Large contribution of deep inelastic processes to reactions of40Ar and48Ca with238U

Differential recoil range distributions have been measured for heavy-reaction products ranging from Te(Z=52) to quasielastic transfer products near the charge and mass of the targets for the reactions of 276 MeV⁴⁸Ca+²³⁸U, 237MeV and 250 MeV⁴⁰Ar+²³⁸U, and 259 MeV⁴⁰Ar+¹⁹⁷Au. The measured recoil range distributions for the⁴⁰Ar+¹⁹⁷Au reaction agree with range distributions calculated from the known projectile-like fragment angular distributions for this reaction. The angular distributions of recoil products formed in the uranium target reactions are deduced and show that the products in the₇₅Re to₈₃Bi region have backward peaked angular distributions characteristic of deep inelastic reactions. The heavy product angular distributions smoothly vary from a (1/sinθ) shape to an exponential shaped backward peak as the atomic number of the product increases from 52 to 83. The trend in the deduced angular distributions for those elements for which recoil range distributions were determined in the⁴⁰Ar+¹⁹⁷Au reaction and the 250 MeV⁴⁰Ar+²³⁸U reaction is similar, suggesting that just as for the Ar+Au system the composite system for the uranium target reaction is also not fully equilibrated along the mass asymmetry coordinate. These conclusions show that the fraction of the total reaction cross section resulting in complete fusion must be re-evaluated for the⁴⁰Ar+²³⁸U reaction and similar heavy-target reactions.     

Fragmentation of12C nuclei in emulsion at 50 GeV/c

A total of 852¹²C-emulsion nucleus interactions at 4.2 GeV/c per incident nucleon was investigated. At least one charged projectile fragment was observed in 733 events, in which the multiplicity and angular distributions ofZ=1,2, and ≧3 projectile fragments were studied. Five events were observed in which¹²C projectile nuclei were fragmented into twoZ=3 fragments. Thus the cross section of this process is about 6×10^?3 of the inelastic cross section. The angular distribution of projectile fragments becomes narrower as the fragment charge increases. At all values of fragment charges, a pronounced peak in the angular distribution can be observed at zero emission angle. In this paper, only the projectile-fragmentation events possessing no heavily ionizing particle (n _h =0 events) have been investigated. Our sample contains 84 of these events, i.e., about 10% of the total inelastic events. The number of events withZ _max, the charge of the emitted principal fragment, equal to 1, 2, 3, 4, and 5 are 11, 52, 13, 4, and 4, respectively. Of these 84 events, 36 interactions have a total charge of emitted projectile fragmentsZ ^* equal to 6, i.e., as much as the beam chargeZ _p . Of the 36 events, 17 produce no charged pions and of the 17 events, 10 only represent the dissociation of¹²C→3α, i.e., 1.2% of the total inelastic interactions. The number of events withZ ^*=5, 4, 3, 2, and 1 are 27, 14, 4, 2, and 1, respectively. The average number of produced charged pions per one interacting projectile nucleon was estimated to be 1.2±0.1. This value agrees with the corresponding one in elementary interaction at the same energy per nucleon, a result pertaining to the incoherent production model in collision of two nuclei. In this class of events,n _h =0, the number of stars in which H, He, Li, Be, and B isotopes were detected are 59, 58, 13, 4, and 4, respectively. The projected angular distributions ofZ=1 and 2 projectile fragments are Gaussian shaped, narrow, consistent with isotropy, and depend on the fragment. These distributions are consistent with quantum mechanical calculations using the sudden approximation and shell-model functions. From the angular measurements ofα-particle tracks in the dissociation¹²C→3α events, the distribution ofα-particle transverse momentum inside the carbon projectile nucleus was deduced. It seems that the dissociation of¹²C→3α happens via an intermediate⁸Be state.     

Deep inelastic collisions in the interaction of 280 MeV 40Ar with 58Ni

Masses and charges of all the nuclei with 5 ≦ Z ≦ 20 produced in the reaction ⁴⁰Ar + ⁵⁸Ni have been identified using combined ΔE · E and time-of-flight techniques. Energy spectra, angular distributions and cross sections have been measured. The formation of an intermediate composite system, in which charge equilibrium is achieved, is discussed. Also, the transition between the quasi-elastic and the deep inelastic process is studied. The angular distribution behaviour is shown to be related to the interaction time. The total cross section of the deep inelastic process has been found to be 700 mb and is compared to the evaporation residue cross section.     

