Dispersive semimicroscopic analysis of nuclear-nuclear collisions on the basis of a corrected folding-model potential

A procedure for correcting the energy dependence determined for the mean-field component of the optical potential on the basis of the double-folding model with allowance for exchange effects in the approximation of single-nucleon exchange knockout is used to calculate the mean field and to analyze data on elastic scattering within the dispersive semimicroscopic optical-potential model. The results of an analysis of all data (including those that were obtained quite recently) on ¹⁶O + ¹²C and ¹⁶O + ¹⁴C interactions at energies of up to 100 MeV per nucleon are presented. The energy dependence of the resulting potentials agrees well with that which was obtained previously within the phenomenological approach. A systematics of the positions of Airy minima in angular distributions versus the reduced mass in the range from 2 to 8 amu is constructed.     

Nuclear rainbow in the elastic scattering of <Superscript>16</Superscript>O nuclei on carbon isotopes

An investigation of refractive effects in heavy-ion scattering is continued. For the elastic scattering of ¹⁶O nuclei on a ¹³C target at E(¹⁶O) = 132 MeV, the differential cross sections are measured for the first time in addition to previous measurements for targets from the carbon isotopes ¹²C and ¹⁴C. Airy structures that are similar for all isotopes and which have close cross sections are observed and are found to be consistent with the energy systematics of Airy minima that were obtained previously. The volume integrals of the real and imaginary parts of the optical potentials found in the present study are nearly identical for all of the isotopes considered here and are also in good agreement with the systematics obtained previously.     

Interpretation of airy minima in 16O+16O and 16O+12C elastic scattering in terms of a barrier-wave/internal-wave decomposition

The observation of refractive effects in ¹⁶O+¹⁶O and ¹⁶O+¹²C elastic scattering data has definitively established the fact that the optical potential for some light heavy-ion systems is relatively transparent and that its real part is deep. Most of the interpretations of the rainbow features of these data rely on the so-called nearside-farside decomposition of the scattering amplitude. Starting from recent optical model analyses of ¹⁶O+¹⁶O and ¹⁶O+¹²C elastic scattering around 100 MeV incident energy as an example, we present an alternative interpretation based on the barrier-wave/internal-wave decomposition first proposed by Brink and Takigawa. This method, which complements the nearside-farside approach, demonstrates clearly the exceptional transparency of the ¹⁶O+¹⁶O, and to a lesser extent ¹⁶O+¹²C, interactions at the investigated energies and makes possible the extraction of the two contributions whose interference explains the Airy oscillations seen in the farside amplitude.     

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.     

Nuclear molecular resonances in α+12C and α+16O systems

The nuclear molecular resonances observed in α+¹²C and α+¹⁶O systems are described in a diatomic-like molecular picture using a Morse-type bonding potential. The depths of the bonding potentials are found to be 11.5 MeV and 11 MeV respectively, with long range of about 15 fm. Both the bound and resonance states of these potentials are calculated which compare quite well with the observed states. The diatomic-like rotational and vibrational picture of the quasi-molecular states proposed earlier for¹²C+¹²C system system is found to be quite valid for α+¹²C and α+¹⁶O systems. In these two systems, the rotational vibrational characteristics are equally well pronounced as in the¹²C+¹²C system.     

16O nucleus in the 4α cluster model

The ¹⁶O nucleus is treated as a bound state of the four-alpha-particle system showing 3α + α clustering. The pair interaction of the alpha particles involved is simulated by a phenomenological potential. Additional three-particle potentials are introduced in order that the entire system and its three-particle subsystems be bound. The parameters of these potentials are determined by fitting the experimental values of the binding energies and the root-mean-square radii of the ¹²C and ¹⁶O nuclei. The calculations are performed on the basis of the s-wave differential equations for the Faddeev and Yakubovsky components. The ground and the first excited state of the ¹⁶O nucleus are investigated. The most probable spatial arrangement of the alpha-particle clusters in the system is determined. The charge form factors are calculated for the ¹²C and ¹⁶O nuclei. The results of our model calculations comply well with experimental data.     

IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.     

