Lead beam experiments at the CERN SPS

The acceleration in 1986 of¹⁶O beams to 200 GeV/nucleon at the CERN SPS created a new frontier of particle and nuclear physics, namely the study of high energy density systems with hundreds of quarks and gluons created in the central collisions of nuclei with heavy targets. In order to produce the largest piece of “quark matter”, beams as heavy as²⁰⁸Pb are needed. The Lead-Injector Project that would provide them is presented. Possible experimental approaches to extract the physics from collisions with thousands of produced particles are discussed.     

Baryon deceleration and partonic plasma creation by strong chromofields in ultrarelativistic heavy-ion collisions

Strong chromofields generated at early stages of ultrarelativistic nuclear collisions may explain not only creation of the quark-gluon plasma but also collective deceleration of net baryons. This is demonstrated by solving classical equations of motion for baryonic slabs under the action of a time-dependent chromofield. We have studied sensitivity of the slab trajectories and their final rapidities to the initial strength and decay time of the chromofield, as well as to the back reaction of the produced plasma. By proper choice of the initial chromofield energy density we can reproduce significant baryon stopping, an average rapidity loss of about two units, observed for Au + Au collisions at RHIC. Using a Bjorken-like hydrodynamical model with the particle production source, we also study the evolution of partonic plasma produced as the result of the chromofield decay. Due to the delayed formation and expansion of plasma its maximum energy density is significantly lower than the initial energy density of the chromofield. It is shown that the fluctuations of the chromofield due to the stochastic distribution of color charges help to populate the midrapidity region in the net-baryon distribution. To fit the midrapidity data we need the chromofields with initial energy densities in the range of 30 to 60 GeV/fm³. Predictions of baryon stopping for Pb + Pb collisions at LHC energies are made.     

Isospin effect in peripheral heavy-ion collisions at Fermi energies

The isospin effect in peripheral heavy-ion collisions was thoroughly investigated within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model. A coalescence approach was used to recognize the primary fragments formed in nucleus-nucleus collisions. The secondary decay process of these fragments was described using the statistical code GEMINI. The production mechanism and isospin effect of the projectile-like and target-like fragments were analyzed using the combined approach. It was found that the isospin migration from the high-isospin density to the low-density matter occurred in the neutron-rich nuclear reactions, i.e., ⁴⁸Ca+²⁰⁸Pb, ⁸⁶Kr+⁴⁸Ca/²⁰⁸Pb/¹²⁴Sn, ¹³⁶Xe+²⁰⁸Pb, ¹²⁴Sn+¹²⁴Sn, and ¹³⁶Xe+¹³⁶Xe. A hard symmetry energy was available for creating the neutron-rich fragments, particularly in the medium-mass region. The isospin effect of the neutron-to-proton (n/p) ratio of the complex fragments was reduced when the secondary decay process was included. However, a soft symmetry energy enhanced the n/p ratio of the light particles, particularly at kinetic energies greater than 15 MeV/nucleon.     

Sub-Coulomb transfer reactions on 208Pb with carbon and oxygen projectiles

Single-neutron transfers induced by ^{12, 13}C and ^{16, 17, 18}O projectiles on ²⁰⁸Pb and the ¹²C(¹⁷O, ¹⁶O)¹³C reaction have been studied at energies close to the Coulomb barrier. These processes are well described by the distorted-wave Born approximation. Coupled-channels effects are found to be small. Normalization factors have been determined for all projectile and target transitions, and also for the triton-deuteron overlap by comparison with previous measurements of the ²⁰⁸Pb(d, t)²⁰⁷Pb reaction. The root-mean-square (rms) radii of single-particle neutron wave functions in ²⁰⁸Pb and ²⁰⁹Pb were calculated using known spectroscopic factors. The distribution of the point neutron excess density in the surface region of ²⁰⁸Pb has been derived and its rms radius determined to be 5.93 ± 0.13 fm with a local potential model. This is in good agreement with theoretical predictions, but is considerably larger than estimates based on Coulomb energy differences. The phenomena of core polarisation by the odd particle or hole outside ²⁰⁸Pb is discussed using the single-particle orbitals determined in this work.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Molecular-orbital X-rays from 1 GeV 208Pb + 208Pb and 209Bi + 209Bi collisions

We have measured the spectra of continuum X-rays above the characteristic K lines for 4.5 to 4.8 MeV/N ²⁰⁸₈₂Pb → ²⁰⁸₈₂Pb, Pb → Bi, Bi → Pb and Bi → Bi collisions. Above ≈400 keV X-ray energy the spectral shape and intensity agree roughly with calculations of Kirsch et al. for the 1sσ molecular-orbital (MO) X-ray spectrum from Pb-Pb. Deviations from the theory below ≈400 keV suggest transitions to other MO's.     

