Equivalent bare optical potentials in heavy-ion inelastic scattering

The equivalent bare optical potentials have been calculated for the inelastic scattering of ¹⁶O and ¹³C by ⁴⁰Ca at 60 and 68 MeV, respectively. The potentials obtained are quite consistent with those found phenomenologically by coupled-channels calculations. The shape of the bare potential is interpreted by showing the significant contribution of the nuclear—Coulomb cross term.     

Polarization effects on heavy-ion scattering in the distorted-wave method

On the basis of an exact formalism for DWBA methods we calculate the distorting potentials to be used in a standard distorted-wave Born approximation for systems with strongly coupled channels. We examine for a practically useful model some simple approximate treatments through comparisons of the polarization potentials in the case of elastic and inelastic ¹⁶O + ¹⁶O scattering. The adiabatic approximation omitting the radial kinetic energy in the propagator is found to lead to satisfactory agreement with the exact coupled-channel cross sections.     

Folding model potentials from realistic interactions for heavy-ion scattering

The double-folding model, with “realistic” nucleon-nucleon interactions based upon a G-matrix constructed from the Reid potential, is used to calculate the real part of the optical potential for heavy-ion scattering. The resulting potentials are shown to reproduce the observed elastic scattering for a large number of systems with bombarding energies from 5 to 20 MeV per nucleon. Some representative inelastic transitions are also reproduced. Exceptions are the elastic scattering of ⁶Li and ⁹Be for which the folded potentials must be reduced in strength by a factor of about two.The same effective interactions are shown to give a good account of two particular cases of alpha scattering as well as some cases of nucleon-nucleus scattering. Some typical examples of inelastic heavy-ion scattering are also predicted successfully.Some general properties of the folding model are reviewed and its theoretical basis is discussed. An explicit density-dependence is examined for one particular realistic interaction and found not to change the results. Single nucleon exchange is included in an approximate way and its importance is studied.In addition to being a study of the folding model, this work also provides a systematic and comprehensive optical model analysis of heavy-ion elastic scattering in this energy range.     

Effective potentials for heavy-ion scattering derived from channel coupling

Starting from coupled-channels equations, we use suitable approximations to derive effective interaction potentials for elastic heavy-ion scattering. These potentials are local, complex and l-dependent, and determined solely by the transition form factors and the zero-order elastic S-matrix elements. Although here we treat the couplings in first order only, our method can easily be extended to higher-order coupling by iteration. As examples we give explicit expressions for coupling to inelastic collective channels, by both Coulomb and nuclear excitation, and to transfer reaction channels. Aside from identifying the dynamical origin of various components of the total elastic interaction, we suggest that our potentials (or appropriate generalizations thereof) may be used in conventional optical model and DWBA codes as a simple substitute for coupled-channels calculations.     

Polarization in heavy-ion reactions

A series of experiments is described in which beta-ray asymmetry has been used to determine polarization of heavy-ion reaction products¹²B and the present status of the studies of polarization phenomena in heavy-ion reactions is reviewed. A large amount of angular momentum sustained by the two colliding nuclei gives rise to polarization phenomena of reaction products. Coupling between the degrees of freedom accompanying the intrinsic and the relative motions is investigated from the systematic behaviour of polarization of reaction products disclosed by the experiments.     

Coulomb potentials in heavy-ion interactions

The usual point charge approximation for the Coulomb potential in heavy-ion interactions is compared with more realistic treatments. Elastic scattering and transfer reaction calculations appear to be insensitive to the form of the Coulomb potential used.     

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.     

Alpha-transfer processes in heavy-ion scattering

In the differential cross sections for the elastic scattering between an α-conjugate target and projectile, a rising oscillatory structure is often observed in the backward-angle region. An α-transfer mechanism is proposed to explain this anomalous phenomenon. A nuclear molecularorbit approximation theory for both 1α- and 2α-transfer processes has been formulated and applied to ¹⁶O + ²⁰Ne and ¹²C + ²⁰Ne scattering systems with different projectile energies. The experimental rising structures shown in these scatterings are well reproduced with parameters fairly consistent with spectroscopic data. An independent-α-particle model wave function has been used for the evaluation of the exchange potential, which gives better agreement with experiment than the Buttle-Goldfarb approximation can usually provide.     