The reactions of 12C with 12C AT 293 MeV

Energy spectra, angular distributions, and elemental yield distributions have been measured for products Z = 1?9 produced in the reactions of ¹²C on ¹²C. A total reaction cross section 1170_?100⁺¹⁷⁰ mb was determined from the measured elemental cross sections and the principle of charge conservation. This total reaction cross section is about 250 mb less than the geometric cross section and agrees with the Glauber-model calculations of DeVries and Peng. The experimental energy spectra, angular distributions, and yield distributions were compared with those from model calculations for the statistical decay of the products of fusion and of incomplete fusion reactions. For both types of calculations, a modified version of the code LILITA was used. By comparing the data to model calculations, an upper limit of 75 mb for the fusion cross section was determined. That limit corresponds to an upper limit of L_crit for fusion of 10? in the sharp-cutoff approximation. The dominant reaction mechanisms appear to be incomplete fusion processes.     

A study of charge,energy and angular momentum transfer in the 56Fe + 197Au and 56Fe + 107, 109Ag reactions at 7.2 and 8.3 MeV/nucleon

Kinetic energy spectra, charge and angular distributions have been measured for thirty elements produced in the reactions of 401 and 460 MeV ⁵⁶Fe + ¹⁹⁷Au and in the reaction of 470 MeV ⁵⁶Fe + ^{107, 109}Ag. In addition, γ-ray multiplicities were measured at the 470 MeV bombarding energy for both targets at a limited number of angles. The charge distributions for the deep-inelastic component of these systems increase monotonically with atomic number in the measured angular range, whereas, those for the quasielastic component are skewed toward Z-values below the projectile. The angular distributions for the Fe-induced reactions show a smooth evolution from a side-peaked to forward-peaked distributions with increasing mass transfer. This side peak is more intense and more persistent for mass transfers from the projectile to the target. In the quasielastic region the γ-ray multiplicity is observed to increase almost linearly with decreasing Q-value whereas for large negative β-values it is essentially constant and independent of the exit channel mass asymmetry. Finally, angular distributions, angle-integrated charge distributions and γ-ray multiplicities have been compared with a diffusion model in which the dynamics of shape evolution, N/Z equilibration, angular momentum and energy exchange occur via one-body forces.     

Fragment angular distributions from fission of238U,209Bi and197Au by 140-MeV4He Ions

The fission fragment angular distributions from reactions of 140-MeV⁴He ions with²³⁸U,²⁰⁹Bi and¹⁹⁷Au have been studied. From the anisotropies in the angular distributions, values for? _eff, the effective moment of inertia at the fission saddle point, have been estimated and compared with results obtained at lower bombarding energies. The derivation of? _eff values has included corrections for the effects of incomplete fusion mechanisms on the orbital angular momentum distribution of the fissioning nuclei and for neutron evaporation prior to fission. The results are also compared with heavy-ion-induced fission data for systems of similar fissility. Also, examination of the forward-backward symmetry of the²³⁸U angular distribution substantiates other results which show that the fraction of fission reactions which follow complete fusion of the target and projectile is less than 0.5 for 140-MeV⁴He-ion bombardment of²³⁸U.     

Angular distributions in quasi-fission reactions

Angular distributions for fission-like fragments were measured in the systems ⁵⁰Ti, ⁵⁶Fe + ²⁰⁸Pb by applying an off-line K X-ray activation technique. The distributions d²σ/dθdZ exhibit forward-backward asymmetries that are strongly Z-dependent. They result from a process (quasi-fission) which yields nearly symmetric masses in times comparable to the rotational period of the composite system. A method for obtaining the variance of the tilting angular momentum, K₀², from these skewed, differential angular distributions is described. The results indicate that the tilting mode is not fully excited in quasi-fission reactions. The results are compared to the sum of the variances of all statistical spin components, measured via γ-multiplicities. Integration of the angular distributions d²σ/dθdZ over all values of Z yields the integral angular distributions dσ/dθ and dσ/dΩ symmetric around 90°. The associated unusually large anisotropies do not at all provide an adequate basis for tests or modifications of the transition-state theory. A deconvolution of d²σ/dθdZ is performed with gaussian distributions depending on rotational angles Δθ extending over a range of up to 540°. From the mean values 〈Δθ〉 a time scale for the evolution of K₀ is calculated.     

