Philip J. Siemens

Shock waves in colliding nuclei

Abstract We consider the circumstances under which nuclear matter at high densities can be produced in heavy ion collisions. We argue that lab energies of a few hundred MeV per nucleon will be suitable : the matter velocity will exceed the speed of isentropic compression waves, while the nuclear matter has sufficient stopping power to generate a shock front. From the hydrodynamic conservation laws we show that there is a maximum attainable compression ratio ν ∞ , determined by the thermal properties of the high-density matter. In an independent-fermion model, ν ∞ = 4, but it can be much larger if the phase of the system changes, for example by excitation of nucleon isobars, production of π-mesons, or the scalar-field condensation conjectured by Lee and Wick. We discuss the propagation of the shock front and subsequent decompression of the dense, hot matter.

On the dynamics of statistical fluctuations in heavy ion collisions

Abstract We show how statistical fluctuations can be treated within the collective approach to heavy ion reactions. In the classical limit, the equation of motion for the distribution d in the collective variables Q μ and their conjugate momenta P μ turns out to be a Fokker-Planck equation. We briefly describe the connection of this equation to one of the Smoluchowski type for a distribution in Q μ only, often used in heavy ion physics. For anharmonic motion our general Fokker-Planck equation is simplified to be linear in the deviations of the Q μ mand P μ from their mean values. The solution of this equation is discussed in terms of a simple Gaussian. The parameters of this Gaussian are determined completely by the first and second moments in Q μ mand P μ . The equations for the first moments are identical to the Newton equations including frictional forces. Those for the second moments are linear differential equations of first order and hence easily solvable. The whole derivation is completely analogous to that for the Newton equation reported recently. Here the starting point is the quantum mechanical von Neumann equation rather than the Heisenberg equations. As an intermediate result we obtain and discuss briefly a quantal equation for the reduced density operator d which includes frictional effects.

Neutron matter computations in Bruckner and variational theories

Abstract The binding energy of dense neutron gas is calculated in lowest-order Brueckner theory, and in Jastrow variational theory using the lowest-order cluster expansion of the energy, with a Reid soft-core potential. Subsidiary healing conditions are imposed on the Jastrow correlation function to simulate the Pauli exclusion effects. Due to the soft-core nature of the potential, the defect parameter k is small even at high densities and hence the lowest-order calculation could be a fair approximation. Up to ρ = 0.5 fm−3 the Brueckner and variational calculations give comparable results. Technical complications in applying the Brueckner theory for ρ>0.5 fm−3 are discussed and the results of only the variational calculation are presented for 0.5

Entropy of hot matter produced in heavy ion collisions

Abstract We show that the observed excess of entropy in fireballs from heavy ion collisions near 1 GeV/nucleon (lab) can be explained by a modified pionic spectrum. Measurements of the dependence of entropy on excitation energy could show a transition from nucleonic to quark matter at higher excitation energies.

Pion condensation and abnormal nuclear matter

Abstract We solve the sigma in neutron matter with nonrelativistic kinematics in mean-field approximation. The solution is characterized by a substantial reduction in the effective nucleon mass. In addition a pion condensate may or may not occur, depending on the value of the renormalized axial charge of the nucleon in the neutron matter.

On the damping of giant resonances and the independent propagation of particles and holes

Abstract In the literature, damping of nuclear collective motion has been attributed to the imaginary part of the self-energies of particles and holes, when assumed to move independently. We examine this picture within a schematic model adapted to the case of giant resonances. In this model we take degenerate 1p-1h states and dress them by a simple analytical form for the self-energies. We are able to calculate the intrinsic response function analytically and thus to study various approximations. We demonstrate that the on-shell approximation appreciably overestimates the widths of the collective vibrations.

Hot nuclear matter at low density

Abstract The equation of state of nuclear matter at high excitation is calculated in a virial expansion of the densities of the light nuclei ( M ⩽4). The virial coefficients are shown to depend only on properties of the S -matrix for light particle scattering. Relative concentrations of these species are estimated and compared to data from heavy-ion experiments to infer a breakup density and temperature. The breakup density is remarkably low, about 1/100th of normal nuclear density.

Damping of shape oscillations and relative motion in heavy ion reactions

The assumption that the damping of nuclear collective motion proceeds by the incoherent production of 1-particle 1-hole excitations implies a proportionality between the damping (friction) coefficients for damping of large- amplitude vibrations and damping of the relative motion in deep-inelastic heavy ion reactions. The coefficients of proportionality are found to be so small that the damping of the relative motion is negligible compared to the damping of the vibrations.

PARTICLE-WAVE AMBIGUITIES IN THE INTERPRETATION OF HEAVY-ION REACTIONS.

Abstract The relations between the partial wave scattering amplitudes in l -space and the reaction cross section angular distributions are derived in the limits of classical and diffractive scattering. It is shown that a measurement of the angular distribution of a “quasi-elastic” heavy ion reaction does not permit an unambiquous inference of the reactions partial-wave amplitudes, even for large l . The ambiguities are illustrated with DWBA calculations.

Color correlations in QCD plasma

Perturbative QCD and the random-phase approximation are used to study the current-current correlation function in quark-gluon plasma. The calculations show that there are damped collective oscillations in the system. An estimate of the Debye screening length gives a value of about 0.5 fm at a temperature of 250 MeV.