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.     

Time-dependent Hartree-Fock study of 136Xe + 209Bi collisions

We have performed axially symmetric Skyrme force time-dependent Hartree-Fock calculations for the ¹³⁶Xe + ²⁰⁹Bi system at E(lab) = 940 MeV and 1130 MeV. The evolution of the nuclear geometry is studied in detail. The calculated final fragment kinetic energies, scattering angles, and charges are in good agreement with experiment, but the fragment charge dispersion is greatly underestimated. Studies of head-on collisions for 900 MeV ? E(lab) ? 2000 MeV show no evidence for fusion and indicate a dramatic transparency for E(lab) ? 1500 MeV.     

Elastic and inelastic scattering of 12C ions at intermediate energies

Elastic and inelastic scattering of ¹²C ions on ¹²C and ²⁰⁸Pb targets have been measured at the incident energies per nucleon E / A = 120 MeV/u and E / A = 200 MeV/u. Optical-model analysis is reported and nuclear surface transparency effects are discussed, together with the nuclear potential-energy dependence. The transparency region extends down to a radial internuclear distance of about 3 fm for the ¹²C-¹²C system and 8 fm for the ¹²C-²⁰⁸Pb system. A decrease of the imaginary potential with increasing incident energy is deduced for the two systems. Anomalous collapse of the real potential in the surface region is observed for ¹²C-²⁰⁸Pb system at 200 MeV/u. DWBA analysis of data on the 2⁺, 4.4 MeV state of ¹²C is reported and trends for the energy dependance of mean-field excitations are deduced.     

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.     

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.     

Analysis of deep inelastic collisions between16O and27Al

Deep inelastic collisions in light systems formed with¹²C,¹⁴N and¹⁶O projectiles and different target nuclei have been studied at incident energies between 5 and 7 MeV/u. A detailed analysis is presented for the results of the¹⁶O+²⁷Al reaction at 80.6 MeV incident energy which is based on trajectory calculations and the transport theory. The questions of angular distributions and the interaction time, the energy dissipation and the fragment deformation as well as the element-distribution and the effect of the nuclear structure are discussed.     

Onset of nuclear matter expansion in Au+Au collisions

Using the FOPI detector at GSI Darmstadt, excitation functions of collective flow components were measured for the Au+Au system, in the reaction plane and out of this plane, at seven incident energies ranging from 100A MeV to 800A MeV. The threshold energies, corresponding to the onset of sideward-flow (balance energy) and squeeze-out effect (transition energy), are extracted from extrapolations of these excitation functions toward lower beam energies for charged products with Z ⩾ 2. The transition energy is found to be larger than the balance energy. The impact parameter dependence of both balance and transition energies, when extrapolated to central collisions, suggests comparable although slightly higher values than the threshold energy for the radial flow. The relevant parameter seems to be the energy deposited into the system in order to overcome the attractive nuclear forces.     

Relativistic effects in heavy-ion collisions at SIS energies

The covariant and non-covariant Quantum Molecular Dynamics models are applied to investigate possible relativistic effects in heavy ion collisions at SIS energies. These relativistic effects which arise due to the full covariant treatment of the dynamics are studied at bombarding energiesE _lab=50, 250, 500, 750, 1000, 1250, 1500, 1750 and 2000 MeV/nucl. A wide range of the impact parameter fromb=0 fm tob=10 fm is also considsered. In the present study, five systems¹²C-¹²C,¹⁶O-¹⁶O,²⁰Ne-²⁰Ne,²⁸Si-²⁸Si and⁴⁰Ca-⁴⁰Ca are investigated. The full covariant treatment at low energies shows quite good agreement with the corresponding non-covariant whereas at higher energies it shows less stopping and hence less thermal equilibrium as compared to the non-covariant approach. The collisions dynamics is less affected. The density using RQMD rises and drops faster than with QMD. The relativistic effects show some influence on the resonance matter production. Overall, the relativistic effects at SIS energies (≦2000 MeV/nucl.) are less significant.     

Fine structure in theα decay of192Po

The production of energetic π^? at 0° has been measured in Ne+NaF and Ni+Ni collisions with incident energies between 1.3 and 2AGeV. In Ne+NaF collisions the investigation was extended to extreme subthreshold processes with lab momenta up to 4.5 GeV/c. In both systems at all incident energies the π^? production cross sections deviate in a systematic way from thermal distributions.     

