The effect of continuum couplings in the fusion of the halo nucleus 11 Be on 208 Pb around the Coulomb barrier is studied using a three-body model within a coupled discretised continuum channels (CDCC) formalism. We investigate in particular the role of continuum-continuum couplings. These are found to hinder total, complete and incomplete fusion processes. Couplings to the projectile 1p 1/2 bound excited state redistribute the complete and incomplete fusion cross sections, but the total fusion cross section remains nearly constant. Results show that continuum-continuum couplings enhance the irreversibility of breakup and reduce the flux that penetrates the Coulomb barrier. Converged total fusion cross sections agree with the experimental ones for energies around the Coulomb barrier, but underestimate those for energies well above the Coulomb barrier.Introduction: The existence and the role of the breakup process of weakly bound projectiles in complete fusion and scattering mechanisms have been extensively investigated in recent years both theoretically [1-6] and experimentally [7][8][9][10][11][12][13][14][15][16], but there is not yet any definitive conclusion. There are contradictory theoretical works which predict either the suppression [1][2][3][4] or the enhancement [5] of the complete fusion cross section due to the coupling of the relative motion of the nuclei to the breakup channel.Recent coupled channels calculations for 11 Be+ 208 Pb [6] have shown that the coupling of the relative motion to the breakup channel has two effects, depending on the value of the bombarding energy, namely (i) a reduction of the complete fusion cross sections at energies above the Coulomb barrier due to the loss of incident flux, and (ii) an enhancement of the complete fusion cross sections at energies below the Coulomb barrier due to the dynamical renormalisation of the nucleus-nucleus potential. Using the isocentrifugal approximation and an incoming boundary condition inside the barrier, this calculation did not include the effect of the projectile's halo structure on the monopole projectile-target potential. Nor did it include the excitation to partial waves other than p 3/2 in the continuum, or the continuumcontinuum and bound excited states couplings in either reaction partner. Moreover, only a small interval of energy for continuum states (up to 2 MeV) was considered.The couplings between continuum states have been shown to be crucial to understand the breakup of 8 B on a 58 Ni target at low energy E lab = 25.8 MeV [19,20]. Therefore, it could be expected that continuum-continuum couplings significantly affect the role of breakup process in fusion of halo nuclei around the Coulomb barrier. We believe that

No abstract

Total (complete + incomplete) fusion excitation functions of 6,7 Li on 59 Co and 209 Bi targets around the Coulomb barrier are obtained using a new continuum discretized coupled channel (CDCC) method of calculating fusion. The relative importance of breakup and bound-state structure effects on total fusion is particularly investigated. The effect of breakup on fusion can be observed in the total fusion excitation function. The breakup enhances the total fusion at energies just around the barrier, whereas it hardly affects the total fusion at energies well above the barrier. The difference between the experimental total fusion cross sections for 6,7 Li on 59 Co is notably caused by breakup, but this is not the case for the 209 Bi target.

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier. DOI: 10.1103/PhysRevLett.98.152701 PACS numbers: 25.70.Jj, 25.70.Mn Recent developments of radioactive isotope accelerators provide an opportunity to investigate on Earth the fusion reactions that form heavy elements in the cosmos. These involve reactions of nuclei far from stability, the most exotic of which are often very weakly bound. Breakup of weakly bound nuclei is thus an important process in their collisions with other nuclei. A major consequence of breakup is that not all the resulting breakup fragments might be captured by the target, termed incomplete fusion (ICF); capture of the entire projectile by the target is called complete fusion (CF). Such ICF processes can dramatically change the nature of the reaction products, as has been investigated in detail for the stable weakly bound nuclei 9 Be and 6;7 Li [1]. There, at energies above the fusion barrier, CF yields were found to be only 2=3 of those expected, the remaining 1=3 being in ICF products. Events where the projectile breaks up and none of the fragments are captured provide an important diagnostic of the reaction dynamics. This we call no-capture breakup (NCBU), also referred to as elastic breakup.In a conventional picture of fusion, two colliding nuclei will fuse if they overcome the potential barrier due to their mutual Coulomb and nuclear interactions. The additional breakup degrees of freedom when one of the colliding nuclei is weakly bound makes the process very much more complicated. An outstanding theoretical challenge is to model the CF and ICF processes in such collisions, since this separation is crucial to understand the effects of breakup on fusion [1,2]. Quantum mechanical few-body approaches, such as the continuum discretized coupledchannel (CDCC) method [3,4] and the time-dependent wave packet method [5], cannot separate incomplete and complete fusion contributions to their absorptive cross sections [6], since both result in depletion of the total few-body wave function. The CDCC method can, however, make reliable predictions of the NCBU process [7], as will be exploited here. What, then, are the alternatives to the above models? A novel optical decoherence model has been suggested [6] but has yet to be implemented. Another approach is to use the concept of classical trajectories which allow CF and ICF events to be separated, as in the two-dimensional model of Ref. [8]...

New measurements of fusion cross sections at deep sub-barrier energies for the reactions 16O+{204,208}Pb show a steep but almost saturated logarithmic slope, unlike 64Ni-induced reactions. Coupled channels calculations cannot simultaneously reproduce these new data and above-barrier cross-sections with the same Woods-Saxon nuclear potential. It is argued that this highlights an inadequacy of the coherent coupled channels approach. It is proposed that a new approach explicitly including gradual decoherence is needed to allow a consistent description of nuclear fusion.

No abstract

The influence on fusion of coupling to the breakup process is investigated for reactions where at least one of the colliding nuclei has a sufficiently low binding energy for breakup to become an important process. Elastic scattering, excitation functions for sub-and near-barrier fusion cross sections, and breakup yields are analyzed for 6,7 Li+ 59 Co. Continuum-Discretized Coupled-Channels (CDCC) calculations describe well the data at and above the barrier. Elastic scattering with 6 Li (as compared to 7 Li) indicates the significant role of breakup for weakly bound projectiles. A study of 4,6 He induced fusion reactions with a three-body CDCC method for the 6 He halo nucleus is presented. The relative importance of breakup and bound-state structure effects on total fusion is discussed.

The classical dynamical model for reactions induced by weakly-bound nuclei at near-barrier energies is developed further. It allows a quantitative study of the role and importance of incomplete fusion dynamics in asymptotic observables, such as the population of high-spin states in reaction products as well as the angular distribution of direct alpha-production. Model calculations indicate that incomplete fusion is an effective mechanism for populating high-spin states, and its contribution to the direct alpha production yield diminishes with decreasing energy towards the Coulomb barrier. It also becomes notably separated in angles from the contribution of no-capture breakup events. This should facilitate the experimental disentanglement of these competing reaction processes.