Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

12C induced transfer reactions on 56Fe

Transfer reactions ⁵⁶Fe(¹²C, xN) have been investigated. Angular distributions of particles following elastic scattering, one neutron and one proton transfer reaction channels leading to low lying states in respective residual nuclei have been measured. These are analysed using the coupled reaction channel (CRC) formalism. Starting with a double folded real potential, the elastic scattering angular distribution is calculated using the computer code FRESCO. Inclusion of couplings to first excited states in both the target and the projectile already tends to describe the experimental elastic scattering distribution. Additional coupling of one neutron transfer reaction to first five excited states in ⁵⁵Fe and one proton transfer reaction to first three low lying states in ⁵⁷Co improves fit to the elastic scattering angular distribution. Further refinement in fit is brought about by addition of a weak imaginary potential to the complex potential calculated by ERESCO to simulate the absorption effects due to those channels whose coupling is not included explicitly. Such a potential describes the experimental angular distributions for elastic, one neutron and one proton transfer channels correctly in shape and magnitude without any arbitrary normalisation.     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

Long range absorption and other optical-model effects from strong inelastic coupling

An optical potential component is constructed to represent the effect of a strongly coupled inelastic excitation upon elastic scattering. In the particular case of quadrupole Coulomb excitation a long range imaginary potential component is derived in closed form. The effects of long range absorption upon the elastic scattering are considered in a general way by inserting this potential into a weak absorption model and deriving an elastic scattering cross section in closed form. Below the Coulomb barrier the formula takes a simple form which may be related to the semiclassical theory of Coulomb excitation. The potential component arising from nuclear excitation of an inelastic state may be evaluated numerically on a computer. Two examples computed (50 MeV α-scattering on ¹⁵⁴Sm and 60 MeV ¹⁶O scattering on ⁴⁰Ca) exhibit strong l-dependence in the potential component.     

Elastic scattering of 1-GeV protons by nuclei

The calculated elastic scattering of 1.04-GeV protons by ²⁰⁸Pb, ⁵⁸Ni, and ⁴⁰Ca is compared with experiment. The effects of the spin-orbit potential, Pauli and short-range correlations, variations in the ratio of the real to the imaginary part of the nucleon-nucleon scattering amplitude at 0° are found to have similar effects. Further experiments are required before these effects can be disentangled. Changes of the neutron density compared to the proton density can be distinguished. The proton polarization by elastic scattering by ²⁰⁸Pb and ⁴⁰Ca is calculated omitting the effects of correlations.     

Anomaly in α-scattering from 6Li between 35 and 45 MeV

The elastic scattering of α-particles on ⁶Li nuclei has been measured from 20° to 170° (c.m.) and the inelastic scattering to the first excited state of ⁶Li has been measured for forward and backward angles. The elastic scattering angular distributions are calculated (i) in terms of pure potential scattering, (ii) in terms of potential scattering with an l-cut-off on the imaginary part of the potential and (iii) in terms of the coherent addition of the potential scattering amplitude and of the exchange amplitude. The third method gives the best fit to the data. The inelastic angular distributions are compatible with the macroscopic calculations, except in the very backward region where exchange phenomena are also shown to dominate.     

Calculation of the 6He + p elastic scattering cross sections within the folding approach and the high-energy approximation for the optical potential

Data on cross sections for the ⁶He + p elastic scattering at energies of tens of MeV/nucleon are analyzed by calculating the microscopic optical potential (OP) (its real and imaginary parts). The effect produced on the cross section by the dependence of the nucleon-nucleon potential on the nuclear matter density, the role of the spin-orbit interaction, and the role of nonlinearity and renormalization of the microscopic OP are studied. A comparison with the experimental data allows sensitivity of cross sections to these effects to be tested.     

The contribution of nuclear inelastic excitation to the optical potential for heavy ions

Using the plane-wave approximation we derive analytical expressions for both the real and imaginary parts of the polarization potential arising from nuclear inelastic scattering. These potentials and the resulting elastic and inelastic cross sections are compared with exact coupledchannel calculations for ¹³C on ⁴⁰Ca at 68 MeV. The agreement, for the most part, is good. We also briefly discuss the numerical non-local potentials for this system and the imaginary polarization potential for ¹⁶O on ²⁰⁸Pb at 104 MeV.     