Factorization in relativistic heavy-ion scattering

We have calculated the total cross sections for relativistic nucleus-nucleus scattering in the Glauber theory and conclude that there will be no factorization, due to the short-range nature of nucleon-nucleon interaction as compared to the sizes of the colliding nuclei.     

Parity dependence in heavy-ion scattering

A range is defined for the effects of parity dependence in heavy-ion scattering. This range is shown to be related to the terms of the antisymmetrizer which exchange the largest number of nucleons between both nuclei. A simple formula, derived in the two-center harmonic oscillator model, gives an upper bound for the parity range. A criterion is proposed to determine whether a parity-dependent real part should be used in heavy-ion optical potentials. The most important parity effects should be expected in scattering between nuclei with neighbouring masses.     

Resonance propagation in heavy-ion scattering

The formalism developed earlier by us for the propagation of a resonance in the nuclear medium in proton-nucleus collisions has been modified to the case of vector boson production in heavy-ion collisions. The formalism includes coherently the contribution to the observed di-lepton production from the decay of a vector boson inside as well as outside the nuclear medium. The medium modification of the boson is incorporated through an energy dependent optical potential. The calculated invariant ρ mass distributions are presented for the ρ-meson production using optical potentials estimated within the VDM and the resonance model. The shift in the invariant mass distribution is found to be small. To achieve the mass shift (of about 200 MeV towards lower mass) as indicated in the high energy heavy-ion collision experiments, an unusually strong optical potential of about −120 MeV is required. We also observe that, for not so heavy nuclear systems and/or for fast moving resonances, the shape, magnitude and peak position of the invariant mass distribution is substantially different if the contributions from the resonance decay inside and outside are summed-up at the amplitude level (coherently) or at the cross section level (incoherently).     

Deformation effects in heavy-ion scattering

Many experiments on the scattering of heavy ions confirm that the elastic cross sections display characteristics of Fresnel diffraction. Recent experiments on the scattering of very heavy ions, however, show marked deviations from the expected Fresnel shapes and an analysis of these experiments using the “quarter-point-recipe” of the Fresnel cross section yields a larger radius for ²⁰⁸Pb than for ²³²Th. It is shown that the deviations may be described in terms of the ground state deformations of the nuclei involved. Taking the deformations into account removes the above anomaly in the radii. The actual fit to the experimental cross sections is not very good and suggests that the real part of the nuclear potential may have an appreciable effect on the orbits of nuclei which are elastically scattered below the Coulomb barrier.     

Pockets in heavy-ion potentials and nucleon transfer

A schematic model is described for taking into account the effect of potential pockets (motivated by positron experiments at GSI) on sub-Coulomb nucleon transfer cross sections. Results for single-neutron transfer in ²³⁸U-²³⁸U collisions bear a remarkable resemblance to data for some bombarding energies.     

Electron-positron scattering matrix in supercritical heavy-ion collisions

The scattering matrix describing the electron-positron excitation during a heavy-ion collision is discussed. It is shown that spontaneous positron emission in the presence of a long nuclear delay time precisely corresponds to the formal resonance condition of Scharf.     

A new interaction for heavy-ion scattering

A new effective nucleon-nucleon interaction gives the real part of heavy-ion optical potential tails correctly when used in a folding model. Exchange effects are discussed.     

Nuclear excitation effects on heavy-ion scattering

The detailed coupled-channel analysis, including a ground state rotational coupling up to the 4⁺ state, for ¹⁶O scattering from ¹⁵²Sm at the incident-ion energy of 72 MeV is performed. It is found that nuclear excitation plays an important role in the reproduction of details of the observed experimental data, and that the extracted nuclear deformation lengths from this analysis agree with those from light-ion experiments.     

Quantal description of inelastic heavy-ion scattering

A model Schrödinger equation for scattering with energy loss is discussed. The equation is linear and is closely related to the coupled-channels approach to elastic and inelastic scattering. A possible parametrization of the model for applications to heavy-ion scattering is considered.