Optical-model analysis of 7Li + 25Mg and 7Li + 27Al elastic scattering at 89 MeV

The elastic scattering angular distributions for ⁷Li + ²⁵Mg and ⁷Li + ²⁷Al were measured at $\text{E(}{}^7\text{Li}\text{) = 89}\text{MeV}$ over angular ranges of 8–55° c.m. and 8–64° c.m. Previously published measurements for ^{24, 26}Mg at 89 MeV and ²⁴Mg at 34 MeV are reanalyzed. The cross sections were analysed using a 6-parameter phenomenological Saxon-Woods potential. No discrete ambiguities were found but the usual continuous ambiguities exist. The data were also analysed with double folded real potentials generated using the M3Y effective interaction. The folded potential must be multiplied by about 0.6 to fit the data. The extent to which ⁷Li optical-model potentials are determined and suggestions for further work on the normalization of the folded potential are discussed.     

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.     

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.     

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.     

Systematic analysis of 17,19F and 16,17O elastic scattering on 208Pb just below the coulomb barrier

The ¹⁷F, ¹⁷O + ²⁰⁸Pb elastic scattering at 90.4 and 78 MeV (just below coulomb barrier), respectively, are analyzed within the framework of the double folding approach. The folded potentials are constructed by folding the density independent M3Y effective nucleon-nucleon interaction over the nucleon density distribution of ¹⁷F and its mirror ¹⁷O nuclei. Gaussian oscillator (GO) density distribution is considered to represent the (core¹⁶O+nucleon) structure for ¹⁷F and ¹⁷O. The knock-on exchange potentials are introduced to construct the real semi-microscopic potentials. The imaginary potentials are supplemented to derive potentials in two forms: either phenomenological Woods-Saxon (WS) or the same form as real folded potentials and different strengths. Moreover, the analysis of ¹⁹F, ¹⁶O + ²⁰⁸Pb elastic scattering at 91, 78 MeV energies, in that order, is applied in comparison to the ¹⁷F, ¹⁷O + ²⁰⁸Pb systems in an endeavor to investigate the behavior and properties of ¹⁷F and ¹⁷O projectiles.     

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.     

Precision measurement of the muonic 5-4 transitions in Pb and 4-3 transitions in ba as a test for the validity of QED

The real parts of the optical model potentials for 104 MeV alpha-particle and 156 MeV⁶Li ion scattering from^{40, 48}Ca are calculated in terms of folding model approaches. The validity of different procedures is tested by comparing the differential cross section predictions with experimental data measured with high angular accuracy. It is found that a refined folding potential accounting for density dependence of an effective nucleon-nucleon interaction is appropriate for alpha particle scattering without any parameter adjustment. However, for⁶Li ion scattering renormalization of the depth of the real potential is necessary.     

Isotopic effects in the 7Li + 10, 11B elastic and inelastic scattering

Angular distributions of the ⁷Li + ¹⁰B elastic and inelastic scattering were measured at the energy E _lab (¹⁰B) = 51 MeV (21 MeV c.m.). These and previously measured ⁷Li + ¹⁰B elastic-scattering data known at the ⁷Li-beam energies 24 MeV (14.1 MeV c.m.) and 39 MeV (22.94 MeV c.m.) were analyzed within the optical model and coupled-reaction channels method to determine the energy dependence of the parameters of the scattering potential and find the difference of these parameters from that of ⁷Li + ¹¹B scattering. It was found that the ⁷Li + ¹¹B potential parameters fail to describe the ⁷Li + ¹⁰B scattering data. The biggest difference is observed between the depths of the imaginary potentials that describe these scatterings.     

Double folding model analysis of elastic scattering of halo nucleus 11Be from 64Zn

Calculations of elastic scattering cross-sections for ^9,10,11Be + ⁶⁴Zn at near-Coulomb barrier energy have been performed using a potential obtained from the double folding model and are compared with the experiment. In the framework of the double folding model, the nuclear matter densities of ^9,10,11Be projectiles and a ⁶⁴Zn target are folded with the complex energy-dependent effective M3Y interaction. The angular distributions of the differential cross-section for ^9,10Be scattering from ⁶⁴Zn at E _c.m≈ 24.5 MeV agree remarkably well with the data, while in case of ¹¹Be, calculations show a Coulomb–nuclear interference peak which is not observed in the data.     

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.     

Comparative analysis of the characteristics of the elastic scattering of protons by lithium isotopes 6, 7, 8, 9Li, performed using Glauber’s multiple diffraction scattering theory

Differential cross sections and vector analyzing powers are calculated for the elastic scattering of protons by lithium isotopes ⁶Li, ⁷Li, ⁸Li, and ⁹Li at energies of 60 and 200 MeV. The calculations are performed using Glauber??s multiple diffraction scattering theory in the two-particle (for ⁷Li) and three-particle (for ^6,8,9Li) models with realistic intercluster interaction potentials. An analysis of the relationship between the differential elastic scattering cross section and various wave functions, calculated using different interaction potentials, is presented for the ^{8, 9}Li isotopes.     

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.     

