Directed and elliptic flow in 197Au+197Au at intermediate energies

Directed and elliptic flow for the ¹⁹⁷Au+¹⁹⁷Au system at incident energies between 40 and 150 MeV per nucleon has been measured using the INDRA 4π multi-detector. For semi-central collisions, the excitation function of elliptic flow shows a transition from in-plane to out-of-plane emission at around 100 MeV per nucleon. The directed flow changes sign at a bombarding energy between 50 and 60 MeV per nucleon and remains negative at lower energies. Molecular dynamics calculations (CHIMERA) indicate sensitivity of the global squeeze-out transition on the σ _NN and demonstrate the importance of angular momentum conservation in transport codes at low energies.     

Out-of-plane emission of nuclear matter in Au+Au collisions between 100 and 800 AMeV

We present new experimental results concerning the azimuthal distributions of proton-likes, light and intermediate mass fragments at midrapidity for Au(100–800 A MeV) +Au collisions measured with the FOPI phase-I detector at GSI in Darmstadt. The azimuthal distributions are investigated as a function of the collision centrality, the incident energy, the fragment charge and transverse momentum. The azimuthal anisotropy is maximum for impact parameters around 7 fm. Intermediate mass fragments present a stronger out-of-plane emission signal than light fragments and a saturation is reached for Z ⩾ 4. The azimuthal anisotropy increases with the fragment transverse momentum and decreases as the incident energy increases. The azimuthal anisotropy of Z = 2 particles investigated as a function of the scaled fragment transverse momentum follows an universal curve for bombarding energies between 250–800 A MeV. A signature for a transition from in-plane to out-of-plane emission is evidenced at the lowest beam energies.     

Heavy ion collisions in three dimensions by the relaxation-time method

A quantum transport equation with two-body collisions included via a relaxation-time method, earlier applied to two-dimensional (slab) collisions, is now extended to three-dimensional calculations A density matrix is constructed from self-consistent field wave functions and is time-evolved in cartesian coordinates. This dynamical model of the nucleus is applicable at all nonrelativistic energies. The semiclassical limit is discussed. Results are shown for ¹⁶O-¹⁶O collisions between 40 and 200 MeV/A lab energies. Hot spots and conditions for fragmentation are discussed. The threshold for breakup of the compound system formed in a head-on collision lies between 40 and 60 MeV/A lab energies. At these energies, the maximum density-averaged thermal excitation energy is 7 and 10 MeV/A (average temperatures 8 and 11 MeV), respectively, compared with a binding energy of 8 MeV/A. The system does not thermalize completely, and the distribution in momentum space is not quite isotropic when breaking up.     

Thermal source parameters in Au+Au central collisions at 35 A MeV

Central Au+Au collisions at 35 A MeV are analyzed to find the characteristics of a thermal source, in the framework of the statistical multifragmentation model SMM. A recently introduced backtracing protocol provides an effective comparison of theory and experiment. For the first time the distributions of the central source parameters (density, mass number, excitation energy) are found. The collective energy of primary fragments is also deduced. It is shown that the backtracing procedure allows an estimation of the pre-equilibrium emission.     

Excitation energy division in 51V + 197Au collisions at and near the barrier

Mass- and charge-yield distributions for 19 < Z < 84 were determined radiochemically for the binary collision products of ⁵¹V + ¹⁹⁷Au collisions at a bombarding energy corresponding exactly to the Bass-model barrier, E _cm = B, and at E _cm = B + 25 MeV. The average excitation energies as a function of Z are determined by comparing the centroids of the experimental, secondary mass distributions for given values of Z with the calculated primary centroids from minimization of the potential energy of the di-nuclear system, i.e. from the missing masses. At the barrier, in striking contrast to a thermal equilibrium, we find an extreme donor-acceptor asymmetry in the excitation-energy division reminiscent of the “sawtooth” phenomenon in low-energy nuclear fission. Here, the excitation energy sharing is apparently dominated by shape fluctuations at scission. At the slightly higher bombarding energy, E _cm = B + 25 MeV, we observe a rapid change toward equipartition of the excitation energy indicating that, here, the excitation energy division due to shape fluctuations is already covered up by the dissipative exchange of nucleons. Also, the balance of integral cross sections for fusion fission, deep-inelastic scattering, and quasi fission is investigated and is shown to contain important information about the dynamical evolution of the ⁵¹V + ¹⁹⁷Au system after having passed the entrance channel barrier.     

