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.     

Mechanism of the 12C(11B,15N)8Be reaction and 8Be + 15N optical-model potential

Angular distributions of the ¹²C( ¹¹B, ¹⁵N) ⁸Be reaction were measured at the energy E_lab(¹¹B) = 49 MeV for the transitions to the ground and 2.94 MeV (2⁺) excited state of ⁸Be and to the ground and 5.270 MeV (5/2⁺) + 5.299 MeV (1/2⁺), 6.324 MeV (3/2^-), 7.155 MeV (5/2⁺) + 7.301 MeV (3/2⁺), 7.567 MeV (7/2⁺) excited states of ¹⁵N. The data were analyzed by the coupled-reaction-channel method. The elastic, inelastic scattering and one- and two-step transfers were included in the coupling scheme. The data of the ¹²C( ¹¹B, ⁸Be) ¹⁵N reaction at E_cm = 9.4-17.8 MeV known from the literature, were also included in the analysis. The mechanism of the ¹²C( ¹¹B, ¹⁵N) ⁸Be reaction and the optical-model potential parameters for the ¹⁵N + ⁸Be channel were deduced. The energy dependence of the optical-model parameters for the ¹⁵N + ⁸Be channel was obtained.     

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     

Optical Potential Parameters for Halo Nucleus System ^6He＋^12C from Transfer Reaction ^11B（^7Li, ^6He）^12C

The optical potential parameters for the halo nucleus system ^6He＋^12C are extracted from fits to the measured angular distributions of ^11B（^7Li, ^6He）12C reaction at energies of 18.3 and 28.3MeV with distorted-wave Born approximation analysis. The characters of the obtained optical potentiM parameters are basically consistent with the results extracted from the fits to the elastic-scattering angular distributions in the literature.     

Study of short-lived silver isotopes with a laser ion source

The continuum part of the⁶Li (a,a)⁶Li (1.47–2.47 MeV) scattering data at E_a=50 MeV are extracted in two discretized bins. Coupled-channel calculations are carried out coupling the 1⁺ ground state of⁶Li with both the resonant, 3⁺ ₁ state, and two non-resonant continuum states. The discretized continuum of the⁶Li (p,p)⁶Li (1.75–3.25 MeV) scattering data at E_p=65 MeV are also analysed on the same footing. In both the cases the effect of coupling is found to be minimal.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

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.     

Elastic, inelastic scattering and fusion of the 14N +59Co system at energies close to the coulomb barrier

Elastic and inelastic scattering differential cross sections were measured in the energy range 30 MeV ≤ E _lab ≤ 55 MeV, for the ¹⁴N +⁵⁹Co system. Ambiguities of the optical potential derived from the analysis of the elastic scattering data were removed by performing calculations at the radius of sensitivity and by comparison with the available fusion cross section data. A simultaneous analysis of the three mechanisms was performed by coupled channel calculations, and a unique energy independent nuclear potential was found to be able to fit the data. Discussions and comparisons concerning the optical model, the threshold anomaly, full and approximated coupled channel calculations are presented. Received: 6 February 1997 / Revised version: 1 August 1997     

Fusion cross-section of the 7Li + 11B reaction

The ⁷Li + ¹¹B reaction has been investigated in the energy range 5.5 MeV < E _lab < 19MeV, by detecting γ-ray resulting from the de-excitation of evaporation residues. Statistical compound-nucleus calculations have been performed in order to extract both the cross-sections of individual exit channels and the fusion cross-section of the system. The total angular momentum that the compoundn ucleus ¹⁸O can support has been deduced and is seen to exhibit saturation for a limiting value of 8.5ħ at the high-energy extreme. The results are discussed in terms of the entrance channel and statistical yrast line limitations.     

Boron+boron sub-Coulomb energy total reaction cross sections

Total reaction cross sections have been measured for the following reactions and energy intervals: ¹¹B+¹¹B, E_c.m. = 1.56–3.65 MeV; ¹⁰B+¹¹B, E_c.m. = 1.61–3.94 MeV; ¹⁰B+¹⁰B, E_c.m. = 1.84–3.66 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by large NaI detectors. The absolute accuracy of the method is thoroughly discussed and tested via a measurement of the ¹²C+¹²C reaction. For all three boron cases measured neither intermediate nor giant type resonances were observed. The cross sections are well described by optical model calculations based on lowenergy ¹¹B+¹¹B elastic scattering parameter sets.     

