Reaction mechanism of <Superscript>6</Superscript>Li scattering at 600 MeV

Elastic scattering and inclusive breakup of ⁶Li particles on ¹²C, ⁵⁸Ni, ⁹⁰Zr, and ²⁰⁸Pb targets are measured at 100A MeV. The elastic scattering data are compared with single channel and Coupled Discretized Continuum Channels calculations. The coupling-effect between the elastic and the breakup channels is important even at an incident energy of 100A MeV and cannot be neglected. The inclusive breakup data are investigated for orbital dispersion effects which are found to be less significant at 100A MeV. The longitudinal momentum distributions are broader than predicted by theoretical expectations. Received: 17 December 1999 / Revised version: 9 February 2000     

Elastic scattering of heavy nuclei and nucleus-nucleus potential with repulsive core

The elastic scattering of ¹⁶O + ¹²C at various collision energies is discussed in the framework of the optical model with repulsive core nucleus-nucleus potential. The cross sections on backward angles are strongly raised due to repulsive core. It is shown by using the near-side/far-side decomposition method that the near-side component of the scattering amplitude mainly contributes to the elastic scattering cross sections on forward and backward angles. The repulsive core of ¹⁶O + ¹²C potential takes place at distances R ≲ 3 fm.     

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.     

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.     

Sensitivity of cross sections for elastic nucleus-nucleus scattering to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions in exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the ⁶He and ¹¹Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in ⁶He and ¹¹Li.     

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.     

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.     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Four-body distorted-wave theory for halo excitations in peripheral fragmentation reactions

A microscopic approach to breakup into the low-energy continuum of Borromean two-neutron-halo nuclei is developed by quantum mechanically taking into account both Coulomb and nuclear dissociation. The crucial role of both elastic and inelastic fragmentation is demonstrated for ⁶He breakup on C and Pb targets at intermediate energies in kinematically complete experiments. For the first time, recent GSI experimental data are analyzed quantitatively, and a rich and complex interplay of reaction mechanisms and low-lying halo excitations is revealed.     

Virtual breakup effects in elastic scattering of polarized deuterons

Elastic scattering of polarized deuterons at E_d = 56 MeV is investigated for ¹⁶O, ⁴⁰Ca, ⁵⁸Ni, ¹¹⁸Sn and ²⁰⁸Pb target nuclei by the use of folding interactions. Effects of virtual breakup of the deuteron to S- and D-states in the continuum region are taken into account by the CDCC method and are found to make indispensable contributions to cross sections and analyzing powers, where continuum-continuum couplings are substantial. The contribution of the D-state admixture in the ground state is important for the tensor analyzing powers. The calculated results agree well with experimental data. The invariant-amplitude method and the second-order sum rule study clarify the characteristic feature of the spin dependence of the effective interactions due to the virtual breakup. The near-side/far-side decomposition of scattering amplitudes illuminates the difference of the reaction mechanism between light and heavy target nuclei. The investigation for the ²⁰⁸Pb target at E_d = 21.5 MeV gives important information on the energy dependence of the effective interactions. The use of different parameter sets for the input nucleon-target optical potentials shows that the detailed results depend significantly on the choice of the parameter sets.     

CDCC Approaches and Roles of Closed Channels in d-Nucleus Reactions

The effect of deuteron breakup in d-nucleus reaction is treated with the continuum discretized coupled channels (CDCC) approach, and the effects on the total reaction cross sections and elastic scattering angular distributions are studied by comparing the calculations of CDCC and spherical optical model with our global deuteron optical potential [Phys. Rev. C 73 (2006) 054605] below 200 MeV, for target nuclei ranging from ¹²C to ²⁰⁸Pb. The contributions from the closed channels to the total reaction and breakup cross sections, and angular distributions of elastic scattering are also seriously discussed.     

Implication of proton-nucleus scattering for density distributions of unstable nuclei

The use of elastic proton scattering at intermediate and high energies to obtain information about the density distributions of unstable nuclei is investigated. A comparison between the relativistic impulse approximation (RIA) and Glauber model for proton scattering from ¹⁶O, ⁴⁰Ca, ⁴⁴Ca and ⁴⁸Ca at medium energies is performed. We used density distributions derived from the relativistic mean-field theory, employing the recent relativistic force NL-RA1, as well as experimental and phenomenological densities. It is found that the eikonal approximation can describe the cross-section only at small scattering angles and is weakly sensitive to the density distributions, while the RIA nicely produced the experimental cross-sections, even at medium and larger angles, and was very sensitive to the nuclear densities. Furthermore, the RIA better describes the isospin dependence of the cross-section. We used the RIA to investigate the density distribution of ⁵⁸Ca for proton scattering at different energies. It is found that the cross-section strongly depends on the parameters of the density distribution even at a small scattering angle. These results are important in extracting information about the structure of unstable nuclei. We also investigated the RIA and its sensitivity in describing halo nuclei such as ⁶He. We used for ⁶He a no-halo Gaussian density and a realistic-halo density that derived in the cluster orbital shell model approximation and contains the extended distribution of the valence nucleons. Comparison with the recent experimental data at GSI at 717 MeV/nucleon shows that the RIA successfully described the data at all considered range of the momentum transfer and on the other hand favor the halo structure of ⁶He. Received: 1 December 2001 / Accepted: 31 July 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: mrashdan@hotmail.com Communicated by P. Schuck     

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.     

