Deep Inelastic Reactions Research Articles

Comparative study of baryon production in hard and soft processes

The production ratios of baryons and mesons in deep inelastic reactions are compared with the corresponding quantities in soft hadronic interactions. Contrary to general believe these ratios are equal within the experimental uncertainties and show the same dependence on the longitudinal momentum, provided that processes are compared, where a fixed number of valence quarks is common to the initial state and the secondary under consideration, i.e. processes which are equivalent in the sense of quark recombination mechanisms.

Electron emission and positron production in deep inelastic heavy-ion reactions

Atomic excitations are used to obtain information on the course of a nuclear reaction. Employing a semiclassical picture we calculate the emission of $\ensuremath{\delta}$ electrons and positrons in deep inelastic nuclear reactions for the example of U+U collisions incorporating nuclear trajectories resulting from two different nuclear friction models. The emission spectra exhibit characteristic deviations from those expected for elastic Coulomb scattering. The theoretical probabilities are compared with recent experimental data by Backe et al. A simple model is used to estimate the influence of a threebody breakup of the compound system upon atomic excitations.

Nuclear Reaction Times in the Deep-Inelastic U + U Collision Deduced fromK-Shell Ionization Probabilities

The K-shell ionization probability P/sub K/ of the uranium-like products has been measured in the deep-inelastic reaction U+U at a beam energy of 7.5 MeV/u as a function of the total kinetic energy loss -Q. P/sub K/ was determined for Q values down to -190 MeV. After the subtraction of the ionization induced by internal conversion of ..gamma.. rays, a strongly Q-dependent P/sub K/ is found in qualitative agreement with theoretical predictions. From the data we infer a nuclear reaction time of approximately 10/sup -21/s at Q = -100 MeV.

Dissipative resistance against changes in the mass asymmetry degree of freedom in nuclear dynamics: The completed wall-and-window formula

The wall-and-window formula, describing the macroscopic energy dissipation for two nuclei in relative motion, is generalized to include the dissipation associated with a time rate of change of the mass asymmetry degree of freedom. The additional term is crucial for the possibility of understanding the existence of deep-inelastic nuclear reactions.

Open questions: Thermalization and flow, kinetic or potential driven?

The fact that neutron drifts seem not to follow the expectations based on energetically dominated statistical descriptions of the deep inelastic reactions is welcomed as keeping open the hope that specific mechanistic aspects of the nuclear flow and thermalization processes might yet emerge from beneath the cover of these reactions' statistical complexity. A one-dimensional Schrödinger DOUBLE WELL model is analyzed to show that its Schrodinger dynamical flow does not conform to the common statistical assumption of total energy dominance. Rather, nucleonic kinetic energy emerges as a stronger determinant of the early flow than potential energy. Since these “kinetic pressures” are very sensitive to the radii of the nucleonic potential wells, their study promises to illuminate the question of differences between the neutron and proton radii. Also, for kinetic pressure dominated exchanges, one-dimensional loci of equilibrium points in the projectile-like (Z,N) plane replace the isolated stationary points of the energy surface. One thus arrives at a two-stage equilibration process, in which the early rapid kinetic pressure driven drift toward a kinetic pressure equilibrium is followed by a slower potential, driven drift along the locus of kinetic equilibria towards the energy equilibrium point. Were the neutron and proton loci of equilibria to separate, an “equilibrium channel” could arise, which would tend to guide the N-Z exchanges in a direction which might even be opposite to the preference of the overall energy.

WIGNER TRANSFORM METHODS IN INCLUSIVE ELECTRON SCATTERING FROM NUCLEI

A multiple scattering series for deep inelastic leptoninduced reactions is derived by using semiclassical Wigner transform methods. In contrast to the usual Glauber theory there is no limitation for the energy loss since a time-dependent formulation is used throughout. A simple parametrization of the generalized profile function yields a closed analytical expression for the longitudinal and transverse response function of p-shell nuclei. Comparison is made with the Saclay data for -'• C. I Introduction It is common knowledge that geometrical optics is valid if the wavelength of the scattering wave is small compared to the dimensions of the scatterer. Under these conditions the phase-space description of the scattering process by means of the Wigner transform is best suited to derive semiclassical approximations /I/. As a simple example consider scattering of a nonrelativistic particle by a potential V(f). The scattering matrix is given by U(oo, -co) where the time evolution operator U(t,t0) obeys (Ti = 1)

Characteristics of Angular Momentum Relaxation inNe20+Er168Collisions at 13.5 MeV/u

The multiplicity, anisotropy, and circular polarization of the ..gamma.. radiation from 270-MeV /sup 20/Ne+/sup 168/Er were measured in coincidence with the projectilelike fragments. The deduced angular momentum transfer in the deep-inelastic reaction component is rather small but can be understood, together with the fluctuations of the spin axis and the prevalence of negative-angle scattering, in terms of a frictional process in concurrence with breakup.

