Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for ⁷Be + ⁹Be system at E_lab = 17, 19 and 21 MeV in the angular range θ_cm=26^○–58°, and for ⁷Li + ⁹Be system at E_lab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the ⁷Li + ⁹Be system fusion cross sections were obtained at E_lab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.     

Strong reaction channels at barrier energies in the system 6Li + 208Pb

Large cross-section reaction channels were measured in the systems ⁶Li( ⁷Li) + ²⁰⁸Pb with high statistical accuracy at 5(3) energies around the Coulomb barrier from 29 to 39 MeV. These channels were assigned (mainly) to the breakup of ⁶Li, very loosely bound, into α + d and to the breakup of ⁵Li, produced by n-transfer to the target, into α + p and to similar processes with ⁷Li beam. The cross-sections with ⁶Li, S _α = 1.475 MeV, are systematically larger than the ⁷Li ones. This reflects, most likely, the higher binding energy of ⁷Li, S _α = 2.468 MeV. Theoretical predictions for the ⁶Li + ²⁰⁸Pb system which include for ⁶Li breakup to continuum states within a continuum discretized coupled-channels approach (CDCC) and resonant breakup plus n-transfer with DWBA reproduce the angular distribution shapes but still underestimate the cross-sections by a factor ∼ 3. Received: 15 January 2001 / Accepted: 3 March 2001     

Multiple particle break-up study of low excited states in <Superscript>9</Superscript>Be: The ghost peak in the <Superscript>8</Superscript>Be excitation energy spectrum visited

The aim of this work is to find out the origin of the anomalous resonance in ⁸Be seen in the reactions through excited states in ⁹Be. We have populated the ⁹Be excited states by β-decay of ⁹Li. Energy and direction of the two α particles has been detected and the neutron spectra reconstructed. In our work we identified the “anomalous resonance" in ⁸Be observed in several reaction studies as coming from the decay of the 2.43 and 2.78 MeV states in ⁹Be. This anomalous resonance appears when the two detected α particles are assumed to form a resonance in ⁸Be. We argued that the main decaying channels for these two levels in ⁹Be do not involve ⁸Be.     

Transfer, sequential decay, and quasi-free reactions induced by 18-MeV 6He beam on 6Li, 7Li, and 12C

The ⁶He + ^6,7Li and ⁶He + ¹²C scattering and reactions have been studied using an 18-MeV ⁶He beam. Experimental results for the elastic scattering on all three targets are in fair agreement with optical model predictions, using the potentials found in the analysis of the ⁶Li scattering on the same targets and at close beam energies. Several two-body exit channels show clear signatures of a direct reaction mechanism allowing extraction of spectroscopic information. The measured angular distribution for the ⁶He + ⁶Li → α + ⁸Li reaction indicated close similarity between the α + 2n configuration in ⁶He and the α + d configuration in ⁶Li. The obtained results for α-particle pickup from both ⁶Li and ⁷Li give large values of α spectroscopic factors for some ¹⁰Be states, indicating their well-developed α + ⁶He cluster structure. The exotic two-proton pickup reaction (⁶He, ⁸Be) was studied, as well as two-neutron and triton transfer reactions. Quasi-free scattering of ⁶He on deuteron and α particle in ⁶Li was also observed. The sequential decay reactions ⁶He + ⁶Li → ⁶He + α + d, ⁶He + ⁶Li → 2α + t + n, ⁶He + ⁷Li → ⁶He + α + t, and ⁶He + ¹²C → ¹⁰Be + 2α were clearly seen, and α clustering of some states in ^6,7Li, ^8–10Be, and ¹⁴C was thus studied. Several new spectroscopic results obtained for some ¹⁰Be states support the existence of a molecule-like rotational band in ¹⁰Be with a very large moment of inertia. The text was submitted by the authors in English.     

Three-body structure of <Emphasis Type="Italic">A</Emphasis> = 9 isobars (Be,Li, and C) and elastic proton scattering

Density profiles and static features (radii, magnetic moments, and quadrupole moments) are calculated with the wave functions found for A = 9 isobars on the basis of the α + α + n three-body model for the ⁹Be nucleus, the ⁷Li + n + n three-body model for the ⁹Li nucleus, and the ⁷Be + p + p three-body model for the ⁹C nucleus. The differential cross sections and analyzing powers for elastic proton scattering on ⁹Be at E = 220 MeV and 1.0 GeV and on ⁹Li and ⁹C at E = 700 and 60 MeV/nucleon (in inverse kinematics) are calculated within Glauber diffraction theory. All of the results are compared with available experimental data and with the results of the calculations performed by other authors.     

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.     

