Emission of helium nuclei in heavy ion interactions at energies ≧ 100 MeV/nucleon

The energy and angular distributions of helium particles emitted in interactions between nuclei in the cosmic radiation and nuclei in photoemulsions at energies ≧ 100 MeV/nucleon have been studied. The data obtained is impossible to interpret on the basis of a statistical decay of excited nuclei. For example, it is found that more than 28% of the helium nuclei are emitted in processes different from simple evaporation. The differential energy distribution of the helium nuclei in the energy interval (40–200) MeV can be represented by the relationN(E)dE=constE ^?a dE, wherea≈1.2. The large spread in angles and energies of the fast helium particles emitted in heavy ion interactions can to a certain degree be understood, if it is assumed that interactions between nucleons and clusters of nucleons occur.     

Pre-equilibrium emission in neutron induced reactions on54,56Fe

The experimentally well known (n, p), (n, α) and (n, 2n) reaction excitation functions, from threshold to 20 MeV incident energy, and neutron and proton emission spectra at 14.8 MeV from^54,56Fe targets are calculated in the frame of the Geometry-Dependent Hybrid pre-equilibrium emission model, including angular momentum and parity conservation, and the Hauser-Feshbach statistical model. Use of a consistent statistical model parameter set enables the validation of the pre-equilibrium emission model. Moreover, an enhanced pre-equilibrium emission from higher spin composite system states, associated with higher incoming orbital momenta, has been evidenced. Higher orbital momenta involved also in the emergent channels of the process are suggested by calculations of the residual nuclei level populations.     

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.     

Hot spots in nuclei by microscopic transport theory

In a previous publication effects of two-body collisions were incorporated with TDHF by the time-relaxation method. This microscopic model is now used to study decays of hot spots in nuclei. Calculations are made in a one-dimensional slab geometry. A temperature-dependent expression is used for the relaxation time. It is based on Tomonaga's formula for heat conduction at low temperatures. At high temperatures we use (recent) calculations of imaginary optical potential and equilibration with penetrating infinite nuclear slabs. Our calculations show pre-equilibrium emission of nucleons. This emission is in general decreased by two-body collisions. Some of our results are presented by contour plots of the Wigner function.     

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.     

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.     

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.     

Thermal hadron production in Si-Au collisions

The most abundantly produced hadron species in Si - Au collisions at the BNL-AGS (nucleons, pions, kaons, antikaons and hyperons) are shown to be in accord with emission from a thermal resonance gas source. Within the uncertainties of the present data, two freeze-out points are possible. The best agreement is obtained for a temperature T ? 110 MeV and a baryochemical potential μ_B ? 540 MeV, corresponding to about 1/3 standard nuclear density. Another possible point lies at about twice nuclear density, with T ? 160 MeV and μ_B ? 620 MeV. Our analysis takes the isopin asymmetry of the initial state fully into account.     

Dynamical aspects of intermediate-energy nucleus-nucleus collisions

Central collisions of heavy nuclei are investigated within the limit of selfconsistent independent single-particle motion in terms of the Wigner transform of the one-body density matrix in space and time. The energy regime considered extends from roughly 15 MeV/u to 150 MeV/u. Special attention is devoted to the relation between energy and momentum of the nucleons in the collision zone of the two nuclei. An initial average energy-momentum distributionf(k;E) is determined within the fully quantal approach which proves to be vital for our understanding of energetic particle production in the very early stage of the heavy-ion reaction. A comparison with related classical quantities shows the peculiar features of quantum dynamics for finite size fermion systems far from equilibrium.     

Fission characteristics of the composite system 32S+50Ti: (I). Correlations between coincident fragments

The characteristics of “fission-like” processes observed in the bombardment of ⁵⁰Ti with ³²S ions of 140 MeV energy are investigated in a coincidence experiment between a time-of-flight telescope and a position sensitive ΔE-E ionization chamber. Coincident particles were identified and their energy and angular correlations in and normal to the reaction plane were measured. The experiment proves the binary nature of the mass division. Both the width and the average value of the total kinetic energy distribution are consistent with the values extrapolated from fission of heavier nuclei. An average number of 3±1 nucleons are emitted during the reaction; α-particle emission is not an important decay mode.     

Is neutron evaporation from highly excited nuclei a poisson random process?

It is suggested that neutron emission from highly excited nuclei follows a Poisson random process. The continuous variable of the process is the excitation energy excess over the binding energy of the emitted neutrons and the discrete variable is the number of emitted neutrons. Cross sections for (HI, x n) reactions are analyzed using a formula containing a Poisson distribution function. The post- and pre-equilibrium components of the cross section are treated separately. The agreement between the predictions of this formula and the experimental results is very good.     