Evidence of incomplete relaxation in the reaction Ag+40Ar at 288 and 340 MeV bombarding energies

The particles emitted in the reaction induced by ⁴⁰Ar on natural Ag at 288 and 340 MeV bombarding energy have been studied. The fragments have been identified in atomic number, their kinetic energy distribution and their angular distributions have been measured. The kinetic energy spectra show two components: a high-energy component related to the beam energy, or “quasi-elastic” component, and a low kinetic energy component, close to the Coulomb energy called “relaxed” component. The relaxed component is present at all angles and for all particles. The quasi-elastic component is present close to the grazing angle for atomic numbers close to that of the projectile. The relaxed cross section increases with atomic number for Z > 9. The increase in cross section is sharper for the lower bombarding energy. The angular distributions are forward peaked, in excess of $\text{1}\text{sin}\text{θ}$ for all the measured atomic numbers. The forward peaking is larger for particles close in Z to the projectile. The results are interpreted in terms of characteristic times associated with a short-lived intermediate complex. The cross sections and angular distributions are satisfactorily reproduced on the basis of a model accounting for a diffusion process occuring along the mass asymmetry coordinate of the intermediate complex.     

Nucleon transfer in highly mass-asymmetric reaction systems between197au and relatively light projectiles in the energy region below 10 MeV/u

Mechanisms of heavy-ion induced nuclear reactions in mass-asymmetric systems were studied by focusing on the nucleon transfer reaction. Excitation functions and projected mean recoil ranges for the target-like products in³⁷-,¹⁶O-,¹⁴N-, and¹²C-induced reactions on¹⁹⁷Au were measured by means ofγ-ray spectrometry. The energy range studied was near the Coulomb barrier of the systems with incident energies below 10 MeV/u. Nucleon transfer reactions were discussed by distinguishing the products from quasi-elastic transfer (QET) and those from deep inelastic transfer (DIT). The tendency towards equilibration of theN/Z value and the energy damping, which are the characteristic features of DIT, were found in the production of Au isotopes. Observations are consistent with the generally accepted concept that QET takes place along a trajectory near the Coulomb trajectory. QET was made to be connected with the interaction radius and most of the cross section ratios were reproduced well by an extended tunneling model.     

The reaction238U +238U at 7.42MeV/u

One-particle-inclusive measurements have been performed for the charge, kinetic energy and angular distributions of reaction products from²³⁸U +²³⁸U at 1 766MeV (7.42MeV/u) incident energy. The deep inelastic products exhibit features similar to those seen in reactions induced by medium heavy nuclei: increasing particle transfer is observed with increasing energy damping, the angular distributions are peaked near the grazing angle, they broaden significantly with increasing energy loss and/or charge transfer. The dominant reaction mechanism, however, is found to be sequential fission of one or both primary reaction products. The reconstructed primaryZ- andQ-value distributions show more particle transfer at a given energy loss than in other systems, i.e. the diffusion process seems to proceed colder in this system. This is confirmed by relatively large cross sections for surviving deep inelastic reaction products belowZ=92. A direct search forα-decay or fission of superheavy nuclei being produced in a deep inelastic reaction and being implanted in a surface barrier detector resulted in an upper cross section limit of 2 ×10^?32cm².     

Fusion excitation function measurements for the 16O+58Ni and 16O+62Ni systems

High precision fusion excitation functions have been measured for the ¹⁶O+⁵⁸Ni and ¹⁶O+⁶²Ni systems from which fusion barrier distributions have been evaluated. Coupled-reaction-channels (CRC) calculations, which describe elastic and quasi-elastic scattering, also satisfactorily reproduce the fusion cross sections and barrier distributions. The small value of Z₁Z₂ in this case leads to barrier distributions with relatively little structure. However, in conjunction with the detailed elastic scattering data for these systems, this allows us to elucidate the role of previously ignored states in ¹⁶O in pushing the entire distribution to lower energies. These shifts are consistent with derived magnitudes of polarization potentials for both systems.     

Intermediate mass fragments emitted in the reaction Ag+14N at 100, 160 and 250 MeV bombarding energy

The fragments produced in the reaction between a ¹⁴N beam of various energies and a natural Ag target have been studied. The atomic numbers of the fragments have been identified up to Z = 17 by means of a E-ΔE counter telescope. The cross sections, the kinetic energy distributions as well as the angular distributions have been measured for each atomic number. The kinetic energy distributions show two components: a high-energy component (quasi-elastic), prevailing at angles close to the grazing angles and for atomic numbers close to Z = 7, and a low-energy component (relaxed), at energies close to the Coulomb repulsion energy, present at all angles and for all the Z. A detailed study of the relaxed components of the kinetic energy seems to account for both them means and the widths of these distributions on a purely statistical basis. The cross sections of the relaxed components appear to be quite large at low Z and to decrease rapidly to a fairly constant value in the region of 10 ≦ Z ≦ 17. A marked even-odd alternation in the cross sections is observed. The angular distributions are strongly forward peaked for Z < 7. For Z > 7 the forward peaking decreases rapidly until, for Z > 13, the limiting form 1/sinθ is attained. Evidence for the existence of a diffusion process along the mass asymmetry coordinate is discussed.     