Nuclear-rainbow scattering and nucleus-nucleus potentials at short distances

The elastic scattering of strongly bound nuclei at energies of 10 to 70 MeV per nucleon shows the phenomenon of “rainbow scattering.” A nuclear rainbow appears because of deflection to negative angles. This process involves a strong overlap of nuclear densities, with values of up to twice the saturation density of nuclear matter. The ¹⁶O+¹⁶O system is studied with a high precision over a wide energy range from 7 to 70 MeV per nucleon in several laboratories. Primary Airy maxima and higher order Airy structures are observed. At all energies, excellent fits are obtained with deep potentials as deduced from the double-folding model involving a nucleon-nucleon interaction weakly dependent on the density. It is shown that Pauli blocking expected at low energies is strongly reduced if the local momenta are calculated self-consistently. Systematics confirms a refractive origin of large-angle scattering, at low energies inclusive. Thus, nuclear-rainbow scattering yields unique information about the properties of cold nuclear matter at higher densities.     

Shallow folding potential for O + C elastic scattering

The ¹⁶O + ¹²C elastic scattering data have been well described, for the first time, with a shallow folded potential obtained from a single folding method. The constituent parameters of the potential, excepting one, for its real part are generated from the nucleon–¹⁶O and α–¹⁶O potentials, and the cluster structure of ¹²C. Only the repulsive part of the α–¹⁶O potential needs some adjustment to fit the data, reflecting the need to include the Pauli exclusion effects among the unclustered nucleons.     

Realistic heavy-ion adiabatic potentials

The K-matrix model of Cusson, Trivedi, Meldner and Weiss has been used to compute static adiabatic heavy-ion cluster potentials in a constrained self-consistent Brueckner-Hartree-Fock scheme. Heavy-ion potentials are found which can simultaneously reproduce the experimentally deduced heavy-ion potentials in the asymptotic region and the total energy versus quadrupole moment in the fused, compound nucleus region. Potentials for α-α, α-¹²C, α-¹⁶O, ¹²C-¹²C, ¹⁶O-¹⁶O are shown and compared with other work. The total energy of ¹²C and ²⁴Mg versus deformation is also given.     

Nuclear surface waves in alpha-particle and ion-ion collisions

Our earlier methods of interpretation of the resonances in ion-ion scattering (such as ¹²C + ¹²C, ¹²C + ¹⁶O, or ¹⁶O + ¹⁶O where they appear both experimentally and via optical-model calculations) in terms of nuclear surface waves are applied to the case of α-⁴⁰Ca scattering. The optical-model resonance results of Brink et al. are here extended in order to render them suitable for a surface-wave picture as well. Recent experimental results on ¹²C + ¹²C scattering are used to demonstrate the existence of surface waves of both Rayleigh and whispering gallery type in this system.     

Multipole expansion of non-local coupling potentials for cluster transfer and application to 16O(16O, 12C)20Ne

When the transfer of clusters and the symmetrization (antisymmetrization) of scattering wave functions is described by cluster models within the coupled-channel formalism, non-local coupling potentials arise. We suggest a procedure to calculate these potentials by a multipole expansion of all potentials and wave functions which depend on sums of vectors. The expansion coefficients are found by least-squares fit. The method is applied to the ¹⁶O(¹⁶O, ¹²C)²⁰Ne reaction, which is treated in the cluster model with two inert ¹²C- and α-clusters as constituents.     

Refractive scattering and reactions,comparison of two systems:16O+16O and20Ne+12C

Elastic, inelastic scattering as well as one-neutron transfer channels have been measured over a wide angular range for systems¹⁶O+¹⁶O at the incident energy of 350 MeV and²⁰Ne+¹²C at 390 MeV, respectively, using the Q3D magnetic spectrometer. In both cases differential cross sections have been measured down to about 50 nb/sr (or d/d _R10^–4) at large angles. For the¹⁶O+¹⁶O system refractive contributions are found at the level of these cross sections, whereas in the²⁰Ne+¹²C case a steeper decrease of the differential cross section with the angle is observed and the refractive contribution can not be determined. The elastic scattering data have been analyzed using standard Woods-Saxon potentials and potentials calculated in different versions of the double-folding model. Some properties of these potentials are tested in the calculations for inelastic scattering and one-neutron transfer within the DWBA. With the refractive pattern observed for the¹⁶O+¹⁶O system, the scattering and transfer data are found to be sensitive to the interaction potential at small internuclear distances down to about 2.5 fm.It should be acknowledged that part of the folding analysis reported here was done while one of the authors (D.T.K.) was staying at the Institute for Theoretical Physics, University of Tübingen. We also thank Prof. H. Clement and H. Abele for numerous discussions and contributions and Prof. G.R. Satchler for helpful comments on the use of the DWBA code PTOLEMY.     