Coulomb reorientation in near-barrier fusion of deformed+spherical systems in classical dynamical approach

A classical rigid-body dynamics model which takes into account all the translational and the rotational degrees of freedom is developed to study Coulomb reorientation of deformed nuclei in heavy-ion collisions. Various aspects of the collision dynamics in the case of near-barrier fusion of ²⁴Mg + ²⁰⁸Pb system due to the Coulomb reorientation are studied; the dependence of the extent of reorientation of the symmetry axis of the deformed nucleus, isotropy of the initial orientations, barrier parameters, and rotational excitation energy are discussed in detail. It is found that the barrier parameters not only depend on the initial orientations of the deformed nucleus but also on the collision energy; with maximum reorientation effect at near- and below-barrier energies. Even small amount of the rotational excitation energy gained by the deformed nucleus at large separation distances is crucial in determining the conditions at the barrier. Study of ¹⁵⁴Sm + ¹⁶O and ²³⁸U + ¹⁶O systems involving heavier deformed nuclei shows that the extent of reorientation also depends on the moment of inertia of the deformed nucleus.     

Systematic analysis of 17,19F and 16,17O elastic scattering on 208Pb just below the coulomb barrier

The ¹⁷F, ¹⁷O + ²⁰⁸Pb elastic scattering at 90.4 and 78 MeV (just below coulomb barrier), respectively, are analyzed within the framework of the double folding approach. The folded potentials are constructed by folding the density independent M3Y effective nucleon-nucleon interaction over the nucleon density distribution of ¹⁷F and its mirror ¹⁷O nuclei. Gaussian oscillator (GO) density distribution is considered to represent the (core¹⁶O+nucleon) structure for ¹⁷F and ¹⁷O. The knock-on exchange potentials are introduced to construct the real semi-microscopic potentials. The imaginary potentials are supplemented to derive potentials in two forms: either phenomenological Woods-Saxon (WS) or the same form as real folded potentials and different strengths. Moreover, the analysis of ¹⁹F, ¹⁶O + ²⁰⁸Pb elastic scattering at 91, 78 MeV energies, in that order, is applied in comparison to the ¹⁷F, ¹⁷O + ²⁰⁸Pb systems in an endeavor to investigate the behavior and properties of ¹⁷F and ¹⁷O projectiles.     

Axially symmetric time-dependent Hartree-Fock study of the 208Pb + 208Pb reaction

A time-dependent Hartree-Fock calculation assuming axial and reflection symmetry constraints is performed for the head-on collision of ²⁰⁸Pb + ²⁰⁸Pb systems at E_lab≈1600 MeV. The calculation suggests the excitation of surface modes in the reaction and the energy loss characteristic of a deep inelastic process. An estimate of neck-radius and neck-formation time is given.     

Dynamical approach to calculating angular distributions of fission fragments

A dynamical approach is proposed for calculating the angular distributions of fission fragments. The relaxation time for the degree of freedom associated with the projection of the total angular momentum of the nuclear system onto the symmetry axis and the coefficient of damping of the fission mode are the basic parameters of this approach. Experimental data on the anisotropy of the angular distributions of fission fragments and on the multiplicities of prescission neutrons are analyzed within the proposed model for ¹⁶O+²⁰⁸Pb (E _lab=110–148 MeV), ¹⁶O+²³²Th (120–160 MeV), ¹⁶O+²⁴⁸Cm (110–148 MeV), and ¹⁶O+²³⁸U (96–148 MeV). The relaxation time and the damping coefficient are estimated at τ_K=(5–6)×10^?21 s and β=4×10²¹ s^?1, respectively.     

Calculation of the energy dependence of the fusion cross section and total cross sections for peripheral reactions on the basis of an analysis of data on elastic heavy-ion scattering: Strongly bound ions

A method is proposed for calculating the energy dependence of the fusion cross section (in general, the sum of the cross sections for complete and incomplete fusion, quasifission, and reactions of deep-inelastic scattering) σ _F (E) and the total cross section for peripheral (or quasielastic) reactions, σ _D (E). The method is based on an analysis of a limited set of angular distributions for the elastic scattering in a given pair of nuclei. The predictive power of the method is illustrated by considering the ¹⁶O + ²⁰⁸Pb, ¹⁶O + ⁴⁰Ca, and ¹⁶O + ²⁸Si systems. For each of these systems, the calculations were performed at energies in the range extending from subbarrier values to those exceeding the barrier height substantially. The results of the calculations are found to be in good agreement with relevant experimental data, whereby the reliability of the method is confirmed. By virtue of this, it is proposed to employ the method to study the energy dependences σ _F (E) and σ _D (E) in collisions involving unstable nuclei, for which it is difficult to determine experimentally the above dependences because of a low intensity of secondary beams.     

Influence of pre-fission neutron emission on fission fragment angular distribution for the system209Bi +16O

The data of fission fragment anisotropies measured for the system¹⁶O +²⁰⁹Bi in the centre of mass energy region of 73 to 95 MeV have been compared with the saddle point statistical model calculations. The corrections to the nuclear temperature and the spin distribution arising due to pre-fission neutron emission have been made. While the resultant calculations reproduce very well the data in the near- and sub-barrier energy regions, they deviate from the data at higher energies. This observation is similar to what was already reported for¹⁶O +²⁰⁸Pb system.     