Quasi-elastic scattering of the proton drip line nucleus 17F on 12C at 60 MeV

The quasi-elastic scattering angular distribution of the proton drip line nucleus ¹⁷F on a ¹²C target was measured at 60 MeV. The experimental data have been compared with the theoretical analysis based onto optical model and continuum discretized coupled channels (CDCC). The couplings between breakup and elastic scattering channels, and between inelastic and elastic scattering channels resulted very weak. In order to explore the breakup effects the total reaction cross-section was deduced from the angular distribution of the quasi-elastic scattering data, and then compared with the existing data for the other weakly and tightly bound nuclei on ¹²C target using a universal function. From this comparison, we concluded that the breakup effect is not important for weakly bound projectiles on the light target as obtained also with the CDCC analysis.     

Nuclear structure studies on halo nuclei by direct reactions with radioactive beams

The investigation of direct reactions with exotic beams in inverse kinematics gives access to a wide field of nuclear structure studies in the region far off stability. The basic concept and the methods involved are briefly discussed. The present contribution will focus on the investigation of light neutron-rich halo nuclei. Such nuclei reveal a new type of nuclear structure, namely an extended neutron distribution surrounding a nuclear core. An overview on this phenomenon, and on the various methods which gave first evidence and qualitative confirmation of our present picture of halo nuclei, is given. To obtain more quantitative information on the radial shape of halo nuclei, elastic proton scattering on neutron-rich light nuclei at intermediate energies was recently investigated for the first time. This method is demonstrated to be an effective means for studying the nuclear matter distributions of such nuclei. The results on the nuclear matter radii of ⁶He and ⁸He, the deduced nuclear matter density distributions, and the significance of the data on the halo structure is discussed. The present data allow also a sensitive test of theoretical model calculations on the structure of neutron-rich helium isotopes. A few examples are presented. The investigation of few-nucleon transfer reactions in inverse kinematics may provide new and complementary information on nuclear structure, as well as astrophysical questions. The physics motivation and the experimental concept for such experiments, to be performed due to momentum matching reasons at low incident energies around 5–20 MeV/u at the new generation low energy radioactive beam facilities SPIRAL, PIAFE, etc., is briefly discussed.     

轻奇特核结构中的核心激发--以11Be为例

近年来,越来越多的实验表明,很多轻奇特核结构中都有核心激发成分。本研究以丰中子晕核11Be为例,介绍核心激发成分的实验和理论研究进展,重点阐述核心激发成分对直接核反应微分截面的影响。实验上,1n移除反应及11Be（p,d）和10Be（d,p）转移反应是测量11Be核心激发成分比例的典型实验类型。理论上,发展了能够包括11Be核心激发成分的Faddeev AGS方法,XDWBA方法以及XCDCC方法。加入核心激发成分后,这些模型的计算结果可以更加合理地描述11Be在各种靶上的弹性散射和碎裂微分截面。通过对比是否包含核心激发成分的计算结果,发现其影响主要体现在弹散微分截面的大质心系角度,以及（p,d）转移反应角分布的小质心系角度。另外,对E_x=0:5s3 MeV的激发能区的碎裂反应,核心激发的影响不可忽略;对E_x=3s5:5 MeV的碎裂反应,核心激发的贡献非常重要。It was found that many light exotic nuclei have the core-excitation components. In this paper, taking one-neutron halo nucleus 11Be for example, the experimental and theoretical research progress, as well as the influences on the direct nuclear reaction differential cross sections of this exotic component were reviewed. The 1n removal, 11Be(p, d) and 10Be(d, p) transfer reactions are typical experimental methods to investigate this component. The Faddeev AGS, the XDWBA, and the XCDCC methods are developed to include this constituent in various theoretical models. With the core-excitation component, the calculated results can more reasonably describe the elastic scattering and breakup differential cross sections of 11Be impinging on various targets. Comparing the full XCDCC calculation with that omitting core-excitation effect, we found that this component mainly affects the elastic scattering differential cross sections at large center-of-mass angles, and the (p, d) transfer reaction angular distributions at small center-of-mass angles. In addition, its effect is non-negligible for the breakup reaction within the excitation energy interval of E_x = 0:5~3 MeV, and is remarkable for E_x =3 5:5 MeV.     

Core-breakup reactions of the halo nuclei 11Be and 11Li: momentum distributions and shadow effects

The halo nuclei ¹¹Be and ¹¹Li have been studied in core-breakup reactions where the halo neutrons are expected to be released without a major distortion due to the reaction. The widths of the halo-neutron momentum distributions have been extracted in coincidence with He fragments, Γ = 32 ± 4 MeV/c, and Li fragments, Γ = 42 ± 4 MeV/c for ¹¹Be and with He fragments, Γ = 42 ± 6 MeV/c for ¹¹Li. The ¹¹Be breakup gives a very low neutron multiplicity of 0.38±0.09 which is a manifestation of the shadowing of the neutron in the core-breakup reaction. This value can be understood from a simple theoretical calculation, which also accounts for the observed transverse momentum widths at small angles.     

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.     

Second-order breakup corrections to elastic deuteron-nickel scattering between 13 and 80 MeV

Breakup corrections to the elastic scattering matrix elements are calculated in the second-order distorted-wave Born approximation at deuteron incident energies of 45 and 85 MeV. The effects of spin are included. The size of the corrections are found to be generally as large as those obtained in a previous study at 13 and 21.6 MeV. The breakup cross section is calculated to first order in the breakup matrix elements by a distorted-wave Born treatment. Comparison with fully coupled calculations shows that the DWBA method overestimates the breakup cross section by a factor of about three.The continuum of breakup states up to a n-p relative momentum 1 fm^?1 is included in the calculations. This continuum is discretized by subdividing it first into two bins, and then into four bins. The finer discretization does not make a large difference in either the elastic cross section or the breakup cross sections. The higher bins give only a small contribution to either quantity.