Coupled-channels study of projectile and target excitation in the scattering of 6Li from 12C and 16O

Coupled-channels calculations are presented tor elastic and inelastic ⁶Li + ¹²C scattering at E_c.m. = 16 MeV and 20 MeV, and for ⁶Li + ¹⁶O at 18.7 MeV. Excitation of states within ⁶Li, ¹²C and ¹⁶O are treated with rotational, rotation-vibration and vibrational models only. The 3⁺⁶Li and 2⁺¹²C states are strongly coupled to the elastic scattering and reduce the strengths of both the real and imaginary potentials. The 3^?16O state reduces only the strength of the imaginary potential. All other states are weakly coupled and have little effect on each other or the potential. The data are reasonably well described, with there being some preference for the 3^? state in ¹²C to be K = 0. Excitation of the 0₂⁺ state in ¹²C requires a combination of β-vibration and monopole breathing-mode form factors. The deformation lengths found are in poor agreement with those deduced from electron or proton scattering.     

Comparison of cross sections for C + O reactions in the second regime of complete fusion

Kinetic energy spectra, angular distributions, and elemental yield distributions have been measured for the ¹² C + ¹⁶ O, ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reaction products over an energy range from 2 to 7 times the Coulomb barrier energy. A careful kinematic analysis of the evaporation residues and comparisons with statistical-model calculations show that fusion proceeds with full momentum transfer followed by a statistical decay of the compound nucleus. The competition between complete fusion process and peripheral reactions in the ¹² C + ¹⁶ O system is less important than for the ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reactions. The unexpectedly high ¹² C + ¹⁶ O complete fusion cross sections are related to the possible occurrence of a superdeformation of the ²⁸ Si compound nucleus.     

Measurement of spin-alignment of excited12C2+ nuclei in interactions of16O with12C usingγ-decay in flight

Measuring energy spectra of nuclei afterγ-decay of excited states in flight the spin alignment of¹²C₂₊ states has been measured. Inelastic scattering,¹⁶O(¹⁶C,¹²C₂₊)¹⁶O and the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O leading to¹²C₂₊ (4.43 MeV) state have been studied. Characteristic line shapes of the¹²C₂₊ peak were observed using a Q3D magnetic spectrometer. The magnetic substate (m-states) population has been deduced from the spectra as function of reaction angle. A comparison of the measuredm-state population with reaction models shows that the first reaction is consistent with inelastic scattering although discrepancies remain. Discrepancies are also obtained if the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O is interpreted using a FRDWBA transfer calculation. At least 1/3 of the cross section can be attributed toα-transfer. A calculation which couples transfer and inelastic scattering channels seems to be necessary.     

Possible mechanisms of fragmentation of 16O nuclei with a momentum of 4.5 GeV/c per nucleon in track emulsions

The angular distributions of doubly charged fragments of ¹⁶O nuclei having a momentum of 4.5 GeV/c per nucleon and interacting with track-emulsion nuclei were studied. The experimental angular distributions of doubly charged fragments of a ¹⁶O nucleus are not described by the statistical model of the fragmentation of nuclei. The possible channels of fragmentation of ¹⁶O nuclei may include ¹⁶O → 2⁸Be → 4α, ¹⁶O → ⁸Be +⁸ Be* → 4α, ¹⁶O → 2⁸Be* → 4α, ¹⁶O → α+¹²C, ¹⁶O → α +¹²C* → α + 3α, ¹⁶O → α +¹²C* → α + pα ⁷Li, ¹⁶O → α +¹²C* → α + 2⁶Li, ¹⁶O → α +¹²C* → α + pt2α, ¹⁶O → Li + B, and ¹⁶O → Li* + B*.