The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, 6 He+

The structure of the three-body Borromean nucleus 6 He is approximated by a two-body di-neutron cluster model. The binding energy of the 2n-α system is determined to obtain a correct description of the 2n-α coordinate, as given by a realistic three-body model calculation. The model is applied to describe the breakup effects in elastic scattering of 6 He on several targets, for which experimental data exist. We show that an adequate description of the di-neutron-core degree of freedom permits a fairly accurate description of the elastic scattering of 6 He on different targets.A. M. MORO et al. PHYSICAL REVIEW C 75, 064607 (2007)

The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations.

The elastic scattering of 6 He on 120 Sn has been measured at four energies above the Coulomb barrier using the 6 He beam produced at the RIBRAS (Radioactive Ion Beams in Brasil) facility. The elastic angular distributions have been analyzed with the optical model and three-and four-body continuum-discretized coupled-channels calculations. The total reaction cross sections have been derived and compared with other systems of similar masses.

Data for scattering of 6 He from 197 Au, 208 Pb, and 209 Bi targets at low energies were consistently analyzed by use of the continuum-discretized coupled-channels method and the dineutron model of the projectile. A very good description of the experimental data was obtained with the strength of the dipole couplings reduced by 50%. We find that the dipole couplings are responsible for the suppression of the Coulomb rainbow and that the quadrupole couplings must be included in the calculations in order to obtain good agreement with the elastic-scattering data at more backward angles. The continuum-discretized coupled-channel (CDCC) method, developed originally to study the effect of deuteron breakup on the process of elastic scattering [1], plays an important role in the study of reactions with weakly bound light nuclei. So far the method has been limited to the three-body systems, allowing the study of interactions of a projectile consisting of two clusters with a target nucleus. Some efforts have been reported recently to extend it to the four-body systems [2][3][4] so that the scattering of 6 He, the nucleus known to have a three-body α + n + n structure, could be studied. However, these approaches are not applicable yet for the processes taking place in the vicinity of the Coulomb barrier because they do not account for the four-body Coulomb breakup of the projectile.Therefore low-energy 6 He elastic-scattering data have been analyzed so far by use of the limited model of this nucleus, with the two neutrons outside the α-particle core coupled to a single particle, a dineutron ( 2 n), [5,6] Au target measured at the Cyclotron Research Centre in Louvain-laNeuve open the possibility for more detailed studies of the applicability of such a simplified approach. The experiment at Louvain-la-Neuve was part of a campaign (by the PH-114 collaboration [8,9]) in which scattering of 6 He by different targets was investigated; details are given in Ref. [10]. In this report we present results of CDCC calculations limited to the three-body systems for these data sets.The calculations follow closely the procedure of Keeley et al. [6]. The two-body α + 2 n model of 6 He was employed, with the spin of the dineutron cluster set to zero. The potential binding the two clusters was of Woods-Saxon form, with the set II parameters listed in Table I of Ref. [11]. All the interactions were derived from empirical optical-model potentials describing elastic scattering of α particles and deuterons from the gold and lead targets [12,13] by use of the single-folding technique. The calculations were performed by means of the computer code FRESCO, version frxp18 [14].The continuum of the α + 2 n cluster states was truncated at relative momentum k = 0.6 fm −1 and discretized into bins of k = 0.1 fm −1 . The relative angular momentum of the cluster states was limited to the values L = 0,1,2. For the L = 2 states the binning scheme was modified because of the presence of the resonant state at an excitation energy of 0.825 MeV above the brea...

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6 He ( 4 He + n + n) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as 9 Be and 12 C, for which actual three-body continuum calculations are very involved.

The inclusive breakup for the 11 Li þ 208 Pb reaction at energies around the Coulomb barrier has been measured for the first time. A sizable yield of 9 Li following the 11 Li dissociation has been observed, even at energies well below the Coulomb barrier. Using the first-order semiclassical perturbation theory of Coulomb excitation it is shown that the breakup probability data measured at small angles can be used to extract effective breakup energy as well as the slope of BðE1Þ distribution close to the threshold. Fourbody continuum-discretized coupled-channels calculations, including both nuclear and Coulomb couplings between the target and projectile to all orders, reproduce the measured inclusive breakup cross sections and support the presence of a dipole resonance in the 11 Li continuum at low excitation energy.

The structure of the Borromean nucleus 9 Be (α+α+n) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate twobody resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These results support the reliability of the method for systems with several charged particles.