Investigation of the dynamics of dissipative U+Au collisions with δ-electron spectroscopy

δ-electron emission in elastic and dissipative collisions of U+Au at E/A = 8.65 MeV has been investigated. The velocity vectors of the reaction products were measured in coincidence with electrons of energies up to 3.2 MeV. The δ-electron yield measured for elastic collisions is in good agreement with coupled-channels calculations. The δ-electron spectra of dissipative reactions show a clear dependence on the violence of the collision, i.e. the total kinetic energy loss (TKEL). The shape of the spectra are analysed with an atomic model by a fitting procedure using phenomenological trajectories. The results indicate an increasing contact time of the united system with increasing total kinetic energy loss reaching 1.16(4) × 10^?21 s at < TKEL > = 375 MeV.     

Flow angle from intermediate mass fragment measurements

Directed sideward flow of light charged particles and intermediate mass fragments was measured in different symmetric reactions at bombarding energies from 90 to 800 A MeV. The flow parameter is found to increase with the charge of the detected fragment up to Z = 3–4 and then turns into saturation for heavier fragments. Guided by simple simulations of an anisotropic expanding thermal source, we show that the value at saturation can provide a good estimate of the flow angle, Θ_flow, in the participant region. It is found that Θ_flow depends strongly on the impact parameter. The excitation function of Θ_folw reveals striking deviations from the ideal hydrodynamical scaling. The data exhibit a steep rise of Θ_flow to a maximum at around 250 – 400 A MeV, followed by a moderate decrease as the bombarding energy increases further.     

Level densities in the Pairing plus Quadrupole model for Erbium isotopes

The level densities, up to about 100 MeV of excitation energy, for even Erbium isotopes are computed using the Pairing plus Quadrupole model, in the framework of the Static Path Approximation (SPA). The resulting level densities are in reasonable agreement with the empiricalA/8 law below 40 MeV of excitation energy. At higher excitation energies (U?60 MeV) the level densities agree with the Fermi gas formula witha?A/10. The inclusion of small amplitude collective motion (RPA-SPA) does not improve the results over the SPA at high excitation energy, and gives small corrections to the ground state energy.     

Breakup temperature of target spectators in 197Au + 197Au collisions at E/A = 1000 MeV

Breakup temperatures were deduced from double ratios of isotope yields for target spectators produced in the reaction ¹⁹⁷Au + ¹⁹⁷Au at 1000 MeV per nucleon. Pairs of ^3,4He and ^6,7Li isotopes and pairs of ^3,4He and H isotopes (p, d and d, t) yield consistent temperatures after feeding corrections, based on the quantum statistical model, are applied. The temperatures rise with decreasing impact parameter from 4 MeV for peripheral to about 10 MeV for the most central collisions. The good agreement with the breakup temperatures measured previously for projectile spectators at an incident energy of 600 MeV per nucleon confirms the universality established for the spectator decayat relativistic bombarding energies. The measured temperatures also agree with the breakup temperatures predicted by the statistical multifragmentation model. For these calculations a relation between the initial excitation energy and mass was derived which gives good simultaneous agreement for the fragment charge correlations. The energy spectra of light charged particles, measured at τ_lab = 150°, exhibit Maxwellian shapes with inverse slope parameters much higher than the breakup temperatures. The statistical multifragmentation model, because Coulomb repulsion and sequential decay processes are included, yields light-particle spectra with inverse slope parameters higher than the breakup temperatures but considerably below the measured values. The systematic behavior of the differences suggests that they are caused by light-charged-particle emission prior to the final breakup stage.     

