Projectile breakup dynamics for 6Li + 59Co : Kinematical analysis of \alpha - d coincidences

A study of the kinematics of the $ \alpha$ -d coincidences in the ⁶Li + ⁵⁹Co system at a bombarding energy of E _lab = 29.6 MeV is presented. With exclusive measurements performed over different angular intervals it is possible to identify the respective contributions of the sequential and direct projectile breakup components. The angular distributions of both breakup components are fairly well described by the Continuum-Discretized Coupled-Channels framework (CDCC). Furthermore, a careful analysis of these processes using a semiclassical approach provides information on both their lifetime and their distance of occurrence with respect to the target. Breakup to the low-lying (near-threshold) continuum is delayed, and happens at large internuclear distances. This suggests that the influence of the projectile breakup on the complete fusion process can be related essentially to the direct breakup to the ⁶Li high-lying continuum spectrum.     

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.     

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     

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.     

Deuteron elastic scattering and (d,p) reactions on 208Pb at Ed = 22 MeV and j-dependence of T20 in (d,p) reaction

An experimental study of deuteron elastic scattering and (d,p) reactions at E_d = 22 MeV was made for ²⁰⁸Pb target. A new j-dependence of T₂₀ for (d,p) reaction at backward angles was observed. A “model independent” optical potential method was applied to analyze deuteron elastic scattering in the 10–22 MeV energy range. A continuum discretized coupled channels (CDCC) analysis was performed for deuteron elastic scattering at 22 MeV and the deuteron breakup effect was elucidated. DWBA and CDCC (d,p) analyses were made for (d,p) reactions.     

The Li exclusive breakup on Si at 13 MeV

We have undertaken the study of ⁶Li breakup on a ²⁸Si target near the Coulomb barrier through an angular distribution measurement. Alpha particles were recorded in coincidence with deuterons in order to determine exclusively the breakup of lithium. The results are analysed and are discussed, in a continuum discretized coupled channel framework (CDCC).     

New treatment of breakup in few-body systems

A new approach to determining breakup amplitudes in few-body systems in the context of a Faddeev formalism based on lattice discretization of a continuum is described. Due to such discretization and use of finite-dimensional representations for all operators in the kernels of integral equations, breakup in few-body systems is interpreted as a partial case of multi-channel scattering and corresponds to transitions between the states of the discretized continuum of an asymptotic channel Hamiltonian. The case study is based on amplitudes of three-nucleon breakup n + d → n + n + p with semi-realistic NN interaction potentials.     

The neutron continuum from the9Be+α reaction

Spectra of the low energy neutron continuum between 0.1 and 2.4 MeV from the Be+α reaction were measured at 5.01, 5.44, 6.37 and 7.44 MeV bombarding energies and different angles of neutron emission. The intensity is strongly peaked in the forward direction and the neutron distributions show maxima between 0.3 and 0.6 MeV. The results are consistent with the assumption that the continuum is due to the sequential decay⁹Be(α, α′)⁹Be*→⁸Be+n. The shape and magnitude of the continuum from a²⁴¹Am-Be(α,n) source were determined as well.     

Coulomb and nuclear interactions in the dynamics of weakly-bound neutron-halo breakup on heavy target

Within our aim to clarify some aspects of the breakup dynamics of loosely-bound neutron-halo projectiles on a heavy target,we apply the continuum discretized coupled-channel formalism to investigate the beryllium¹¹Be breakup on a lead²⁰⁸Pb target atE_lab=140 MeV incident energy.By evidencing that the continuum–continuum couplings are much stronger in the nuclear breakup than in the Coulomb breakup,we conclude that the strength of these couplings in the total breakup is dominated by the nuclear contribution,with the diagonal monopole nuclear potential in the projectile–target center-of-mass having negligible effect on the total and nuclear breakup cross-sections.For this kind of reaction,we show that the condition for the total breakup to approach its dominant component in the absorption region is strongly dependent on the continuum–continuum couplings and the diagonal monopole nuclear potential.     

Partial fusion of a weakly bound projectile with heavy target at energies above the Coulomb barrier

Partial-fusion cross-sections for the systems ⁶Li + ²⁰⁸Pb, ⁹Be + ²⁰⁹Bi have been determined. The effect of breakup on fusion for weakly bound projectiles ⁶Li and ⁹Be incident on ²⁰⁸Pb or ²⁰⁹Bi targets has been discussed comparing experimental fusion cross-section excitation functions to those evaluated with a semi-classical approach. It is shown that complete fusion of a weakly bound projectile with heavy target is reduced, whereas the breakup process has very little influence on the total-fusion cross-section for some of the studied systems at energies above the Coulomb barrier.     

