Influence of breakup on elastic and α-production channels in the ~6Li+~(116)Sn reaction

The effects of breakup reactions on elastic and α-production channels for the ~6Li+~(116)Sn system have been investigated at energies below and near the Coulomb barrier. The angular distributions of α-particle production differential cross sections have been obtained at several projectile energies between 22 and 40 MeV. The measured breakup α-particle differential cross sections and elastic scattering angular distributions have been compared with the predictions of continuum-discretized coupled channels(CDCC) calculations. The influence of breakup coupling has also been investigated by extracting dynamic polarization potentials(DPP) from the CDCC calculations. From the predictions of CDCC calculations the relative importance of the nuclear, Coulomb, and total breakup contributions have also been investigated. The nuclear breakup couplings are observed to play an important role in comparison to the Coulomb breakup for the direct breakup mechanisms associated in the reaction of ~6Li projectile with ~(116)Sn target nuclei. The influence of strong nuclear breakup coupling exhibits suppression in the Coulomb-nuclear interference peak. The direct breakup cross sections from the CDCC calculations under-predict the measured α-particle differential cross sections at all energies. This suggests that the measured α particles may also have contributions from other possible breakup reaction channels.     

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.     

Generalized fresnel model for very heavy ion scattering: (III). Dynamic polarization effects

It is shown that the large deviations from the typical Fresnel shape of heavy ion angular distributions, observed recently in the elastic scattering from deformed nuclei, can be described quite adequately by a very simple modification of the closed formulae for the differential cross section ratio $\text{gs(θ)}\text{σ}{}_{\mathrm{R}}\text{(θ)}$ of the generalized Fresnel model presented in parts I and II of this work. Our treatment rests basically on the relatively long range of the dynamic polarization potential that describes the Coulomb excitation to which the large deviations from the normal Fresnel pattern are attributed. We also calculate the effects of nuclear coupling in an adiabatic approximation and show that these lead to another modification, this time of the damping function F(z), which is however much smaller than that for Coulomb excitation and hardly discernible in angular distributions for very heavy ion scattering.     

Halo structure of 11Li in proton scattering: A folding model description with isospin,density and momentum dependent effective interaction

Recent ¹¹Li+p elastic scattering data at 62, 68.4, and 75 MeV and inelastic scattering data at 68.4 MeV, taken at RIKEN, are analysed with an isospin, density and momentum dependent finite range effective interaction (SBM) and M3Y interaction in a single folding model. The M3Y folded ¹¹Li+p potentials are found to be almost similar to the folded ⁹Li+p potentials. But the SBM folded ¹¹Li+p potentials are distinctly different, causing small but significant change in the angular distribution. Folded potentials need appreciable reduction factors indicating possible effects of strong breakup channel coupling. No significant change in results is found if ⁹Li core + Gaussian two-neutron halo density is used instead of the COSM density of ¹¹Li although the radial extent of the latter is much larger. The angular distribution of the recently discovered excited state at 1.3 MeV, well reproduced by the SBM folded potential, is found to be predominantly dipole in nature.     

Global optical model potentials for symmetrical lithium systems: 6Li+6Li, 7Li+7Li at Elab = 5–40 MeV

Angular distributions of ⁶Li+⁶Li elastic scattering were measured for E_lab = 5–40 MeV. An optical model analysis of these data together with older data of ⁷Li+⁷Li elastic scattering taken at E_lab = 8–17 MeV was performed with the aim to search for a “global” OM potential which describes elastic scattering in both LiLi systems in a broad energy range. Both surface and volume absorbing potentials can be found which fulfill this requirement if a linear energy dependence is assumed of the depths of the real as well as the imaginary potential. These depths, if fitted to individual angular distributions, are found to vary in a correlated manner with the beam energy. This is taken as indication of strong coupling between elastic, inelastic, and reaction channels. This is corroborated by the existence of resonances in reaction channels at these energies where the potential depths are most pronouncedly changing.     

Coulomb and nuclear excitation in the sequential break-up of6Li

The dissociation of⁶Li in the field of²⁰⁸Pb has been measured above the Coulomb barrier along with the elastic scattering. The inelastic angular distributions showing typical Coulomb nuclear interference structure can be very well reproduced by refined optical model calculations.     

Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the ³²S+¹⁸⁴W reaction near Coulomb barrier energies are measured. The experimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of ³²S+^90,96Zr in an energy range from above to below the Coulomb barrier are measured and analyzed within a semi-classical model. The obvious effect of positive Q-value multi-neutron transfers on the sub-barrier fusion enhancement is observed in the ³²S+⁹⁶Zr system. In addition, the excitation functions of quasi-elastic scattering at a backward angle have been measured with high precision for the systems of ¹⁶O + ²⁰⁸Pb, ¹⁹⁶Pt, ¹⁸⁴W, and ^154,152Sm at energies well below the Coulomb barrier. Considering the deformed coupling effects, the extracted diffuseness parameters are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. The elastic scattering angular distribution of ¹⁷F+¹²C at 60 MeV is measured and calculated by using the continuum-discretized coupled-channels (CDCC) approach. It is found that the diffuseness parameter of the real part of core-target potential has to be increased by 20% to reproduce the experimental result, which corresponds to an increment of potential depth at the surface region. The breakup cross section and the coupling between breakup and elastic scattering are small.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

Channel coupling and exchange of an alpha-particle cluster in deuteron scattering on 6Li nuclei

Existing experimental data on elastic and inelastic deuteron scattering on ⁶Li nuclei in the energy range from 8 to 50 MeV were analyzed within the approach of coupled reaction channels. The coupling of elastic scattering and inelastic scattering accompanied by the transition to the 3⁺ state at E _x = 2.186 MeV and the mechanism involving the exchange of an alpha-particle cluster were taken into account in respective calculations. The phenomenological potentials obtained from the present analysis describe well experimental angular distributions at all energies and in full angular ranges. The depths of the real and imaginary parts of the potentials in question depend smoothly on energy at fixed values of the remaining parameters. The energy dependence of relevant volume integrals agrees well with similar data for the p + ⁶Li, ?? + ⁶Li, and ¹²C + ¹²C systems and with the predictions of a microscopic theory.     

Elastic scattering and total reaction cross section for the He + Al system

The elastic scattering of the radioactive halo nucleus ⁶He on ²⁷Al target was measured at four energies close to the Coulomb barrier using the RIBRAS (Radioactive Ion Beams in Brazil) facility. The São Paulo Potential (SPP) was used and its diffuseness and imaginary strength were adjusted to fit the elastic scattering angular distributions. Reaction cross-sections were extracted from the optical model fits. The reduced reaction cross-sections of ⁶He on ²⁷Al are similar to those for stable, weakly bound projectiles as ^6,7Li, ⁹Be and larger than stable, tightly bound projectile as ¹⁶O on ²⁷Al.     

Elastic and inelastic scattering of 6Li and 7Li by 54Fe at E = 36–50 MeV

Detailed angular distributions for the elastic and inelastic scattering of ⁷Li at E = 36, 42, and 48 MeV and of ⁶Li at E = 38, 44, and 50 MeV by ⁵⁴Fe have been measured. It is not possible to describe both sets of data with the same set of optical-model parameters. The ratio of $\text{U}\text{W}$ is 0.8 for ⁷Li and 1.4 for ⁶Li at the strong absorption radius, implying stronger absorption for ⁷Li than for ⁶Li. No energy dependence in the optical-model parameters was necessary for either ⁶Li or ⁷Li. The inelastic scattering from the ⁵⁴Fe 2⁺, 1.41 MeV state was well described by the DWBA and the extracted deformation length (βR = 0.62) was the same for both ⁶Li and ⁷Li scattering. It was not possible to describe the ⁷Li projectile excitation data with collective-model DWBA calculations showing that more detailed calculations for the projectile excitation are necessary.     

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.     