A quantum-mechanical model of coupled proton and neutron asymmetries and the fast charge equilibration process in deep-inelastic collisions

A quantum-mechanical model of coupled harmonic oscillators in collective coordinates of proton and neutron asymmetries is solved analytically, in a non-perturbative formalism, for the charge and neutron distributions in deep-inelastic reactions. The time evolution of the mean values (centroids) and the variances (widths) is studied for the initial distribution taken to be a two-dimensional Gaussian function. Model calculations are presented that show the detailed dependence of the relevant quantities on the variables of our model. Fits to the experimental data are made for the reactions 129Xe on 116Sn and 124Sn.

Light-particle emission in the reactions of 16O with Ti

Inclusive energy spectra and angular distributions for heavy ions (Z ≧ 3) produced in the reactions of 227 MeV and 310 MeV 16O with Ti were measured. Also measured at the projectile energy of 310 MeV were energy and angular correlations between light charged particles ( Z ≦ 2) and heavy ions. From comparisons with statistical model calculations upper limits to the complete fusion cross sections of 647 mb and 265 mb were derived for projectile energies of 227 MeV and 310 MeV, respectively. At 310 MeV the cross section of incomplete fusion processes was estimated to be over 505 mb. Emission of fast, high-energy α-particles and protons was observed to be a characteristic feature of quasi-elastic, deep-inelastic and fusion-like reactions. Average multiplicities of fast light particles in coincidence with heavy ions at +20° and +40° were estimated to be of the order of 1. The prompt emission of light appears to be the principal mechanism which limits complete fusion. A second component of α-particles observed in coincidence with deep-inelastic projectile-like fragments and having an energy comparable to Coulomb energies of particles emitted from target-like and projectile-like fragments appears as an excess yield in the direction of the recoiling target-like fragments. This component cannot be accounted for in terms of sequential emission processes and may result from a mechanism other than the one which leads to fast particle emission.

A nearside-farside analysis of deep inelastic reactions

Continuum multi-step direct-reaction theory is combined with a decomposition of the scattering amplitude into its near-and farside components. It is possible with these techniques to explain, in a quantum-mechanical framework, the increased importance of negative-angle scattering for large energy losses in deep inelastic collisions.

Deep inelastic reactions and fusion

During the last decade considerable progress has been made in our understanding of the mechanisms of reactions between complex nuclei. In Session 3, some aspects of this progress as well as some of the outstanding problems are reviewed for damped or deep inelastic reactions and fusion.

The phenomenology of deep-inelastic processes

The field of heavy-ion deep-inelastic reactions is reviewed with particular attention to the experimental picture. The most important degrees of freedom involved in the process are identified and illustrated with relevant experiments. Energy dissipation and mass transfer are discussed in terms of particles and/or phonons exchanged in the process. The equilibration of the fragment neutron-to-proton ratios is inspected for evidence of giant isovector resonances. The angular momentum effects are observed in the fragment angular distributions and the angular momentum transfer is inferred from the magnitude and alignment of the fragments spins. The possible sources of light particles accompanying the deep-inelastic reactions are discussed. The use of the sequentially emitted particles as angular momentum probes is illustrated. The significance and uses of a thermalized component emitted by the dinucleus is reviewed. The possible presence of Fermi jets in the prompt component is shown to be critical to the justification of the one-body theories.

