reactions

Abstract Employing the Boltzmann-Uehling-Uhlenbeck equation the reaction 44 A MeV Ar + Ni is simulated. Depending on the impact parameter four domains are observed. At b ⩽ 1 fm fusion is seen. Small and large impact parameter reactions show two large remnants and limit a domain where three heavy remnants are found. The formation of the three clusters are discussed in detail.

Confrontation of Theoretical Approaches and Experimental Data on High Energy Heavy Ion Collisions

We give an overview of high energy heavy ion collisions. The merits and drawbacks of macroscopic and microscopic theoretical approaches (Fluid Dynamics, TDHF, Cascade, Vlasov-Uehling-Uhlenbeck, Classical and Quantum Molecular Dynamics) are discussed. The importance of nonequilibrium transport properties (viscosity, mean free path, effective in-medium cross sections) and of the nuclear potential (equation of state) is pointed out. The liquid-vapour phase transition and multifragmentation have been studied. The possibility of meassuring Machshock fragments in inverse kinematics experiments is also pointed out. It is demonstrated that the projectile and target are stopped at YCM if central collisions are studied. The stopping is only sensitive to σeff. The predicted bounce-off of the rather cold fragments in the reaction plane and the predicted accompanying squeeze-out of the hot participant baryons perpendicular to the reaction plane are experimentally discovered. These effects are sensitive both to the viscosity (σeff(ρ,E,Ω)) and to the generalized equation of state (optical potential U(ρ, E)). The data clearly ask for a repulsive potential interaction. We conclude that nuclear matter produced in relativistic collisions is a hot, dense, viscous and rather incompresible fluid, with important quantum properties.