A nuclear matter approach to the mean free path of a nucleon in a system of colliding ions

We calculate the mean free path of the projectile nucleons in an ion-ion system. The lab. bombarding energies correspond to 70 MeV/A to 220 MeV/A above the Coulomb barrier. The effect due to the Pauli blocking is studied.     

Target fragmentation in proton-nucleus and16O-nucleus reactions at 60 and 200 GeV/nucleon

Target remnants withZ<3 from proton-nucleus and¹⁶O-nucleus reactions at 60 and 200 GeV/nucleon were measured in the angular range from 30° to 160° (?1.7<η<1.3) employing the Plastic Ball detector. The excitation energy of the target spectator matter in central oxygen-induced collisions is found to be high enough to allow for complete disintegration of the target nucleus into fragments withZ<3. The average longitudinal momentum transfer per proton to the target in central collisions is considerably higher in the case of¹⁶O-induced reactions (≈300 MeV/c) than in proton-induced reactions (≈130 MeV/c). The baryon rapidity distributions are roughly in agreement with one-fluid hydrodynamical calculations at 60 GeV/nucleon¹⁶O+Au but are in disagreement at 200 GeV/nucleon, indicating the higher degree of transparency at the higher bombarding energy. Both, the transverse momenta of target spectators and the entropy produced in the target fragmentation region are compared to those attained in head-on collisions of two heavy nuclei at Bevalac energies. They are found to be comparable or do even exceed the values for the participant matter at beam energies of about 1–2 GeV/nucleon.     

Alpha-induced fragmentation of 28Si in a statistical model

Within the context of a statistical model, that incorporates final-state interaction between a pair of fragments, we have calculated the energy spectra associated with the production of different isobaric pairs as a function of their lab kinetic energy and isobaric and elemental distributions of nuclei produced in the ⁴He$ + $²⁸Si reaction at cm incident energies of 102.7, 173.7, 300, 500, and 1000MeV. Double differential cross-section of isobars 16, 20, and 24 as a function of their lab kinetic energies at 30^° and the same for isobar 24 at 10^°, 30^°, 60^°, and 90^° have been calculated at cm incident energies of 102.7 and 173.7MeV and compared with the data of Woo et al. Calculated yields follow the trend of the data at each angle, and calculated angular distributions also reproduce the general trend of the observed ones. A key feature of the model is that it allows for fragments to be emitted in ground states as well as in excited states that are allowed by the conservation of energy. The analysis establishes that the fragments are emitted in excited state. The excitation energies for A = 24 and 16 are deduced from the data. The observed angular distributions for A = 7, 12, 16, 20, 24, and 28 are well accounted for assuming them to be emitted in excited states. The relative production probabilities for different elements and isobars are energy dependent. The yields for unstable elements, ⁵Li, ⁸Be, and ²⁶Al, are found to be significant. The relative fragmentation probabilities of all allowed isotopic pairs have been presented.     

30MeV/u40Ar+159Tb反应中中等质量碎片的发射时标与发射机制

报道30MeV/u⁴⁰Ar+¹⁵⁹Tb反应中碎片-碎片关联函数的实验结果．利用三体弹道模型从关联函数提取了中等质量碎片发射时间．中等质量碎片的平均发射时间随碎片能量而变化，从低能时的约500fm/c下降至高能时的约100fm/c．中等质量碎片发射时间随束流能量的升高而下降，表明随着束流能量的升高中等质量碎片发射机制逐渐从相继两体衰变向多重碎裂发射过渡．对于⁴⁰Ar+¹⁵⁹Tb反应，此过渡能区在35—45MeV/u之间 关键词：     

The disassembly of nuclear matter

A statistical model is applied for multi-fragment final states in nuclear collisions with bombarding energies E/A ≈ 100 MeV. A portion of the intermediate system formed is assumed to decay according to the available classical non-relativistic phase space, calculated in a grand canonical ensemble. The model correlates and predicts many experimental observables in terms of three parameters: the available energy per nucleon, the isospin asymmetry, and the effective interaction volume.     

