Factorization in relativistic heavy-ion scattering

We have calculated the total cross sections for relativistic nucleus-nucleus scattering in the Glauber theory and conclude that there will be no factorization, due to the short-range nature of nucleon-nucleon interaction as compared to the sizes of the colliding nuclei.     

Quasielastic electron scattering in relativistic mean-field theory

The density-dependent relativistic hadron (DDRH) field theory proposed recently is extended to investigate the longitudinal response function and the Coulomb sum rule in quasielastic electron scattering in the relativistic random phase approximation (RPA). The results in the DDRH model are compared with those in other models systematically. It is found that meson effective masses induced by the nonlinear terms in the nonlinear Walecka model should be used to obtain the meson Greens functions when the longitudinal response function and the Coulomb sum rule are calculated. The effects of the and mesons are clearly shown in quasielastic electron scattering, and the isospin-dependent attractive potential between nucleons due to the exchange of the -meson cancels the isospin-dependent repulsive contribution of the -meson to a certain extent. The obtained results in the DDRH model are in good agreement with experimental data except for the Coulomb sum rule in ²⁰⁸Pb.     

Equilibration in intermediate-energy heavy-ion collisions within a relativistic mean-field two-fluid model

A two-fluid model with meanσ- andω-fields is formulated for the treatment of heavy-ion collisions at incident energies around 1 GeV/u. In this energy range Fermi and Bose statistics for baryons and pions, respectively, cannot be replaced by Boltzmann statistics. The collisional coupling between the two fluids is formulated in terms of the effective nucleon-nucleon cross-sections in nuclear medium taking Pauli blocking into account. For two counterstreaming nuclear fluids the comparison of results obtained from our relativistic mean-field two-fluid model (RMF-TFM) and the relativistic Landau-Vlasov equation shows good agreement in the gross properties of the equilibration process.     

Stationary Fokker-Planck equation applied to fission dynamics

By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus ¹⁶⁸Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus ²¹³At.     

Constrained relativistic mean-field approach with fixed configurations

A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean-field model. As an example, the potential energy surfaces of ²⁰⁸Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. It is shown that the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to follow the evolution of single-particle orbits till the very deformed region, and to obtain several well-defined deformed excited states which can hardly be expected from the adiabatic PESs.     

Dirac equation and quantum relativistic effects in a single trapped ion

We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.     

Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions

A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when the timescales are too short to achieve equal thermalization of transverse and longitudinal degrees of freedom. The approach is based on the energy–momentum and entropy conservation laws, and may be regarded as a minimal extension of the boost-invariant standard relativistic hydrodynamics of the perfect fluid. We show how the formalism may be used to describe the isotropization of the system (the transition from the initial state with no longitudinal pressure to the final state with equal longitudinal and transverse pressure).     

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences Zitterbewegung, represents a gauge non-invariant variable in our model. Hence our particle does not experience the undesirable Zitterbewegung. C) In the non-relativistic limit spin is described by three-vector, as it could be expected.     

An equation of state for nuclear and higher-density matter based on relativistic mean-field theory

A model stress tensor for high-density matter based on a linearized relativistic quantum field theory is examined. The two coupling constants are fit to nuclear matter. Other properties of nuclear and neutron matter and neutron stars are then implied.     

On semi-quantal approximations to heavy-ion scattering

The coupled-channel equations for heavy-ion scattering are approximately solved in a closed form, in the context of semi-quantal approach. Our solutions are shown to contain dynamic polarization potentials (arising from two and/or multi-step processes) in a natural way. A closed form treatment, of the effects of dynamic polarization by Coulomb excitation, on the elastic scattering of deformed heavy-ions is also presented. As an example, we compare our results for quadrupole Coulomb excitation of¹⁸⁴W ions by¹⁸O ions at 90 MeV, with those obtained from optical model treatments.     

Dirac equation with cylinder-symmetrical potential

For a potential V(?), $\text{?=(x}{}^2\text{+y}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, the Dirac equation is reduced to a pair of first-order differential equations in ?. The fine structure of relativistic “channeling” electrons bound to a crystal axis is calculated.     

The realistic QCD equation of state in relativistic heavy-ion collisions and the early Universe

The realistic equation of state of strongly interacting matter, that has been successfully applied in the recent hydrodynamic studies of hadron production in relativistic heavy-ion collisions at RHIC, is used in the Friedmann equation to determine the precise time evolution of thermodynamic parameters in the early Universe. A comparison with the results obtained with simple ideal-gas equations of state is made. The realistic equation of state describes a crossover rather than the first-order phase transition between the quark–gluon plasma and hadronic matter. Our numerical calculations show that small inhomogeneities of strongly interacting matter in the early Universe are moderately damped during such crossover.     

Transition to hot quark matter in relativistic heavy-ion collision

The nuclear matter-quark matter phase transition density is calculated as a function of temperature. The result suggests a transition to quark matter in heavy-ion collision at laboratory kinetic energies of a few GeV per nucleon. The transition may be inferred by observing a limiting temperature for the hadrons produced by the collision.     

The Hadron to quark-gluon transition in relativistic heavy-ion collisions

In this paper we construct a scenario for the QCD transition from the hadron phase to the quark/gluon phase using physical models for these phases. The hadron phase is modeled by a spectrum of hadrons with masses which drop (with a common scaling factor) towards zero at chiral symmetry restoration. The number of hadronic effective degrees of freedom is limited by the number of microscopic degrees of freedom in the quark/gluon phase. This limitation can be imposed either by fiat or through the introduction of a temperature-dependent excluded volume. Given that the number of degrees of freedom in hadrons and in quarks and gluons are roughly equal, the QCD phase transition is inhibited by the bag constant. The only phase transition seen in lattice-gauge calculations, once low-mass quarks are included, is the restoration of chiral symmetry which occurs at the relatively low temperature of ˜ 150 MeV. At present, lattice gauge calculations do not have the resolution to determine the properties of the higher hadronic states accurately. They do, however, demonstrate that chiral restoration takes place in the (ρ. a₁), ( +)), ( −)) and (π, σ) systems by yielding “screening masses” for chiral partners which are distinct for T < T _xSR and identical for T>T _xSR. Further, within numerical accuracy, these “screening masses” are consistent with pure thermal energies and show no evidence of remaining bare masses once chiral symmetry is restored. These, and other lattice-gauge results, will be discussed in the light of our scenario. We shall also consider the consequences of our picture for relativistic heavy-ion experiments.     

Probing the QCD critical point with relativistic heavy-ion collisions

We utilize an event-by-event relativistic hydrodynamic calculation performed at a number of different incident beam energies to investigate the creation of hot and dense QCD matter near the critical point. Using state-of-the-art analysis and visualization tools we demonstrate that each collision event probes QCD matter characterized by a wide range of temperatures and baryo-chemical potentials, making a dynamical response of the system to the vicinity of the critical point very difficult to isolate above the background.     

Time-dependent density-functional theory meets dynamical mean-field theory: real-time dynamics for the 3D Hubbard model

We introduce a new class of exchange-correlation potentials for a static and time-dependent density-functional theory of strongly correlated systems in 3D. The potentials are obtained via dynamical mean-field theory and, for strong enough interactions, exhibit a discontinuity at half-filling density, a signature of the Mott transition. For time-dependent perturbations, the dynamics is described in the adiabatic local density approximation. Results from the new scheme compare very favorably to exact ones in clusters. As an application, we study Bloch oscillations in the 3D Hubbard model.