Microscopic description of giant resonances in highly excited nuclei

Giant resonances of general multipolarity in highly excited nuclei, which are produced in compound nuclear and deep inelastic heavy ion reactions, are described microscopically in the finite temperature linear response formalism. The linear response function is calculated in the finite temperature (FT) quasi-particle RPA approximation (FT-HFB-RPA) and is based on the corresponding self-consistent quasi-particle basis (FT-HFB). The theory is derived from the small amplitude limit of FT-TDHFB. The inclusion of cranking constraints allows the investigation of giant resonances in nuclei with large intrinsic excitation energy and high spin. A schematic model for the FT-HFB-RPA is developed and applied to the isovector giant dipole resonance in hot spherical nuclei. It is shown that the energy of the resonance depends only weakly on temperature in these systems. The experimentally observed lowering of the giant mode in highly excited nuclei is to be attributed to different effects. The descritpion of resonance damping lies beyond the scope of the random phase approximation. Possible extensions in this direction and qualitative features of the width of giant resonances at finite temperature are discussed.

Oscillatory structure of the harmonic oscillator Wigner function

Some simple closed-form approximations are derived for the oscillatory part of the Wigner function F for a system of degenerate fermions completely filling the first M shells of an oscillator potential in N dimensions. The formalism for a general dimensionality is retained since various properties of the physical case (N=3) may be related to similar systems in one dimension higher or lower. In particular the magnitude of the oscillations increases with N, but it is shown that if the last shell is only half filled the structure is decreased to that obtained for a closed-shell system in one dimension lower. The structure is shown to decrease slowly in the 'classical' or 'macroscopic' limit of large particle number, when the density is shown to tend to its Thomas-Fermi value. The formula for the full-shell case is sufficiently simple to generalise to the problem of almost degenerate fermions at a finite temperature T, where it is seen that substantial damping of the oscillations may be obtained for any particle number. An explicit expression for the damping is derived and this implies that for deep-inelastic nuclear reactions at a temperature of around 2 to 3 MeV, considerable structure may still be present in F. A simple expression relating the Fermi energy and the particle number of the system at finite temperature is given.

Dynamical thresholds for compound-nucleus formation in symmetric heavy-ion reactions

We study the effect of the nuclear macroscopic energy, nuclear dissipation, and shape parametrization on dynamical thresholds for compound-nucleus formation in symmetric heavy-ion reactions. This is done by solving numerically classical equations of motion for head-on collisions to determine whether the dynamical trajectory in a multidimensional deformation space passes inside the fission saddle point and forms a compound nucleus, or whether it passes outside the fission saddle point and reseparates. Specifying the nuclear shape in terms of smoothly joined portions of three quadratic surfaces of revolution, we take into account three symmetric deformation coordinates. However, in some cases we reduce the number of coordinates to two by requiring the ends of the fusing system to be spherical in shape. The nuclear potential energy of deformation is determined in terms of a Coulomb energy and a nuclear macroscopic energy that is usually taken to be a double volume energy of a Yukawa-plus-exponential folding function, although a double volume integral of a single-Yukawa folding function and ordinary surface energy are also considered. The collective kinetic energy is calculated for incompressible, nearly irrotational flow by means of the Werner-Wheeler approximation. Four possibilities are studied for the transfer of collective kinetic energy into internal single-particle excitation energy: (1) zero dissipation, (2) ordinary two-body viscosity, (3) one-body wall-formula dissipation, and (4) one-body wall-and-window dissipation. For systems with $\frac{{Z}^{2}}{A}$ larger than a threshold value ${(\frac{{Z}^{2}}{A})}_{\mathrm{thr}}$ which depends somewhat upon dissipation, the center-of-mass bombarding energy must exceed the maximum in the one-dimensional interaction barrier by an amount $\ensuremath{\Delta}E$ in order to form a compound nucleus. For all four possibilities considered, we find that the dependence of $\ensuremath{\Delta}E$ on $\frac{{Z}^{2}}{A}\ensuremath{-}{(\frac{{Z}^{2}}{A})}_{\mathrm{thr}}$ is more complicated than the lowest-order quadratic dependence found in some previous approximate solutions. For both types of one-body dissipation, our calculated values of $\ensuremath{\Delta}E$ are an order of magnitude larger than those for zero dissipation and ordinary two-body viscosity. We compare our results calculated for symmetric systems with experimental values for asymmetric systems by use of a tentative scaling involving ${(\frac{{Z}^{2}}{A})}_{\mathrm{mean}}$, defined as the geometric mean of $\frac{{Z}^{2}}{A}$ for the combined system and an effective value ${(\frac{{Z}^{2}}{A})}_{\mathrm{eff}}$, for the projectile and target. When compared in this way, the experimental values of $\ensuremath{\Delta}E$ agree better with results calculated for two-body viscosity than with results calculated for either type of one-body dissipation.NUCLEAR REACTIONS $^{110}\mathrm{Pd}$ + $^{110}\mathrm{Pd}$\ensuremath{\rightarrow}$^{220}\mathrm{U}$, symmetric nuclear systems leading to compound nuclei with $37.0\ensuremath{\le}\frac{{Z}^{2}}{A}\ensuremath{\le}41.5$. Calculated dynamical thresholds for compound-nucleus formation. Macroscopic nuclear model, Yukawa-plus-exponential model, single-Yukawa model, liquid-drop model, nuclear inertia, nuclear dissipation, ordinary two-body viscosity, one-body dissipation, classical equations of motion, dynamical trajectory, compound-nucleus formation, heavy-ion fusion, fast fission, deep-inelastic reactions, time-dependent Hartree-Fock approximation.

