Description Of Heavy Ion Reactions Research Articles

Cluster formation in precompound nuclei in the time-dependent framework

Background: Applications of nuclear time-dependent density functional theory (TDDFT) are often capable of providing quantitative description of heavy ion reactions. However, the structure of pre-compound states produced in heavy ion reactions are difficult to assess theoretically in TDDFT as the s.p. density alone is a weak indicator of shell structure and cluster states. Purpose: We employ the time-dependent nucleon localization function (NLF) to reveal structure of pre-compound states in nuclear reactions involving light and medium-mass ions. We primarily focus on spin saturated systems with N = Z. Furthermore, we study reactions with oxygen and carbon ions, for which experimental evidence for {\alpha} clustering in pre-compound states exists. Method: We utilize the symmetry-free TDDFT approach and compute the NLFs to describe $^{16}$O + $^{16}$O, $^{40}$Ca + $^{16}$O, $^{40}$Ca + $^{40}$Ca, and $^{16,18}$O + $^{12}$C collisions at energies above the Coulomb barrier. Results: We show that NLFs reveal a variety of time-dependent modes involving cluster structures. For instance, the $^{16}$O + $^{16}$O collision results in a vibrational mode of a quasi-molecular \alpha-$^{12}$C-$^{12}$C-\alpha{} state. For heavier ions, a variety of cluster configurations are predicted. For the collision of $^{16,18}$O + $^{12}$C, we showed that the pre-compound system has a tendency to form {\alpha} clusters. This result supports the experimental findings that the presence of cluster structures in the projectile and target nuclei gives rise to strong entrance channel effects and enhanced {\alpha} emission. Conclusion: The time-dependent NLF is a good indicator of clusters structures in complex pre-compound states formed in heavy-ion fusion reactions. The localization reveals the presence of collective vibrations involving cluster structures, which dominate the initial dynamics of the fusing system.

Different realizations of Cooper–Frye sampling with conservation laws

Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One crucial step in such hybrid approaches is the so-called particlization, which is the transition between the hydrodynamic description and the microscopic degrees of freedom. For this purpose, individual particles are sampled on the Cooper–Frye hypersurface. In this work, four different realizations of the sampling algorithms are compared, with three of them incorporating the global conservation laws of quantum numbers in each event. The algorithms are compared within two types of scenarios: a simple ‘box’ hypersurface consisting of only one static cell and a typical particlization hypersurface for Au+Au collisions at . For all algorithms the mean multiplicities (or particle spectra) remain unaffected by global conservation laws in the case of large volumes. In contrast, the fluctuations of the particle numbers are affected considerably. The fluctuations of the newly developed SPREW algorithm based on the exponential weight, and the recently suggested SER algorithm based on ensemble rejection, are smaller than those without conservation laws and agree with the expectation from the canonical ensemble. The previously applied mode sampling algorithm produces dramatically larger fluctuations than expected in the corresponding microcanonical ensemble, and therefore should be avoided in fluctuation studies. This study might be of interest for the investigation of particle fluctuations and correlations, e.g. the suggested signatures for a phase transition or a critical endpoint, in hybrid approaches that are affected by global conservation laws.

Forced canonical thermalization in a hadronic transport approach at high density

Hadronic transport approaches based on an effective solution of the relativistic Boltzmann equation are widely applied for the dynamical description of heavy ion reactions at low beam energies. At high densities, the assumption of binary interactions often used in hadronic transport approaches may not be applicable anymore. Therefore, we effectively simulate the high-density regime using the local forced canonical thermalization. This framework provides the opportunity to interpolate in a dynamical way between two different limits of kinetic theory: the dilute gas approximation and the ideal fluid case. This approach will be important for studies of the dynamical evolution of heavy ion collisions at low and intermediate energies as experimentally investigated at the beam energy scan program at RHIC, and in the future at FAIR and NICA. On the other hand, this new way of modeling hot and dense strongly interacting matter might be relevant for small systems at high energies (LHC and RHIC) as well.

Semi-classical, Microscopic Approach to the Liquid Drop Model --- A Possible Way of the Description of Heavy Ion Reactions

An isospin and spin dependent form of the equation of state for nuclear matter is presented. This form is used for the description of nucleon interaction in a new dynamic model. Preliminary calculations show that the new approach makes possible predicting the alpha structures appearing in the case of the ground state even-even nuclei.