Basic parameters of the gamma-decay process and properties of the <Superscript>174</Superscript>Yb nucleus that manifest themselves in radiative resonance-and thermal-neutron capture

An independent analysis of available data on the intensities of primary gamma rays from the capture of ≈2-keV neutrons by a ¹⁷³Yb nucleus is performed. The distribution of the scatter of these intensities around the average value is approximated in various intervals of energies of primary gamma transitions. An extrapolation of the distributions obtained in this way to zero detection threshold for the intensity of a primary gamma transition makes it possible to estimate, independently of other experimental procedures, the expected number of levels of both parities for spins in the range J = 1–4 and the total possible sum of partial widths with respect to electric and magnetic dipole gamma transitions to levels whose excitation energies extend up to about 4 MeV. The results obtained in this way for the level density and the sum of radiative strength functions confirm the characteristic features of analogous data extracted from the intensities of two-step gamma-ray cascades initiated by radiative thermal-neutron capture by 40 ≤ A ≤ 200 nuclei and also make it possible to assess the sign and magnitude of their systematic uncertainty associated with a very strong dependence of radiative strength functions for cascade gamma transitions on the structure of the excited level, at least for excitation energies below half the neutron binding energy. A comparison with model concepts of the level density reveals that the ¹⁷⁴Yb nucleus is in a superfluid states for the bulk of excited levels, at least below 3.5 to 4 MeV.     

Systematics of stopping and flow in Au+ Au collisions

Excitation functions of flow and stopping observables for the Au+ Au system at energies from 40 to 1500MeV per nucleon are presented. The systematics were obtained by merging the results of the INDRA and FOPI experiments, both performed at the GSI facility. The connection to the nuclear equation of state is discussed.     

Decay of the compound nucleus179Au formed in the cold fusion reaction90Zr+89Y

For the compound nucleus¹⁷⁹Au formed at an excitation energy of 26 MeV in the fusion reaction⁹⁰Zr+⁸⁹Y, the energy spectra of promptly emitted protons,α particles andγ rays were measured in concidence with the evaporation residues. On the basis of the measured total decay energy, the 1p and 1α decay channels were separated from all other evaporation-residue channels. The energy spectra and absolute cross sections, together with previously measured excitation functions for various decay channels, are successfully described by statisticalmodel calculations with the Monte Carlo code CODEX.     

On the origin of the radial flow in low energy heavy-ion reactions

The average transverse energy of nucleons and intermediate mass fragments observed in the heavy-ion reaction Xe(50A MeV) + Sn shows the same linear increase as a function of their mass as observed in heavy-ion collisions up to the highest energies available today and fits well into the systematics. At higher energies this observation has been interpreted as a sign of a strong radial flow in an otherwise thermalized system. Inverstigating the reaction with quantum molecular dynamics simulations we find in between 50A MeV and 200A MeV a change in the reaction mechanism. At 50A MeV the apparent radial flow is merely caused by in-plane flow and Coulomb repulsion. The average transverse fragment energy does not change in the course of the reaction and is equal to the initial fragment energy due to the Fermi motion. At 200A MeV, there are two kinds of fragments: those formed from spectator matter and those from the center of the reaction. There the transverse energy is caused by the pressure from the compressed nuclear matter. In both cases we observe a binary event structure, even in central collisions. This demonstrates as well the non-thermal character of the reaction. The actual process which leads to multifragmentation is rather complex and is discussed in detail.     

Studying the energy dependence of elliptic and directed flow within a relativistic transport approach

The energy excitation functions of directed flow (v₁) and elliptic flow (v₂) from E_beam=90 A MeV to E_cm=200 A GeV are explored within the UrQMD framework and discussed in the context of the available data. The radial and the elliptic flow of the particles produced in a relativistic heavy-ion collision are intimately connected to the pressure and its gradients in the early stage of the reaction. Therefore, these observables should also be sensitive to changes in the equation of state. To prove this connection, the temporal evolution of the pressure, pressure gradients and elliptic flow are shown. For the flow excitation functions it is found that, in the energy regime below E_beam≤10 A GeV, the inclusion of nuclear potentials is necessary to describe the data. Above 40 A GeV beam energy, the UrQMD model starts to underestimate the elliptic flow. Around the same energy the slope of the rapidity spectra of the proton directed flow develops negative values. This effect is known as the third flow component (“antiflow”) and cannot be reproduced by the transport model. The difference between the data and the UrQMD model can possibly be explained by assuming a phase transition from hadron gas to quark–gluon plasma around E_lab=40 A GeV. This would be consistent with the model calculations, indicating a transition from hadronic matter to “string matter” in this energy range. Thus, we speculate that the missing pressure might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au + Au (Pb + Pb) collisions already at lower SPS energies. PACS 25.75.-q; 25.75.Ld; 25.75.Dw; 25.75.Gz; 24.10.Lx     