Elastic and inelastic scattering of 58Ni +90,94Zr

Pure elastic and inelastic scattering cross sections have been measured for the systems ⁵⁸Ni +^90,94Zr at energies near the Coulomb barrier where not only quasi-elastic and fusion but also deep-inelastic process come into play. Coupled channels calculations including both projectile and target inelastic excitations can successfully explain the elastic and inelastic scattering angular distributions with an energy-independent semi-empirical bare potential. The calculation reproduces also the sum of the total quasi-elastic, fusion and deep-inelastic cross sections. Received: 14 September 1998 / Revised version: 21 October 1998     

Semiclassical theory of analysing powers for polarised heavy-ion elastic scattering

A unified semiclassical theory of analysing powers of all ranks for polarised heavy-ion elastic scattering from a spin-zero target at energies above the Coulomb barrier is presented. Illustration is provided for by specialising to the two interactions, spin-orbit and tensor. The present approach recovers the phenomenological result, obtained by taking the difference of the nuclear overlap between unpolarised and aligned projectiles (shape-effect model), which successfully explained the structureless pattern of rank-2 observables for aligned ⁷Li + ⁵⁸Ni at E_lab ～ 20 MeV. Deviations observed for ⁷Li + ¹²C (oscillations) are interpreted as due to interference between diffraction (positive-angle) and negative-angle scattering terms.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.     

Scattering of radioactive nuclei 6He and 3H by protons: Effects of neutron skin and halo in 6He, 8He,and 11Li

In an experimental study of ⁶He+p and ³H+p collisions at ∼70 A MeV, the elastic scattering angular distributions were measured and the known excited state ⁶He_1.8¹ was observed. Comparative analysis of existing experimental data on proton elastic scattering by ⁴He, ⁶He, ⁶Li, ⁸He, ⁹Li, and ¹¹Li was performed. Effects of valence neutrons were investigated using the eikonal approach. A difference between ¹¹Li and ^6,8He was found.     

Experimental study of the elastic scattering of ~(10)Be on ~(208)Pb at the energy of around three times the Coulomb barrier

Elastic scattering of 10Be on a 208Pb target was measured at ELab=127 MeV,which corresponds to three times the Coulomb barrier.The secondary 10Be beam was produced at the Radioactive Ion Beam Line in Lanzhou of the Heavy-Ion Research Facility in Lanzhou.The angular distribution of elastic scattering in the 10 Be+208Pb system shows a typical Fresnel diffraction peak.Optical model analysis of the angular distribution was performed using the Woods-Saxon,double-folding and global potentials.With the global potential,different density distributions were used.The results indicate that different density distributions for the projectile induce distinct effects in the angular distribution.     

A comparative analysis of the density distributions and the structure models of <Superscript>9</Superscript>Li

In the present study, we have analysed the elastic scattering cross-section data of ⁹Li + ¹²C system at E _lab = 540 MeV and ⁹Li + ²⁰⁸Pb system at E _c.m. = 28.3 MeV for some cluster models and various density distributions of the ⁹Li nucleus. First, we have obtained five different density distributions of the ⁹Li nucleus to generate real potentials with the help of double-folding model. For these densities, we have calculated the elastic scattering angular distributions. Secondly, using a simple approach, we have investigated some cluster models of the ⁹Li nucleus consisting of ⁶He + ³H and ⁸Li + n systems. We have presented the comparison of elastic scattering angular distributions for each system with each other as well as with the experimental data. Finally, we have given the cross-section values obtained from the theoretical calculations for all the systems studied in this paper.     

Elastic scattering and reactions of light exotic beams

The present work provides a literature survey of elastic scattering of exotic nuclei from ⁶He to ¹⁷F. It presents a set of definitions that allow different analyses to be put into a common language. A calculational approach is proposed that yields consistent results across different beams and targets so that conclusions concerning the influence of virtual and real breakup as well as transfer couplings on the elastic scattering may be drawn. Calculations of elastic scattering around the Coulomb barrier are emphasised, employing a Pb target whose large Z allows the interplay between nuclear and Coulomb forces to be exploited to maximise possible effects arising from proton or neutron haloes or skins. A series of test calculations is performed and where possible compared to data, demonstrating that there are instances where coupling to transfer channels can have a large effect on the elastic scattering angular distributions. By careful choice of target/beam combination, different aspects of the coupling effects may be emphasised.     

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the ⁶Li + ¹¹⁸Sn and ⁶Li +²⁰⁸Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state (E_x = 2.18 MeV, J^π = 3⁺) of ⁶Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier (¹¹⁸Sn: E/E_c ≈ 1.3; ²⁰⁸Pb: E/E_c ≈ 0.9) are: neutron transfer (⁶Li, αp) and the non-sequential α + d break-up of ⁶Li. The latter spectra are consistent with a quasi-free break-up mechanism. No ³He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of ⁶Li into α + p + n.