Effect of the structure of neutron-rich <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li isotopes on the characteristics of proton elastic scattering

The differential cross sections of proton elastic scattering from ⁸Li and ⁹Li nuclei in inverse kinematics have been calculated. The cross sections were determined within the Glauber diffraction theory with the wave functions of nuclei in the three-particle α-t-n, α-t-2n, and ⁷Li-n-n models. Comparison with the existing experimental data for E = 700 and 60 MeV/nucleon made it possible to draw a conclusion about the quality of the wave functions and the adequacy of the potentials used for their calculations.     

Nuclear molecular resonances in α+12C and α+16O systems

The nuclear molecular resonances observed in α+¹²C and α+¹⁶O systems are described in a diatomic-like molecular picture using a Morse-type bonding potential. The depths of the bonding potentials are found to be 11.5 MeV and 11 MeV respectively, with long range of about 15 fm. Both the bound and resonance states of these potentials are calculated which compare quite well with the observed states. The diatomic-like rotational and vibrational picture of the quasi-molecular states proposed earlier for¹²C+¹²C system system is found to be quite valid for α+¹²C and α+¹⁶O systems. In these two systems, the rotational vibrational characteristics are equally well pronounced as in the¹²C+¹²C system.     

7Li quasi-free scattering off the α-cluster in 9Be nucleus

Spectra of coincident charged particles from the reactions induced by a 52 MeV ⁷Li beam incident on a beryllium target were measured. Strong contributions of the ⁷Li quasi-free scattering off the α-cluster in ⁹Be nucleus were observed. This observation supports the conclusions from the study of complete fusion of weakly bound light nuclei at low energies that the “fragility” of the nuclei makes their fusion less probable. Received: 1 June 1998     

Influence of projectile breakup on complete fusion

Complete fusion excitation functions for ^11,10B+¹⁵⁹Tb and ^6,7Li+¹⁵⁹Tb have been reported at energies around the respective Coulomb barriers. The measurements show significant suppression of complete fusion cross-sections at energies above the barrier for ¹⁰B+¹⁵⁹Tb and ^6,7Li+¹⁵⁹Tb reactions, when compared to those for ¹¹B+¹⁵⁹Tb. The comparison shows that the extent of suppression of complete fusion cross-sections is correlated with the α-separation energies of the projectiles. Also, the measured incomplete fusion cross-sections show that the α-particle emanating channel is the favoured incomplete fusion process. Inclusive measurement of the α-particles produced in ⁶Li+¹⁵⁹Tb reaction has been carried out. Preliminary CDCC calculations carried out to estimate the α-yield following ⁶Li breaking up into α+d fail to explain the measured α-yield. Transfer processes seem to be important contributors.     

Low–energy photodisintegration of 9Be and α+α+n→9Be +γ reactions at astrophysical conditions

A semi–microscopic model for the low–energy photodisintegration of the ⁹Be nucleus is constructed, and the experimental data are analyzed with its help. The older radioactive isotope data are supported by this analysis. The theoretical photodisintegration cross section is derived. The astrophysical rates for the reaction α+α+n→⁹Be+γ and the reverse photodisintegration of ⁹Be are calculated. The new reaction rate for α+α+n→⁹Be+γ is compared with previous estimations. Received: 19 January 1998     

Microscopic three-cluster study of the low-energy 9 Be photodisintegration

The ⁹Be and ⁹B nuclei are investigated in a microscopic three-cluster model involving α + α + n (or α + α + p) configurations. The ⁸Be (0 ⁺ , 2 ⁺ ) + n and ⁵He (3/2 ^- , 1/2 ^- ) + α (or mirror) channels are included by taking account of the unstable nature of ⁸Be and ⁵He. Spectroscopic properties of ⁹Be and ⁹B are analyzed. We show that the ⁵He + α configurations cannot be neglected to derive accurate results. The ⁹Be(γ,αα)n photodisintegration cross-section is shown to be mainly determined by ⁸Be + n channels at low energies, but ⁵He + α channels become important beyond E _γ≈ 4 MeV. Received: 7 September 2001 / Accepted: 19 November 2001     

Neutron excess nuclei of hydrogen and helium at ACCULINNA

Attempt to observe a ⁷H resonance produced in the reaction ²H(⁸He,³He)⁷H resulted only in setting a limit dσ/dΩ≤ 20 μb/sr for the reaction exit channel which could populate a resonance lying between 0 and 3 MeV above the ⁷H decay threshold. The quasi-free scattering of the α core bound in ⁶He was explored keeping in mind the possible study of the cluster structure of this halo nucleus. For the first time coincident particles emitted in the ⁴He(⁶He, 2α)nn reaction were detected in wide angular ranges giving a wide kinematical range of the measured angular and momentum distributions. The contribution of processes, competing with QFS in the α+ α+n+n output channel, was considerably suppressed by the selection of events with E_α1(2)-nn>10 MeV. A number of experimental distributions, relevant to the reaction mechanism and to the ⁶He structure, were compared with the results of MC simulations based on the PWIA formalism. The PWIA predictions showed consistency with the experimental data.     

