Astrophysical <Emphasis Type="Italic">S</Emphasis> factor for the radiative-capture reaction <Emphasis Type="Italic">p</Emphasis><Superscript>6</Superscript>Li → <Superscript>7</Superscript>Beγ

A new measurement of differential cross sections for elastic p ⁶Li scattering in the energy range 0.35–1.2 MeV was performed. A partial-wave analysis of the data obtained in this way was carried out, and potentials simulating the p ⁶Li interaction were constructed. Various experiments devoted to studying elastic p ⁶Li scattering over the broad energy range of 0.5–50 MeV were analyzed on the basis of the optical model. By using the potentials obtained from the partial-wave analysis, the possibility of describing the astrophysical S factor for radiative proton capture on ⁶Li at low energies was considered within the potential cluster model involving forbidden states.     

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.     

Radiative neutron capture by 2H, 7Li, 14C, and 14N nuclei at astrophysical energies

The possibility of describing experimental data on the total cross sections for the n ²H, n ⁷Li, n ¹⁴C, and n ¹⁴N radiative-capture processes within the potential cluster model involving forbidden states and their classification according to Young’s tableaux is considered. It is shown that this model and the methods used here to construct potentials make it possible to describe correctly the behavior of the experimental cross sections at energies between 5 to 10 meV (5 × 10^?3–10 × 10^?3 eV) and 1 to 15MeV.     

Elastic scattering of protons from 9Li in inverse kinematics within diffraction theory

The differential cross section for elastic scattering of protons from the ⁹Li nucleus has been calculated within the framework of the Glauber multiple scattering theory. The calculations were carried out with two versions of cluster wave functions for the nucleus obtained within the α-t-2n and ⁷Li-n-n three-body models with realistic potentials of intercluster interactions. The differential cross section was calculated at E = 700 and 60 MeV/nucleon. A comparison with the experimental data allows the conclusion that the wave function in the ⁷Li-n-n model describes the cross section better than in the α-t-2n model.     

Structure of light neutron-rich nuclei and mechanism of elastic proton scattering

Differential cross sections for elastic p ⁶He, p ⁸Li, and p ⁹Li scattering at two energies of 70 and 700 MeV per nucleon were calculated within the Glauber theory of multiple diffractive scattering. Threeparticle wave functions (α-n-n for ⁶He, α-t-n for ⁸Li, and ⁷Li-n-n for ⁹Li) were used for realistic potentials of intercluster interactions. The sensitivity of elastic scattering to proton-nucleus interaction and to the structure of nuclei was explored. In particular, the dependence of the differential cross section on the contribution of higher order collisions, on scattering on the core and peripheral nucleons, and on the contribution of small wave-function components and their asymptotic behavior was determined. A comparison with available experimental data and with the results of calculations within different formalisms was performed.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor of the <Emphasis Type="Italic">p</Emphasis><Superscript>7</Superscript>Li → <Superscript>8</Superscript>Beγ capture at low energies

The interaction potentials describing some phases of elastic p ⁷Li scattering for energies up to 0.8 MeV and the ground bound P ₀ state of the ⁸Be nucleus in the p ⁷Li cluster channel are obtained. The astrophysical S-factor of the p ⁷Li → ⁸Beγ radiative capture is considered for the potential cluster model.     

Electric dipolarizability of <Superscript>7</Superscript>Li

We calculate the electric dipolarizability of ⁷Li nucleus within the cluster model and estimate a value of about 0.0188 fm³. We also discuss the possibility of observing this in the scattering of ⁷Li from a ²⁰⁸Pb target at energies about 30 MeV.      

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.     

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.     

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.     

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.     

Evidence for the constant-matrix-element mechanism in the breakup of the3He+7Li system and highly excited states in6Li

The inclusive alpha particle spectra from the breakup of the³He+⁷Li system atE ³He=42.9 MeV are analyzed in the frame of the nuclear reaction model whose matrix element does not depend on the relative energies of the outgoing particles and is therefore constant. The comparison with a recent analysis of thep+⁹Be interaction, leading to the same composite system, has shown the correlation of the final-state configuration on the entrance-channel cluster structure.the existence of broad excited states for⁶Li excitation energies between 19 and 28 MeV is confirmed.     

Vector analyzing power of π+7Li scattering in the region of the Δ33 resonance

Within Glauber diffraction theory, the vector analyzing power iT ₁₁ is calculated at three energies of positively charged pions, 134, 164, and 194 MeV, incident to ⁷Li nuclei. These energy values lie in the region of the Δ₃₃ resonance in π^± N interaction, the resonance maximum being at 180 MeV. The calculation of iT ₁₁ was performed with several model ⁷Li wave functions, including the αt-cluster and shell-model ones. The properties of π⁺⁷Li scattering are found to be sensitive to the structural features of the target nucleus. A comparison of the results of the calculations with experimental data shows that the wave functions in question and the potentials used to calculate them are quite appropriate.     

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.     

Optical model and DWBA analysis of the7Li(d,d)- and7Li(d,p 0)-reactions in the energy region 1.0 to 2.6 MeV

Absolute differential cross sections for the elastic scattering of deuterons by⁷Li have been determined in the energy range of 1.0 to 2.6 MeV. Two excitation curves measured at laboratory angles of 90° and 160° vary smoothly with energy. At higher energies an extremely strong enhancement of the cross section relative to the Rutherford value was observed at large angles. It was, however, possible to find realistic optical potentials that describe these distributions fairly well over the whole energy region. For two of these potentials good fits could be obtained with DWBA calculations on the⁷Li (d, p ₀)-reaction, one of them yielding a spectroscopic factor in close agreement with shell model predictions.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor of radiative <Emphasis Type="Italic">p</Emphasis><Superscript>6</Superscript>Li capture at low energies

A possibility of describing experimental data for the astrophysical S-factor of p⁶Li capture at low energies is discussed within the potential cluster model with forbidden states.     

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.     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.