Collective Flow in Ultra-relativistic Collisions

The Fluid Dynamical (FD) models are considered to be a good description of heavy ion reactions with higher collision energies. Recent results indicate that the collective flow develops in the Quark Gluon Plasma (QGP) phase, what results in the Constituent Quark Number (NCQ) scaling of the flow. At the same time, between the deconfined ideal QGP and the Hadronic Matter, a so-called “Quarkyonic Matter” is predicted, where the dominant degrees of freedom are quarks. In FD model we assume the formation of the quarkyonic matter in the final Freeze Out (FO) stage, which includes deconfinement and the simultaneous formation of constituent quarks. Then we reach the conclusion that collective flow must have frozen out early when the quarks were the dominant constituents of matter, and the final hadron masses are reached subsequently.

Jet Energy Loss in Hot and Dense Matter

We discuss the the GLV Reaction Operator formalism for computing the non-abelian energy loss of jets propagating through hot and dense matter. We incorporate our results on induced gluon bremsstrahlung together with the effects of nuclear shadowing and multiple scattering in a two component soft+hard description of heavy ion reactions at RHIC energies. We demonstrate that good agreement between data and theory can be achieved in the measured moderate p_T <= 5 GeV window at root(s)=130 AGeV and we extend our predictions for the high p_T part of the hadronic spectra. We focus on the perspectives of using jet tomographic methods for probing not only the density and geometry of the quark-gluon plasma but also its parton composition at various center of mass energies.

Pseudo-Particle Models for Nuclear Reactions with Heavy Ions

For ten years, the Boltzmann equation (with some modifications to take into account some quantum effects) has been the basis of models for the description of heavy ion reactions; these models have the common feature that they simulate the Boltzmann equation (under various names as: Landau-Vlasov, Boltzmann-Uehling-Uhlenbeck, Boltzmann-Nordheim...) rather than they solve it explicitly. This report presents the basic numerical principles of the Boltzmann models in Heavy Ion Physics and their links with other modelizations of the N -Body Problem used in other fields of Physics. It discusses their validity and some applications arbitrarily chosen among the most relevant ones.

Consequences of a covariant description of heavy-ion reactions at intermediate energies

Heavy ion collisions at intermediate energies are studied by using a new RQMD code, which is a covariant generalization of the QMD approach. We show that this new implementation is able to produce the same results in the nonrelativistic limit (i.e. 50MeV/nucl.) as the non-covariant QMD. Such a comparison is not available in the literature. At higher energies (i.e. 1.5 GeV/nucl. and 2 GeV/nucl.) RQMD and QMD give different results in respect to the time evolution of the phase space, for example for the directed transverse flow. These differences show that consequences of a covariant description of heavy ion reactions within the framework of RQMD are existing even at intermediate energies.

Description of heavy ion collisions with medium dependent forces

One of the proclaimed goals of heavy ion collisions with 100 MeV up to 2000 MeV per nucleon is the determination of the equation of state of nuclear matter, which one needs for example for neutron stars, supernova explosions and the early universe. But the situation in heavy ion collisions is quite different from thermal equilibrium with a spherical momentum distribution and a fixed temperature. The effective nucleon-nucleon interaction as determined for example by the solution of the Bethe-Goldstone equation depends through the Pauli operator and through the single particle energies on the surrounding nuclear matter. This dependence is especially pronounced since the nucleon-nucleon interacting is highly momentum dependent: It is attractive at small relative momenta and repulsive at higher values. Thus the effective nucleon-nucleon interaction in heavy ion collisions depends on the distribution of the surrounding nuclear matter in orbital and momentum space. Here results are presented using for the description of heavy ion reactions at intermediate energies Quantum Molecular Dynamics (QMD) in a non-relativistic and in a completely covariant (RQMD) form. We show that the production of gamma-rays, pions and the inclusive spectra of nucleons and light nuclei are not sensitive to the equation of states. An observable sensitive to the equation of state is the perpendicular momentum distribution in heavy ion collisions. Also sensitive is the production of heavier particles like K + and K − mesons and antiprotons below the NN threshold. These collisions can have enough energy to compress and heat up nuclear matter and since they are below the NN threshold several nucleons must cooperate.