The characteristics of the <Superscript>8</Superscript>Be ground state in the effective-range approximation

We find the vertex constant for the synthesis α + α → ⁸Be and the corresponding asymptotic normalization coefficient of the Gamov wave function for ⁸Be in the ground state. We use modern data on the position and width of the narrow resonance of this state as well as the energy dependence of the αα scattering phase shift in the s-wave known from the literature. The effective-range theory was applied with the Coulomb interaction taken into account. The parameters of the standard effective-range function expansion up to the member with k ⁴ (k being the relative momentum) were found.     

Complete and incomplete fusion in reactions of 7Li + 56Fe at E(7Li) = 50 and 68 MeV from analysis of recoil range and light-particle measurements

Excitation functions for the production of eight radioactive products of the reactions of ⁷Li on ⁵⁶Fe have been measured up to E(⁷ Li) = 89 MeV. Recoil range distributions for these products, together with inclusive proton, deuteron, triton and alpha spectra, have been measured at energies of 50 and 68 MeV. The α, t and d spectra show characteristic “break-up” components at forward angles, while the recoil distributions show evidence of complete fusion and incomplete-fusion process ⁵⁶Fe( ⁷Li,α) ⁵⁹Co ^* . A parallel study on ⁵⁵Mn shows some evidences of the ( ⁷Li,t) incomplete-fusion process, but the cross-section for this process is significantly less than for the triton fusion process. The recoil distributions can be reproduced on the assumption that essentially all the observed break-up fragments are in fact associated with incomplete fusion, but uncertainties in normalisation leave open the possibility of a significant contribution of pure break-up. A diffraction model of the ( ⁷Li,α) transfer process reproduces the observed break-up α spectra with some success. Received: 29 March 2001 / Accepted: 12 November 2001     

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.     

Structure of low-lying <Superscript>12</Superscript>C resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of ¹²C in the 3α model. We use Ali-Bodmer potentials and compare results for other potentials α-α with similar ⁸Be properties. A three-body potential is used to adjust the ¹²C resonance positions to desired values extending the applicability of the method to many-body systems decaying into three α-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two 0⁺, three 2⁺, two 4⁺, one of each of 1^±, 2^-, 3^±, 4^-, and 6⁺. The partial-wave decomposition of each resonance is calculated as a function of the hyperradius. Strong variation is found from small to large distance. The connection to previous experimental and theoretical results is discussed and agreements as well as disagreements are emphasized.     

The α-<Superscript>12</Superscript>C scattering studied via the Trojan-Horse method

The Trojan-horse method has been suggested as a means to study a two-body reaction at astrophysical energies via a three-body breakup reaction. In order to test this method the ⁶Li(¹²C,α¹²C)²H reaction was studied in a kinematically complete experiment at an incident energy of 18 MeV. Coincidence spectra show the presence of the quasi-free α-¹²C scattering process. The excitation function of the three-body reaction is calculated in the plane wave impulse approximation assuming quasi-free scattering and is compared with the experimental data. Also, the excitation function of the virtual α-¹²C elastic scattering is extracted from the three-body reaction cross section at low deuteron momenta and compared with the behaviour of the free scattering cross section. Received: 4 June 1999 / Revised version: 15 November 1999     

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.     

Interaction at the barrier in the systems 9, 10, 11Be + 209Bi: Well-established facts and open questions

The experimental data relative to the interaction for the systems ^{9, 10, 11}Be + ²⁰⁹Bi at the Coulomb barrier are critically discussed and compared also with present theories. The break-up (BU) of the two loosely bound projectiles, ^{9, 11}Be, seems to influence the fusion process by “hindering” the fusion cross-sections; but, contrary to expectations, the ¹¹Be halo structure has no influence, since no “enhancement” is evident from the existing data. Attempt to describe simultaneously all the ⁹Be + ²⁰⁹Bi system data: fusion, elastic scattering and BU, within a coupled-channel (CC) approach is only partly successful. It is important, from a theoretical viewpoint, to include in the CC formalism as well as possible the BU process both to continuum states as well as to unbound resonances. More accurate and well-focused experiments are also necessary to pin down this problem. Received: 1 May 2001 / Accepted: 4 December 2001