Isobar dynamics and pion-nucleus elastic scattering

A new formalism is developed for studying pion-nucleus scattering in a model which takes into account the dynamics of the (3, 3) pion-nucleon resonance, or Δ isobar. This treatment is used to calculate π⁺ elastic scattering from ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb at energies from 114 to 240 MeV. Some results for π^? elastic scattering are also given. From fits to π⁺ scattering data it is found that the Δ-nucleus interaction is well described by a spherical local complex potential proportional to the nuclear density. The central strength of this potential depends on energy but not on nuclear mass number. Some difficulties in determining the parameters of this potential from elastic scattering are discussed.     

Proton elastic scattering and coupling to pickup channels

Calculations have been carried out for elastic scattering of protons on ⁴⁰CA in which pickup channels are strongly coupled to the elastic channels. These calculations strongly suggest that transfer channels contribute significantly to both the real and imaginary parts of the local optical potential.     

Calculation of the imaginary part of the heavy ion potential

The paper contains a numerical evaluation of the expressions for the absorptive potential in heavy ion reactions given earlier. With a standard folding expression for the real part of the ion-ion potential general good agreement is found with experimental data for the angular distributions of elastic and inelastic scattering. Special interest is attached to the case of ¹⁶O + ²⁸Si where the calculated imaginary potential is very small at low bombarding energies.     

Pauli Correlation Effect for the Elastic Scattering of Protons by Different Nuclei at 800 MeV

The angular distributions of the elastic scattering of protons at an energy of 800 MeV by ¹⁶O and ²⁰Ne nuclei are described in terms of the optical model scattering theory. Single folding model is applied to calculate the optical potential taking the effective nucleon-nucleon interaction to be in two forms. One form includes the zero-range pseudo-potential term and the other includes a two-body Pauli correlation function. Analytical expressions for the real part of the optical potential are obtained for both forms. The imaginary part of the optical potential is taken to be of the Woods-Saxon's shape. It is found that introducing the Pauli correlation function improves the agreement with the experimental data for the elastic scattering differential cross-sections of protons with the target nuclei ¹⁶O and ²⁰Ne.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

A new look at nuclear glory

It is shown that the surface transparency of the nuclear optical potential is responsible for the rise of the elastic cross section at large angles. We suggest the interpretation that by decreasing the radius of the imaginary potential, the formation of surface waves is supported. Numerical results applied to the elastic scattering of-particles on⁴⁰Ca are compared fairly well with experiment over a large range of c.m. angles.     

Large-angle 6Li + 28Si elastic and inelastic scattering at 27 and 34 MeV

Elastic and inelastic scattering data extending to θ_c.m ≈ 175° are reported for ⁶Li + ²⁸Si at 27 and 34 MeV. Optical model analyses of the elastic data were made using a variety of real potential forms. The large-angle data cannot be fitted with a Woods-Saxon real potential, but are well described by Woods-Saxon squared, double-folded or Fourier-Bessel potentials. The real potential is the same at both energies, but the imaginary potential is weaker at 27 MeV. The inelastic data were analyzed using the DWBA and coupled channels techniques with folded real form factors and deformed Woods-Saxon imaginary potentials, with the deformations taken from electron scattering. The 2⁺ state was fitted well at both energies with the DWBA, while the prediction decreased too rapidly at large angles for the 4⁺ state. The large-angle 4⁺ data were better described when two-step excitations were included in the coupled-channels calculations. The forward-angle 2⁺ data are sensitive to the interference between Coulomb and nuclear scattering and show that the nuclear and Coulomb deformation parameters β₂ are equal for this transition.     

Energy dependence of the optical potential for 16O + 28Si,elastic scattering in the energy range of E = 55–215 MeV

The energy dependence of an optical potential which reasonably fits all of the existing experimental data on ¹⁶O + ²⁸Si elastic scattering in the energy range of E = 54.7–215.2 MeV is studied. The real part of the potential found for this system shows a transition from a proximity to a double-folding type of the potential as a result of quenching of the Pauli principle effects with an increase of the incident energy. The imaginary part shows a transition from a surface-transparent to a strongly absorptive type of the potential.     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

A nuclear structure approach to the nucleon-nucleus optical potential at low energy

An antisymmetrized microscopic calculation of the optical potential for nucleon-⁴⁰Ca elastic scattering is derived. RPA correlations taken into account in the one-particle mass operator are shown to bring a correction to the first-order real potential at low energies and to lead to an imaginary potential. Both are calculated for incident nucleon energies between 10 and 50 MeV. Their general properties are studied in great detail and, after comparison with empirical imaginary potentials, the reliability of such an approach is discussed according to the value of the incident energy.