Description of heavy ion reactions with medium dependent forces

The collision between two nuclei is calculated in the Quantum Molecular Dynamics (QMD) approach for C-C and Nb-Nb reactions using a collision term for the nucleon-nucleon cross section which is determined in the nuclear medium using the Brueckner G-matrix with the appropriate Pauli operator and the self consistent single particle energies for the densities of the projectile and the target at the collision point of the two nucleons. The QMD approach is very similar to the Vlasov-Uehling-Uhlenbeck or Boltzmann-Uehling-Uhlenbeck approach, but taking into account the finite extension of the wave packet representing a nucleon in position and momentum space. Usually one uses in the collision term a constant (40 mb) or the free nucleon-nucleon cross section. Using a local density approximation the Bethe-Goldstone equation is solved for two colliding nuclear matters of which the densities are determined by the local densities obtained in the QMD approach at the collision point of the two nucleons inside the nuclear medium. Comparing the momentum transfer in transverse and longitudinal direction and the number of emitted particles calculated with the G-matrix cross section and the isotropic constant cross section (40 mb) we find for this inclusive data only minor differences between the results in the C-C collision, but larger ones for the Nb-Nb case. The double differencial cross section for charge particle emission in the C-C reaction at E lab = 84 MeV/n is described in good agreement with the data.

Scaling properties in the hydrodynamical description of heavy-ion reactions

Abstract We discuss scaling properties of heavy-ion reactions which are consequences of a simple hydrodynamical model. In certain kinematic regions the experimentally observed inclusive cross sections satisfy this scaling and so do the cross sections numerically calculated using hydrodynamics. The simple thermal model obeys the same scaling laws, but leads to a differential cross section with a characteristically different shape at very high and very low energies of the outgoing nucleons. The specific experimental data analyzed do not show evidence for a hydrodynamical flow.

Investigating the pairing phase transition in rapidly rotating deformed nuclei with heavy ion two-nucleon transfer reactions

A classical description of heavy ion reactions involving deformed nuclei is used to investigate two-nucleon transfer reactions which populate states of high angular momentum. The sensitivity of the calculated cross sections to variations of the monopole pairing gap with increasing angular momentum is studied. In order to observe the effect of a total collapse in pairing, the bombarding conditions must be such that the transferred angular momentum through Coulomb excitation is two to three times the critical spin value. However, a partial decrease in the pairing gap could be observed by comparing the relative transfer cross sections for populating low and high spin states.

Exploring the surface of deformed nuclei with heavy ion reactions: Classical treatment

A description of heavy ion reactions involving deformed nuclei in terms of classical trajectories is presented. The scheme takes into account the three-dimensional aspects of the relative motion and the nuclear rotation and provides predictions of cross sections for inelastic excitation and transfer. Contours of the transfer double differential cross section as a function of the rotational angular momentum and the scattering angle display characteristic patterns depending on the localization of the transfer form factors. The results can be used to explore the amplitude of nucleon wave functions along the surface of the deformed nucleus.

On the single-particle Schrodinger fluid

The coherent state basis is employed to obtain, in the semiclassical limit, the Euler equation of hydrodynamics corresponding to the single-particle Schrodinger equation. This may also correspond to a collective vibrational mode of the system. By introducing unobserved modes, the concept of viscosity (and the Navier-Stokes equation) is extracted. The motivation for the study stems from the physics that underlies the increasing use of macro-concepts and of hydrodynamical ideas in nuclear physics, particularly in the description of heavy-ion reactions and of fission and fusion processes.

The role of the giant resonances in deep inelastic collisions between heavy ions

A unified description of heavy ion reactions which includes all the most important nuclear degrees of freedom in an average way is attempted, in terms of the semiclassical coupled equations.

Heavy-ion scattering at intermediate and high energies

We investigate the elastic scattering of two heavy ions. Elastic scattering gives us information on the heavy-ion optical potential and forms a basis for a further description of heavy-ion reactions using either the DWBA or the semi-classical approach to these processes. To extract the nuclear parameters from elastic scattering, one can use an exact phase-shift analysis, which at high energies is tedious and difficult (the Coulomb barrier sets the energy scale), or one can use various approximation schemes to compute the phase shifts. Here we investigate the validity of the WKB approximation and its high-energy eikonal limit (the “Glauber approximation”). The high-energy limit has the advantage that it is very simple and gives a useful picture of the scattering process in terms of straight-line eikonal trajectories. We also look at the systematic V / E corrections to the high-energy phase shift. The exact scattering amplitude is compared with the various approximations to it for an optical potential which fits 60 Ni( 16 O, 16 O) 60 Ni at low energies. The simple high-energy approximation is shown to provide an accurate description of the scattering process at energies and scattering angles of practical interest. We give some analytical expressions for the heavy-ion scattering amplitude in the high-energy approximation and also look at the model problem of heavy-ion scattering by a totally absorbing black sphere.