Multi-nucleon transfer reactions and the formation of light charged particles in the systemnatAg+40Ar (285 MeV)

In the reaction^natAg+⁴⁰Ar (285 MeV) there have been measured the energy spectra of the isotopes of elements from H to Cl at an emission angle of 40°, the energy spectra and angular distributions of¹H,²H,³H, and⁴He, and the angular distributions of Li, Be, B, and C. The contribution from multinucleon transfer reactions to the formation of light charged particles is discussed.     

Calculation of resonance reduced neutron widths by semiclassical description

Peripheral interactions of¹²C nuclei with protons and carbon nuclei have been investigated in a 2m propane bubble chamber at 4.2 GeV/c per nucleon. Energetic and angular characteristics ofγ-quanta accompanying the production of multicharged fragments withZ _f =5 and 6 have been analyzed. It is shown that in the fragment rest system there is an excess of γ-quanta with ε_γ<40 MeV over the background from known sources (π ⁰→2γ decays, bremsstrahlung and nuclear excitation).     

Proton transfer in quasi-elastic and deep-inelastic reactions in the systems86Kr on88Sr,90Zr and92Mo at energies close to the coulomb barrier

Reaction products corresponding to the transfer of one and several protons have been measured over a large angular range for incident energies of 380 MeV and 400 MeV in reactions of⁸⁶Kr with⁸⁸Sr,⁹⁰Zr and⁹²Mo. For transitions with smallQ-values (total kinetic energy loss TKEL≦10 MeV) the transfer probabilities are deduced. The magnitudes and slopes of these probabilities as function of the distance of closest approach between two nuclei are discussed. The results for single proton transfer are well described by tunneling, whereas the transfer of two and more nucleons into low lying states of the final nuclei seems to be influenced by intermediate transfer steps with larger TKEL. The data give the possibility to discuss the relation between deep-inelastic and quasi-elastic processes. The deep-inelastic data are analyzed successfully by including deformations, charge transfer and statistical fluctuations into the frictional model of Gross and Kalinowski.     

Sequential fission angular distributions from mass-asymmetric heavy-ion reactions

The angular distributions of sequential fission fragments have been measured for the reactions of ⁴⁰Ar with ¹⁹⁷Au and ²³⁸U as a function of reaction Q-value and charge transfer. These angular, distributions are used to study the angular momentum and alignment of the deep-inelastic products which undergo fission. All of the fission fragment angular distributions are strongly focused into the plane defined by the beam and the projectile-like fragment velocity vectors. The in-plane angular distributions from reactions with uranium are isotropic for small energy losses and become anisotropic as the energy loss increases. For large negative Q-values, the in-plane anisotropy increases as the deep-inelastic products become more symmetric. The variation of the in-plane anisotropy with mass asymmetry for the two systems in this work was compared to a compilation of previous work and a consistent pattern was found. These alignment data are compared to equilibrium statistical calculations.     

Folding model analysis of 10, 11B, 12C + 27Al, 39K and 40Ca

Elastic scattering angular distributions for ^{10, 11}B + ⁴⁰Ca at E_lab = 46.6 and 51.5 MeV and¹²C+³⁹K at E_lab = 54 and 63 MeV have been measured and compared with Woods-Saxon and double-folding optical models. The oscillatory structure observed previously for ¹²C + ⁴⁰Ca disappears when the projectile is changed to ^10,11B or the target is changed to ³⁹K. The angular distributions are adequately reproduced by a double-folding analysis, which employs the nucleon-nucleon potential of Bertsch et al., with a range of real normalizations N_R = 1.0–1.38. This same range of real normalizations was also able to describe previously measured ^10,11B, ¹²C + ²⁷A1 data. The double-folding analysis of ¹²C + ⁴⁰Ca scattering indicates that this system behaves differently from neighboring systems.     

Application of the incoming wave boundary condition to16O+16O and12C+12C elastic scattering

The elastic scattering of¹²C+¹²C and¹⁶O+¹⁶O has been studied in the framework of an incoming wave boundary condition model. Different logarithmic derivatives for the incoming waves have been tested and their effects investigated with the help of Fourier analyses. It is shown that a logarithmic derivative obtained from a JWKB approximation leads to strong absorption of the low partial waves while a logarithmic derivative constant for all partial waves causes reflections. These reflections are necessary to describe the high energy elastic scattering of¹²C+¹²C. The fits thus obtained with shallow real potentials are comparable to those obtained with deep folding potentials. It is shown that not the lowest partial waves, but those within a window just below the grazing angular momentum are most important for the higher energy¹²C+¹²C angular distributions.