Electromagnetic processes in silver isotopes

Peculiarities of electromagnetic interactions in silver isotopes are considered. Excited states of Ag isotopes are studied as a function of the mass number A = 95–117. Low-lying excited states reveal clear features that are specific for rotational spectra for the energies E < 4–5 MeV. In the energy domain above the nucleon separation threshold of 5–10 MeV, single-particle excited states overlap and produce a continuous spectrum. For energies E = 10–35 MeV, excitation of giant dipole resonance plays the most important role in Ag isotopes. Experimental data on the cross sections of photonuclear reactions in Ag isotopes are analyzed.     

Nuclear excitation by electron transition near the <Emphasis Type="Italic">K</Emphasis>-shell ionization threshold of an atom

A model of nuclear excitation by electron transition near the K-shell ionization threshold of an atom is proposed. The nuclear excitation cross sections have been calculated for ¹⁹⁷Au, ¹⁹³Ir, and ¹⁸⁹Os as functions of the energy of the photons ionizing the atomic shell. It is shown that excitation of ¹⁸⁹Os begins under the K-shell photoionization threshold of Os, while excitation of ¹⁹⁷Au and ¹⁹³Ir begins above the K-shell photoionization threshold of Au and Ir, respectively.     

Relative population of oblate and prolate structures in189Au

High spin states of¹⁸⁹Au were populated via the¹⁷⁴Yb (¹⁹F, 4n reaction at 86, 90, 95 and 100 MeV beam energies. The study of the relative population of oblate and prolate structures shows a striking disappearance of the prolate band relative to the oblate ones as the beam energy goes from 86 to 100 MeV.     

Temperature and excitation energy of hot nuclei in the reaction of 40Ar+197Au at 25 MeV/nucleon

The coincidence measurements between heavy fission fragments and light charged particles with Z ⩽ 2 were carried out for the ⁴⁰Ar+¹⁹⁷Au reaction at 25 MeV/nucleon, to study the properties of hot nuclei in heavy ion induced reactions. The linear momentum transfers (LMTs) were deduced from the folding angle and the time-of-flight difference between two fission fragments of heavy residues. The relationship of the nuclear temperature (slope parameter of the energy spectrum) and the excitation energy was determined independently from the measurement of the kinetic energy spectra in the frames of the emitting sources and from the LMT analysis. Both the temperature and the excitation energy increase with decreasing impact parameter, which suggests that a plateau temperature of 5.5 MeV is reached at an excitation energy of 3.1 MeV/nucleon. The result was also compared with various statistical models that explain the plateau by the multifragmentation process, where the excitation energy is assumed to be stored in compression and expansion effects.     

The nuclear structure of198Au from the reaction197Au(n, γ)198Au

Precise energies and intensities of about 450γ-rays of the¹⁹⁷Au(n, γ)¹⁹⁸Au reaction have been investigated in the energy range from 30 keV to 1 MeV with a bentcrystal spectrometer. Prompt and delayedγ-γ coincidences have been studied with Ge(Li) detectors. A half-life of 124±4 ns has been measured for the state at 312.036 keV, which is found to decay to the ground state through the cascade 97.195–214.841 keV. A new level scheme based on these results has been constructed which contains 160 transitions. Spin and parity assignments have been made for most of the levels.     

A study of the127I(n, γ)128I reaction

The reaction¹²⁷I(n, γ)¹²⁸I has been investigated at the tangential facility of the McMaster University Nuclear Reactor using a pair spectrometer. A total of 248 transitions were observed in the photon energy range 4.5–6.8 MeV. Below an excitation energy of 1 MeV more than 50 levels have been inferred. Through use of 28 levels with well established energies, a neutron separation energy of 6826.12±0.05 keV was determined. The level density up to an excitation of 2.5 MeV was examined on the basis of a statistical model and found to agree with current parameter values. TheE1 andM1 strength functions were determined and the influence of the giant dipole resonance on the former investigated.