Alpha-particle emission from the reaction 1354 MeVHo165+Ta181

The emission of $\ensuremath{\alpha}$ particles from the deep-inelastic reaction 1354 MeV $^{165}\mathrm{Ho}$ + $^{181}\mathrm{Ta}$ has been studied. Alpha particles were detected in coincidence with a projectilelike fragment, both in and out of the reaction plane. Average velocity diagrams, $\ensuremath{\alpha}$-particle energy spectra as a function of angle, and $\ensuremath{\alpha}$-particle angular distributions are presented. The in-plane data show that the bulk of the $\ensuremath{\alpha}$ particles in coincidence with the deep-inelastic exit channel can be explained by evaporation from the fully accelerated fragments. The out-of-plane $\ensuremath{\alpha}$-particle angular distribution data together with gamma-ray multiplicity data from previous work give a consistent picture of the transfer and partitioning of angular momentum between the two fragments.NUCLEAR REACTIONS $^{181}\mathrm{Ta}(^{165}\mathrm{Ho}, \mathrm{HI}\ensuremath{\alpha})$${E}_{\mathrm{lab}}=1354$ MeV: measured ${\ensuremath{\sigma}}_{\ensuremath{\alpha}}({E}_{\ensuremath{\alpha}}, {\ensuremath{\theta}}_{\ensuremath{\alpha}}, {\ensuremath{\varphi}}_{\ensuremath{\alpha}})$, in- and out-of-plane anisotropies; deduced $\ensuremath{\alpha}$-particle multiplicity, nuclear temperature.

Fast fission: A dissipative mechanism following sometimes fusion

We discuss the conditions under which the fusion of two heavy ions is possible. We describe the results of a dynamical model for dissipative heavy ion collisions which shows that a fused trajectory can lead either to a compound nucleus, or to fast fission. This latter process is a mechanism which is intermediate between compound nucleus formation and deep inelastic reactions. The conditions under which fast fission occurs are discussed in detail. The results of the model are compared with experimental data suggesting the existence of fast fission.

Exotic nuclei in deep-inelastic and fusion reactions

A review is given on recent progress in studies of nuclei far from beta stability, with particular emphasis on the use of heavy-ion beams.

Angular-momentum transfer and alignment in deep-inelastic reactions for nearly symmetric heavy-ion systems

The magnitude and alignment of the spin transferred to the fragments in the deep-inelastic reactions of 8.5 MeV/nucleon 165Ho on 176Yb, 148Sm, and natAg were investigated using continuum γ-ray multiplicity and anisotropy techniques. The detection system consisted of a highly redundant arrangement of particle and γ-ray detectors and a γ-ray multiplicity filter. By using suitable reduced quantities, we show that for the most negative Q-values the multiplicity data are consistent with rigid-rotation of the intermediate dinuclear complex. The anisotropy data are compared to an equilibrium statistical model calculation. The sensitivity of the calculation to different assumptions concerning the composition of the γ-ray spectra is investigated. The magnitude and alignment of the spin imparted to the individual fragments as a function of Q-value are extracted for the three reactions.

Multipolarity of statistical γ-rays from f-p shell nuclei produced in deep-inelastic heavy-ion reactions

Measurements of the circular polarization and the angular correlation of γ-rays from highly excited polarized nuclei, produced in 16O+ 58Ni deep-inelastic reactions, indicate a strong quadrupole component in the spectra of statistical γ-decay at E λ >2 MeV. Differences in the anisotropies observed for the 16O+ 58Ni and the 16O+ 48Ti reactions are attributed to the influence of nuclear structure.