The transverse-energy distributions of 32S-nucleus collisions at 200 GeV per nucleon

Transverse-energy distributions have been measured for the collisions of the ³²S nucleus with Al, Ag, W, Pt, Pb, and U target nuclei, at an incident energy of 200 GeV per nucleon. The shapes of these distribution reflect the geometry of the collisions, including the deformation effects. For central collisions, the transverse-energy production in the region −0.1<η_lab<2.9 increases approximately as A^0.5, where A is the atomic mass number of the target. This increase is accompanied by a relative depletion in the forward region η_lab > 2.9. These results are compared with those obtained under similar conditions with incident ¹⁶O nuclei. A comparison is also made with the predictions of a Monte Carlo generator based on the dual parton model. Finally, we give estimates of the energy density reached and its dependence on the atomic mass number of the projectile.     

Simple models of the contribution of intermediate stage gluons to J/ψ suppression at the CERN SPS

We construct three simple scenarios of the time dependence of density of intermediate stage gluons in nuclear collisions in the CERN SPS energy range. Gluons with energy of about 0.6–1.0 GeV are assumed to be produced in nucleon-nucleon collisions in a Glauber type model. The rate of gluon production is given by the parameter n _g/nn equal to the average number of gluons produced per nucleon-nucleon collision. The value of this parameter determines the behaviour of the gas of gluons. The number of gluons increases due to gluon branching and processes like g+g → g+g+g and decreases due to the hadronization. Gluons are assumed to be able to dissociate J/ψ in g+J/ψ collisions, the dissociation cross-section σ _gγ is taken as a free parameter. In the first scenario, the energy density of the gas of gluons never reaches the critical energy density ε _c ≈ 0.7 GeV/fm³ and gluons rapidly hadronize. In the second scenario, the critical energy density is reached but the system of gluons is unable to reach thermalization. In the third scenario gluons reach thermalization and the thermalized system suppresses J/ψ by the Matsui-Satz mechanism. The third scenario under the assumption of a small value of σ _gψ is able to describe qualitatively the data on J/ψ suppression in Pb?Pb interactions obtained by the NA50 Collaboration. Other scenarios have problems with getting the rather abrupt onset of J/ψ suppression.     

Density-constrained time-dependent Hartree-Fock calculation of <Superscript>16</Superscript>O + <Superscript>208</Superscript>Pb fusion cross-sections

We present a fully microscopic study of the ¹⁶O + ²⁰⁸Pb fusion using the density-constrained time-dependent Hartree-Fock theory. The calculated fusion cross-sections are in good agreement with the experimental data for the entire energy range indicating that the incorporation of dynamical effects is crucial in describing heavy-ion fusion.     

On the information value of angular distributions in elastic scattering of heavy ions

A method is developed for computing the total cross section σ_F of complete and incomplete fusion, quasifission, and deep-inelastic collisions, as well as the total cross section σ_D of peripheral reactions, on the basis of analysis of angular distributions for elastic scattering of heavy ions. The method makes it possible, on a unified basis, to explain the mechanism of formation of σ_F and σ_D both for strongly and for weakly bound ions. The method permits the calculation of quantitative characteristics of fusion enhancement (and, accordingly, suppression of peripheral reactions) for strongly bound ions and, conversely, the suppression of fusion (and, accordingly, enhancement of peripheral reactions) for weakly bound ions. The potential of the method is demonstrated for two systems, ¹⁶O+²⁰⁸Pb and ⁹Be+²⁸Si, the projectile ion being strongly bound in the former system and weakly bound in the latter one.     

Angular anisotropy of the fusion-fission and quasifission fragments

The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the ¹⁶O + ²³⁸U , ¹⁹F + ²⁰⁸Pb and ³²S + ²⁰⁸Pb reactions is studied by analyzing the angular-momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of the axial symmetry axes of the colliding nuclei relative to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that there is a large contribution of the quasifission fragments in the ³²S + ²⁰⁸Pb reaction to the deviation of the experimental angular anisotropy from the statistical model results. Enhancement of anisotropy at low energies in the ¹⁶O + ²³⁸U reaction is connected with the quasifission of the dinuclear system having low temperature and relatively small effective moment of inertia.     

High energy structures in heavy ion collisions: A multi-phonon description

Energy spectra of fragments from the³⁶Ar+²⁰⁸Pb reaction at 11 MeV/n exhibit structures at high excitation energies. These structures are interpreted in terms of target multi-phonon excitations built from giant resonances. The importance of such processes for the kinetic energy dissipation in heavy ion collisions is emphasized.     

On the energy dependence of the real central optical potential for proton-nucleus scattering

The energy dependence of the real central optical potential in the energy range 25–1000 MeV has been determined from optical model analyses of p+¹²C, p+¹⁶O, p+²⁷Al, p+⁴⁰Ca and p+²⁰⁸Pb elastic scattering data. The volume integral and the strength can be represented by a relation linear in the incident energy only if a limited energy range is chosen. When the energy range 25–1000 MeV is considered a logarithmic energy dependence gives a better representation of the phenomenological results, especially for the light nuclei.