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.     

半微观质子光学势

基于原子核壳模型单体密度矩阵的折叠模型计算光学势的实部,配以唯象光学势虚部,构造半微观光学势.通过拟合质子弹性散射实验数据,得到适用于质量数28~90,能量到200 MeV的半微观质子光学势.该光学势用于质子弹性散射计算分析,在参数大为减少的情况下,计算得到的角分布和分析本领与实验数据的符合程度,总体上好于Koning-Delaroche普适光学势的计算结果.     

Elastic scattering of 11B from 209Bi in the energy range 49.8 ⩽ E ⩽ 84.1 MeV

The elastic scattering of ¹¹B from ²⁰⁹Bi has been measured at laboratory energies of 49.8, 51.3, 52.2, 52.8, 54.3, 55.8, 59.8, 64.8, 69.8, 74.8 and 84.1 MeV. These data have been analyzed using a microscopic optical model and the energy dependence of the real and the imaginary parts of the optical potential at near barrier energies has been determined. The “threshold anomaly” observed in the real part of the potential is found to be consistent with the dispersion relation which connects the real and the imaginary parts of the potential. Inelastic scattering and transfer reactions have also been measured at energies of 51.3, 55.8, 59.8 and 74.8 MeV. DWBA calculations for the 3⁻ state in ²⁰⁹Bi are made. From the measured transfer probabilities, using a semiclassical approach the strength of the form factors have been obtained. The fusion cross sections have been derived at these energies from the corresponding quasi-elastic scattering angular distribution data. The fusion cross sections calculated using the energy dependent barriers extracted from the energy dependent real parts of the potential compare well with, that determined from quasi-elastic scattering data and are also in good agreement with simplified coupled channels calculation for fusion incorporating important inelastic and transfer channels.     

Microscopic analysis of the elastic scattering of 11Li neutron-rich nuclei on protons

Amicroscopic optical potential is used to calculate cross sections for elastic ¹¹Li +p scattering at the energies of 62, 68.4, and 75 MeV per nucleon, and the results are compared with available experimental data. The potential used does not involve free parameters, but the depths of its real and imaginary parts are renormalized. The known trend in the energy dependence of the volume integrals of the optical potential is taken into account in analyzing experimental data. The role of spin-orbit interaction is studied, and the total reaction cross sections that are proposed to be measured in future experiments are calculated.     

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.     

Modeling of a microscopic optical pion-nucleon potential at energies in the (3, 3)-resonance region and nuclear-matter effect on the pion-nucleon amplitude

Differential cross sections for elastic pion scattering on a number of nuclei at energies between 130 and 290 MeV are calculated. For this purpose, use is made of a microscopic optical pion-nucleus potential that was obtained on the basis of the Glauber theory of high-energy scattering and which is determined by the density distribution of pointlike target nucleons and by the pion-nucleon scattering amplitude. The calculation of the cross sections in question is based on solving the respective relativistic wave equation. Three parameters of the pion-nucleon amplitude are fitted in performing a comparison with experimental data. These are the total cross section for pion-nucleon scattering, the ratio of the real to the imaginary part of the forward pion-nucleon scattering amplitude, and the slope parameter. The resulting values of these parameters are then compared with their counterparts for scattering on free nucleons. The character of nuclear-matter-induced changes in these parameters is studied.     

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.     

The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.     

The proton optical-model potential near the Coulomb barrier

Proton elastic scattering data from ¹⁹⁷Au, ²⁰⁸Pb and ²⁰⁹Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths V_R and W_SF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of V_Rnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction.     

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.     

Elastic scattering and fusion cross-sections in 7Li + 27Al reaction

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the ⁷Li + ²⁷Al reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies (E _lab?=?8.0–16.0 MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured α-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of 1n-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.     

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.     

Microscopic study on proton elastic scattering of light exotic nuclei at energies below than 100 MeV/nucleon

The proton elastic scattering data on some light exotic nuclei, namely, ^{6, 8}He, ^{9, 11}Li, and ^{10, 11, 12}Be, at energies below than 100MeV/nucleon are analyzed using the single folding optical model. The real, imaginary, and spin-orbit parts of the optical potential (OP) are constructed only from the folded potentials and their derivatives using M3Y effective nucleon-nucleon interaction. These OP parts, their renormalization factors and their volume integrals are studied. The surface and spin-orbit potentials are important to fit the experimental data. Three model densities for halo nuclei are used and the sensitivity of the cross-sections to these densities is tested. The imaginary OP within high-energy approximation is used and compared with the single folding OP. This OP with few and limited fitting parameters, which have systematic behavior with incident energy, successfully describes the proton elastic scattering data with exotic nuclei.     

Total cross sections,real part of the amplitude,and slope of diffraction cones of the pp and ¯pp forward scattering

In the framework of the model described in [6], analytic expressions are obtained for the ratio of the real part of the forward scattering amplitude to its imaginary part, and for the total cross sections and the slopes of diffraction cones for hadron-hadron and hadron-antihadron interactions. A comparison with the existing experimental data for pp and pp interaction shows that that the computed values of parameters of the elastic scattering are in good qualitative and fair quantitative agreement with their observed values in a wide range of energies s = 5 to 546 GeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 65–70, May, 1990.     

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.     

Parametrization of woods-saxon potential for heavy-ion systems

Several elastic scattering angular distributions of ~(12)C from target nuclei of A ≥39 are analyzed to extract the Woods-Saxon potential parameters with the fixed imaginary potential and Coulomb radius parameters.Using the best fitted diffuseness parameters,the correlations of the real part parameters with A_1~(1/3)+ A_2~(1/3) and incident energy are revealed, and the systematic Woods-Saxon potential parameters are presented for nucleus-nucleus interaction.The proposed potential parameters can reproduce not only the elastic scattering angular distributions induced by ~(12)C,but also many elastic scattering angular distributions induced by the projectiles other than ~(12)C,thus providing important inputs for the study of nuclear reactions of heavy-ion systems.     

The real part of the nucleus-nucleus interaction

The real part of the interaction potential for several pairs of magic nuclei has been derived from the Skyrme interaction density functional. The matter density of each nucleus is described by a Fermi distribution adjusted to reproduce the Skyrme-Hartree-Fock densities. Exchange effects due to antisymmetrization are taken into account in an approximate way. The tail of the resulting potential can be accurately approximated with a Woods-Saxon shape beyond the inflexion point of the calculated potential. The parameters of these Woods-Saxon potentials show regularities with respect to the masses of the target and projectile. We have tested the validity of the real part of the potential against elastic scattering data by choosing an imaginary part with the same geometry and a variable strength. For the energy range we consider the calculated grazing angles are somewhat larger than the experimental ones.