Resonance-like structures in10B(10B,α)16O excitation functions

Excitation functions of the¹⁰B+¹⁰B elastic scattering at 80° (c.m.) and of the¹⁰B(¹⁰B,α)¹⁶O reaction at 5° (cm.) and 175° (c.m.) have been measured simultaneously for c.m. energies between 3 and 10 MeV. Whereas the elastic scattering is varying smoothly with energy, large resonant structures of intermediate width of about 600 keV have been found for the first time near 40 MeV excitation of²⁰Ne in most reaction channels to¹⁶O.     

Optical Potential Parameters of Weakly Bound Nuclear System 17F+13C

Elastic scattering angular distributions of the 14^N＋16^O system and the angular distributions of transfer reaction 16^O（14^N,13^C）17^F at ELab=76.2 MeV and 57 MeV have been measured and calculated by means of the exact finiterange distorted-wave Born approximation with the PTOLEMY code. The optical potential parameters for the weakly bound nuclear system 17^F＋13^C have been deduced and applied to analyse the elastic scattering angular distributions of the similar systems 17^F＋12^C and 17^F＋14^N which are taken from literature. The result shows that the transfer reaction with stable projectile and target combination can be used as an alternative method to extract the optical potential parameters for the weakly bound nuclear system.     

Fusion and neutron-transfer cross sections for 13C + 10B and 13C + 11B reactions at subbarrier energies

The cross sections for the ¹⁰B(¹³C, ¹²C)¹¹B neutron-transfer reaction, leading to the ¹¹B 4.45 and 6.74 MeV and ¹²C 4.44 MeV excited states, and for ¹³C + ¹⁰B fusion have been measured by the characteristic and total γ-ray yield methods, respectively, over the energy (c.m.) interval 2.4–5.8 MeV. For ¹³C + ¹¹B, with no transfer reactions present, the fusion cross sections have been measured between E_c.m. = 2.3 and 6.4 MeV. The fusion cross sections for ¹³C + ¹⁰B and ¹³C + ¹¹B are found to be almost equal and slightly enhanced with respect to those for ¹²C + ¹⁰B and ¹²C + ¹¹B.     

The astrophysical S-factor of the reaction 7Be (p, γ)8B in the direct capture model

The astrophysical S-factor for the reaction ⁷Be(p, γ)⁸B up to an energy of 2 MeV (c.m.) and the capture cross section of ⁷Li(n,γ)⁸Li up to 1 MeV (c.m.) are calculated using the Direct Capture model (DC). Both calculations are in good agreement with experimental data.     

Refractive scattering and reactions,comparison of two systems:16O+16O and20Ne+12C

Elastic, inelastic scattering as well as one-neutron transfer channels have been measured over a wide angular range for systems¹⁶O+¹⁶O at the incident energy of 350 MeV and²⁰Ne+¹²C at 390 MeV, respectively, using the Q3D magnetic spectrometer. In both cases differential cross sections have been measured down to about 50 nb/sr (or d/d _R10^–4) at large angles. For the¹⁶O+¹⁶O system refractive contributions are found at the level of these cross sections, whereas in the²⁰Ne+¹²C case a steeper decrease of the differential cross section with the angle is observed and the refractive contribution can not be determined. The elastic scattering data have been analyzed using standard Woods-Saxon potentials and potentials calculated in different versions of the double-folding model. Some properties of these potentials are tested in the calculations for inelastic scattering and one-neutron transfer within the DWBA. With the refractive pattern observed for the¹⁶O+¹⁶O system, the scattering and transfer data are found to be sensitive to the interaction potential at small internuclear distances down to about 2.5 fm.It should be acknowledged that part of the folding analysis reported here was done while one of the authors (D.T.K.) was staying at the Institute for Theoretical Physics, University of Tübingen. We also thank Prof. H. Clement and H. Abele for numerous discussions and contributions and Prof. G.R. Satchler for helpful comments on the use of the DWBA code PTOLEMY.     