Results on two-, three-, and four-body events from the100Mo+100Mo and120Sn+120Sn collisions aroundE/A=20 MeV

Events with 2, 3 and 4 heavy-fragments (A≧20) have been detected in the reactions¹⁰⁰Mo+¹⁰⁰Mo atE/A =18.7, 23.7 MeV and¹²⁰Sn+¹²⁰Sn atE/A=18.4 MeV. The experiments were performed with an array of 12 detectors which together covered a large fraction of the forward hemisphere and allowed a high detection efficiency for these events. Masses and energies of all fragments have been reconstructed by means of an improved version of the kinematic coincidence method. The probabilitiesP ₃ andP ₄ of producing 3- and 4-body events were found to depend mainly on the dissipated energy rather than on the bombarding energy, thus indicating that their origin lies more in the decay properties of the excited fragments than in the dynamics of the interaction. Emission of light particles from the composite system is shown to become more relevant with increasing bombarding energy and may explain the drop of theP ₃ andP ₄ curves at high energy losses. Small deviations of theP ₃ andP ₄ curves at 23.7A · MeV from those at lower bombarding energies were used to estimate the amount of a possible pre-equilibrium light particle emission as a function of impact parameter.     

Pre-equilibrium alpha emission accompanying deep-inelastic16O+58Ni collisions

α particles were measured in coincidence with projectile-like reaction products (oxygen and carbon) produced in deep-inelastic¹⁶O+⁵⁸Ni collisions at about 6 MeV/N bombarding energy. The kinematic analysis of the HI andα energies measured as a function ofΘ _α gives strong evidence for a sequential process: the target-like fragments are excited by the deep-inelastic collision and undergo subsequentα decay. In contrast, the angular correlations show a pronounced forward peak, indicative of direct or pre-equilibriumα emission. The emission time for the latter is estimated to be of the order of 2×10^?21 s. To resolve this conflict of co-existing statistical and direct features of the pre-equilibrium emission, the concept of a hot spot is proposed. From the angular correlation and from theα multiplicities, a local temperature ofT?3.5 MeV is deduced which agrees well with the temperature derived from the shape of theα spectra. The spot size is estimated to be 1/5 of the sphere.     

Pre-equilibrium emission effect in (n,p) reaction cross-sections at 14.8 MeV

The influence of pre-equilibrium emission on (n, p) reaction cross-sections at 14.8 MeV has been studied. Cross-sections for (n, p) reactions have been measured by the activation technique at 14.8 .1; 0.5 MeV neutron energy. The experimental cross-section values have been compared with the calculated values at 14.8 MeV with and without considering the pre-equilibrium emission. Equilibrium calculations have been performed according to the statistical model of Hauser and Feshbach while the hybrid model has been used to include the pre-equilibrium contribution. Pre-equilibrium emission has been considered only in the first emission step. The comparison of experimental and calculated values clearly indicates the presence of pre-equilibrium emission.     

A semi-empirical correlation energy for nuclei

A semi-empirical interaction is used to calculate higher order corrections to the binding energies of even—even nuclei close to the line of stability. These corrections are taken to come from two phonon configurations and are treated as a perturbation with respect to the BCS nuclear ground state which is obtained from applying the energy density method to finite nuclei. The overall correspondence between theory and experiment for the 60 nuclei calculated between A =52 and A =234 is good, with excellent agreement for the non-deformed nuclei situated within the regions A = 72 to 144 and A = 200 to 212. The large correction enegies (several MeV per nucleus on the average) indicate that these correlations are of importance for explaining nuclear binding energies and that it is necessary to include them within energy functional itself. The fact that these correlations come almost exclusively from nucleons close to the fermi surface is also discussed.     

Study of the out-of-plane emission of protons and light fragments in symmetric heavy-ion collisions

Midrapidity protons from²⁰⁹Bi+²⁰⁹Bi collisions were measured with the Kaon Spectrometer at SIS at incident energies of E _Lab /A=400, 700 and 1000 MeV. Additionally, light fragments were analysed at 400 MeV. We have investigated the azimuthal emission pattern of the particles relative to the reaction plane as function of transverse momentum, bombarding energy and impact parameter. We observe an enhanced emission of particles perpendicular to the reaction plane at all bombarding energies. The ratio of the number of particles emitted out-of-plane/in-plane increases strongly with the particles transverse momentum. The anisotropy decreases with increasing beam energy. Composite particles show a much stronger effect than protons.     

Quasi-elastic and deep-inelastic dissipative processes

Quasi-elastic and deep inelastic rates are calculated assuming that the colliding nuclei move on classical trajectories and that the excitations and the particle or energy exchanges are due to the shell-model wells interacting with the nucleons. (One-body collisions). This allows a microscopic, parameter free, calculation of the optical potential, as well as the energy and the angular momentum losses, and is a good approximation as long as the collision is peripheral. The correction due to two-body collisions between individual nucleons is also evaluated. The focus will be on the evolution of the various reaction rates as a function of energy. The system chosen for the discussion is ¹⁶O + ¹⁶O from 3 MeV/A to 60 MeV/A.