Spin-alignment and g-factor measurement of the I^{\pi} = 12+ isomer in 192Pb produced in the relativistic-energy fragmentation of a 238U beam

Reactions of a 16.8 MeV ⁶He beam with a ⁹Be target have been investigated using highly segmented detector setup covering a large solid angle. Data on elastic and quasi-free scattering, as well as two-neutron transfer, are reported. The results for elastic scattering are fairly well reproduced by a CDCC calculation, in agreement with the interpretation of a breakup effect already observed for the scattering of ⁶He on other light targets. Exotic quasi-free scattering of ⁶He on $ \alpha$ -cluster in ⁹Be is clearly observed. Inclusive and coincident events were used to extract information on the two-neutron transfer reaction ⁹Be(⁶He, $ \alpha$ )¹¹Be . Sequential decay of the ¹¹Be state at the excitation energy $\ensuremath E_x = 10.6$ MeV through different channels is discussed.     

Systematic CDCC calculations for ~11Be+p elastic scattering

Continuum discretised coupled-channels(CDCC) method with a ~(10)Be(0~+) + n two-body cluster model is applied to systematically analyze the elastic scattering of the halo nucleus ~(11)Be from the proton target at various incident energies below 100 MeV/nucleon.Using the renormalized ~(10)Be- p potential deduced from the ~(10)Be+ p elastic scattering data, the differential cross sections of ~(11)Be + p scattering are well reproduced by the CDCC calculations without any further adjustment parameters, demonstrating the applicability of this approach for describing the scattering of exotic nuclei based on the scattering of the less exotic core nuclei.     

Coupling effects of resonant and discretized non-resonant continuum states in 4He + 6Li scattering at 10 MeV/A

Alpha-particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of ⁶Li is studied at incident energy 10 MeV/A. The α + d breakup continuum part within the excitation energy E _ex = 1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

The four-neutron system

The development of light, neutron-rich beams has opened new perspectives for the study of many-neutron systems in the last decade. Breakup experiments at GANIL are described, using beams of ^6,8He, ¹¹Li, ¹⁴Be and ¹⁵B at several tens of MeV/N. Our approach is based on the detection in coincidence of the breakup fragment and the neutrons in order to investigate the different correlations in the final state of these very neutron-rich systems, in particular, 2n correlations in ⁶He, ¹¹Li and ¹⁴Be, three-body correlations in ¹⁴Be, and 4n correlations in ⁸He and ¹⁴Be.     

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.     

Influence of experimental conditions on the spectroscopy investigation of~(14)Be by Coulomb breakup reaction

The two-body(core+2n) cluster structure was implemented to describe the two-neutron halo nucleus~(14 )Be, where the core12 Be was assumed inert and at a ground state and the dineutron was assumed at a pure 2S0 state. Based on such a structure the three-body continuum-discretized coupled-channel(CDCC) calculation was successfully used to deal with the~(14) Be breakup reactions of~(14)Be+Pb at 35 Me V/u. Consequently, we modeled the kinematically complete measurement experiment of this reaction with the help of Geant4. With the simulation data the relative energy spectrum was constructed by the invariant mass method and B(E1) spectrum was extracted using the virtual photon model. The influence of the target thickness and detector performance on the energy spectroscopy was investigated.     

Transitions Between Rotational Nuclear Few-Body States in the Continuum

Continuum to continuum transitions are used to investigate the continuum properties of ⁸Be. The dependence of the cross section on the α?α potential and the rotational character of the ⁸Be energy spectrum are investigated.     

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.     

Light Nuclei in the Continuum

The development of light, neutron-rich beams has opened in the last decade new perspectives for the study of many-neutron systems. Breakup experiments at GANIL are described, using beams of ^6,8He, ¹¹Li, ¹⁴Be and ¹⁵B at several tens of MeV/N. Our approach is based on the detection in coincidence of the breakup fragment and the neutrons in order to investigate the different correlations in the final state of these very neutron-rich systems. Several particular cases are discussed: fragment-n correlations in unbound ⁷He, ¹⁰Li and ⁹He; 2n correlations in ⁶He, ¹¹Li and ¹⁴Be; and three-body and 4n correlations in ⁸He and ¹⁴Be.     

Determination of 8B(p, γ )9C Reaction Rate From 9C Breakup

The astrophysical factor of the ⁸B(p, γ )⁹C reaction at zero energy, S ₁₈(0), is determined from three-body model analysis of ⁹C breakup processes. The elastic breakup ²⁰⁸Pb(⁹C,p ⁸B)²⁰⁸Pb at 65 MeV/nucleon and the one-proton removal reaction of ⁹C at 285 MeV/nucleon on C and Al targets are calculated with the continuum-discretized coupled-channels method (CDCC) and the eikonal reaction theory (ERT), respectively. As a result of the present analysis, S ₁₈(0) extracted from the two reactions shows good consistency, in contrast to in the previous studies.