Total reaction and fusion cross sections at sub- and near-barrier energies for the system 7Li + 28Si

Fusion cross sections are extracted for the ⁷Li$ + $²⁸Si system, via reaction cross section and transfer measurements at sub- and near-barrier energies ( E _lab = 5.7 to 14MeV). The energy evolution of transfer to reaction cross section ratios is determined with the aid of CDCC calculations, which subsequently allows the deduction of fusion cross sections at sub- and near-barrier energies. It is shown that fusion can be well represented in a BPM context. Fusion cross sections are compared for the systems ⁷Li$ + $²⁸Si and ⁶Li$ + $²⁸Si, the latter studied previously, and are found to exhibit different strengths. Last, the direct channels determined at 13MeV, are found to be dominated by a 2n -transfer mechanism.     

Role of multi-step processes in 16O(11B,12C)15N at 41.25 MeV

The ¹⁶O(¹¹B,¹²C)¹⁵N reaction at 41.25 MeV has been investigated using the kinematical coincidence method. Polarization tensors t₂₀ and t₄₀ of ¹²C[2⁺ ₁] for the quantization axis taken along the direction of propagation have been measured at center-of-mass angles (Θ_c.m.) between 48^° and 62^° by analyzing the energy spectrum of ¹²C[2⁺ ₁] modulated by the effect of γ-ray emission. The cross-sections of the transfer reactions leading to the ¹²C[g.s.]+¹⁵N[g.s.], ¹²C[2⁺ ₁]+¹⁵N[g.s.] and ¹²C[g.s.]+¹⁵N[3/2^- ₁] final states have also been measured in the range 48^°≤Θ_c.m.≤ 120^°. The polarization tensor terms of ¹²C[2⁺ ₁] largely deviating from zero have been observed, contrary to the prediction by the distorted-wave Born approximation (DWBA). The one-step DWBA calculation also fails in describing the transfer reaction cross-sections. It is shown that the coupled channel model calculation including excitations and reorientations in ¹¹B and ¹²C satisfactorily reproduces both the tensor terms and the cross-sections of the transfer reactions. The multi-step processes passing through the excited states of ¹¹B are found to significantly contribute to the reaction. Received: 3 July 2000 / Accepted: 15 September 2000     

Angular Distribution of the 12C(6He, 7Li)11B Reaction

Angular distribution of the ¹²C(⁶He,⁷Li)¹¹B transfer reaction is measured with a secondary ⁶He beam of 36.4MeV for the first time. The experimental angular distribution is well reproduced by the distorted-wave Born approximation (DWBA) calculation. The success of the present experiment shows that it is feasible to measure one-nucleon transfer reaction on a light nucleus target with the secondary beam facility of the HI-13 tandem accelerator at China Institute of Atomic Energy (CIAE), Beijing.     

7Li+11B 体系唯象光学势的研究

实验测量了7Li+11B 体系的弹性散射角分布,其中弹核7Li 的入射能量分别为9.85,13.3,18.3,23.3 和28.3 MeV,测量的角度范围为θc:m: ≈ 15◦ ∼ 80◦。通过对本次实验数据以及文献中34 MeV 的数据拟合,抽取了该体系的唯象光学势参数。结果表明,在固定作用势形状因子下,势深度与能量具有线性相依的关系:实部深度随着弹核能量的增加而线性减小,而虚部深度则在平均值10.35 MeV 附近变化。Angular distributions of 7Li+11B elastic scattering were measured at Elab(7Li)=9.85, 13.3, 18.3, 23.3 and 28.3 MeV within the angular range of θc:m: ≈ 15◦ s 80◦. The analyse of these angular distributions together with the data taken from literatures at Elab(7Li) = 34 MeV have been performed to extract the parameters of optical model potential. With the fixed geometrical shapes, the potential strengths show a concise relation to the reaction energy: the depths of real potential decrease linearly with energy increasing, whereas the depths of imaginary part just slightly vary around the average value of 10.35 MeV.