Classical many-body model for heavy-ion collisions (II)

A four-parameter classical many-body model, specifically designed for heavy-ion collisions, is presented. Binding energies and densities of infinite and finite nuclei (N = Z) are satisfactorily reproduced. So also is the viscosity moment of the two-body scattering cross section at lab energies between 100 and 300 MeV.     

Hard photons and neutral pions as probes of hot and dense nuclear matter

The dynamics of heavy-ion collisions is studied in an energy domain in the vicinity of the Fermi energy. The early history of the collision is analyzed from the theoretical and experimental point of view in which the message conveyed by bremsstrahlung photons and neutral pions is exploited. The Boltzmann-Uehling-Uhlenbeck model and the Dubna Cascade Model, both based on similar principles but each adopting different computation technics, are briefly described and their respective predictions are discussed. In particular the emission pattern of bremsstrahlung photons is discussed. The photon production has been measured in the systems ⁸⁶Kr+⁵⁸Ni at 60A MeV, ¹⁸¹Ta+¹⁹⁷Au at 40A MeV and ²⁰⁸Pb+¹⁹⁷Au at 30A MeV and energy spectra, angular distributions and two-photon correlations have been analyzed. We find that bremsstrahlung photons are emitted from two distinct sources that can be correlated with nuclear-matter density oscillations. The properties of photon emission are discussed in terms of collective properties of nuclear matter. The high energy tail of the photon spectrum is interpreted by π⁰ and Δ decay but predominantly by radiative capture of pions. The π⁰ absorption in the nuclear medium is further analyzed by examining their emission pattern.     

The breakup of 16O into He: An event-by-event study of nucleus-nucleus collisions at 75, 175 and 2000 MeV/A

We present an event-by-event study of the breakup of the ¹⁶O in ¹⁶O + emulsion nucleus interactions at 75, 175 and 2000 MeV/A. The events are categorized according to their multiplicity of projectile He nuclei. The multiplicity depends on the degree of target destruction. Although the fragmentation model describes the gross features of inclusive He spectra, an event-by-event study reveals deviations from the model. The momenta of the He nuclei, emitted from the projectile, depend on helium multiplicity and the breakup properties of the target nucleus. The probability that the ¹⁶O projectile breaks up into multiple He fragments is larger at 75 MeV/A than at 2000 MeV/A. At 75 MeV/A the mean velocity of projectile He is on the average 0.06c below the projectile velocity. This recoil velocity depends on the target nucleus destruction also for the most peripheral collisions.     

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.     

12C(12C, 8Be)16O angular distributions and excitation functions between 35 and 69 MeV bombarding energy

An array of eight detectors has been developed for identifying the particle unstable ⁸Be nucleus from nuclear reactions with high detection efficiency. Absolute cross sections have been measured for the reaction ¹²C(¹²C, ⁸Be_g.s.)¹⁶O to the ground state and to several excited states in ¹⁶O. Excitation functions at seven angles from 15° to 45° (lab) in 5° steps have been measured for bombarding energies between E¹²_C(lab) = 35 and 69 MeV. Excitation functions were obtained for the following states in the residual nucleus ¹⁶O which were found to be strongly populated: g.s.(0⁺); 6.1 MeV (0⁺, 3^?); 6.9 MeV (2⁺); 10.4 MeV (4⁺); 11.1 MeV (4⁺); 14.7 MeV (6⁺,…) and 16.3 MeV (6⁺,…). The energy range is covered in 250 keV (c.m.) steps; at certain energy ranges in ¹²⁵ keV or 50keV steps. All excitation functions exhibit a strong energy dependence of the cross section; pronounced gross structures with superimposed fine structures, similar to those observed for ¹²C+¹²C elastic and inelastic scattering at these energies, are observed. At 19.3 MeV, where resonant structures were observed in the reactions ¹²C(¹²C, p)²³Na, ¹²C(¹²C, n)²³Mg and ¹²C(¹²C, d)²²Na, no resonance is found for the reaction studied here. At 60, 61 and 63 MeV angular distributions have been measured in 1° and 2.5°(lab) angular steps. The excitation functions have been analyzed in terms of Ericson fluctuations and cross-correlation functions.