Elastic scattering and single nucleon transfer reactions for 7+11B and 7Li+13C at 34MeV

Elastic scattering cross sections for 10–170° c.m. have been measured for ⁷Li+¹¹B and ⁷Li + ¹³C at 34 MeV. These data have been analyzed with the optical model using Woods-Saxon potentials, or potentials with a double-folded real part. The double-folded potentials were found to fit the data better, and quadrupole contributions were required to fit the large angle ⁷Li+¹¹B data. In addition angular distributions for the (⁷Li, ⁸Li), (⁷Li, ⁶Li) and (⁷Li, ⁶He) reactions were measured. The transfer data were analyzed with finite-range DWBA calculations which were able to describe the shape of the data well and produced spectroscopic factors in agreement with theoretical and other experimental values. A phase shift of about 3° between the calculations and the data was found for the (⁷Li, ⁶Li) and (⁷Li, ⁶He) reactions.     

Examination of the <Superscript>16</Superscript>O + <Superscript>28</Superscript>Si system with microscopic and phenomenological potentials

The ¹⁶O + ²⁸Si reaction has been widely studied both experimentally and theoretically and has been claimed to show indications of chaotic scattering. In order to examine this claim and to address whether reaction models such as the optical one could explain the experimental data, we have analyzed the ¹⁶O + ²⁸Si system within the framework of the optical model for ten energies from 29.0 to 45.0 MeV, by using microscopic folded potentials, which are based on M3Y nucleon-nucleon, alpha-alpha effective interactions and a phenomenological shallow potential. All potentials describe the individual angular distributions very well at forward angles. However, they fail to describe the individual angular distributions over the whole angular range up to 180°. Nevertheless, we have been able to explain the experimental data by modifying the surface region of the microscopic real potentials by adding two surface potentials. With these correction potentials, we have obtained very good agreement for the individual angular distributions over the whole angular range for the given energies as well as for the experimental data near the Coulomb barrier. The failure of these optical potentials in explaining the scattering observables of this reaction without corrections puts a question mark on the model and supports the idea of a chaotic behavior. The text was submitted by the authors in English.     

Comparison of 7Li , 7Be + 9Be elastic scattering in the coupled-reaction-channels approach

The data for the ⁷Li + ⁹Be and ⁷Be + ⁹Be elastic scattering at the energies E _lab(⁷Li) = 15.75 , 24, 30, 34, 63 and 130MeV and E _lab(⁷Be) = 17 , 19 and 21MeV were analyzed within the optical model and coupled-reaction-channels method. The elastic and inelastic scattering, reorientation of ⁷Li , ⁷Be and ⁹Be as well as most important transfer reactions were included in the coupled-channels scheme. The resulting ⁷Li and ⁷Be potentials are very similar and have the same energy dependence. The real potential for recently derived ⁸Be + ⁹Be scattering potentials is very similar to that for ⁷Li , ⁷Be but the imaginary part of the ⁸Be one has a much greater strength at longer range.     

Breakup effects of 6,7li on elastic and inelastic scattering from 12C at 18–28 MeV/nucleon

The differential cross sections for elastic scattering of ^6,7Li from ¹²C and inelastic one from the lowest three excited states of ¹²C have been measured at bombarding energies of 18–28 MeV/nucleon. Theoretical analyses of the data have been performed in which consistent treatments of density distributions for the ground and excited states of both projectile and target nuclei are made in the framework of microscopic cluster models for ^6,7Li and ¹²C and projectile-target interactions are generated by the double folding of the M3Y effective nucleon-nucleon interaction. About 25% reduction of the real part of folded potentials is required both in the analyses of elastic scattering with the single-channel calculation and in those of inelastic scattering with the coupled-channel calculation including the excited states of ¹²C. This reduction can be explained as a projectile breakup effect on elastic and inelastic scattering in comparison with a coupled-discretized-continuum-channels (CDCC) calculation and an extended CDCC one which allows mutual excitations of both projectile and target nuclei for ⁶Li case, respectively. It is also seen that an effect due to the target excitation on elastic scattering is of less importance than that of the ^6,7Li projectile breakup processes even fora deformed nucleus like ¹²C. Discrepancy between the extended CDCC calculation and inelastic data for the 0⁺₂ state of ¹²C suggests a strong influence from the ¹²C → 3α breakup channels in the ⁶Li case.     

A Comprehensive Theoretical Analysis of <Superscript>6,7</Superscript>Li + <Superscript>64</Superscript>Zn Elastic Scattering in a Wide Angular Range Around the Coulomb Barrier

In this paper, the elastic scattering angular distributions of ^6,7Li on ⁶⁴Zn have been investigated by using various nuclear potentials. For this, we use the phenomenological Woods-Saxon potential, the real double folding potential with the density-independent M3Y effective interaction supplemented with an imaginary part in Woods-Saxon form and the double folding potentials multiplied with a normalization factor of the real and imaginary parts via the density-independent and CDM3Y6 density-dependent versions of the M3Y effective interaction have been used. The results have been compared with each other as well as with the experimental data. It has been observed that the agreement between the theoretical results and earlier reported data is perfect. Finally, the change of the total reaction cross sections with energy has been investigated.     

Particles versus fields in $$ \mathcal{P}\mathcal{T} $$-symmetrically deformed integrable systems

The elastic scattering and the ⁶He angular distributions were measured in ⁷Li + ⁷Li reaction at two energies, E _lab = 20 and 25 MeV. FRDWBA calculations have been performed to explain the measured ⁶He data. The calculations were very sensitive to the choice of the optical model potentials in entrance and exit channels. The one-step proton transfer was found to be the dominant reaction mechanism in ⁶He production.