The 11 Li breakup on a 208 Pb target is studied in the Coulomb-corrected eikonal approximation by using a 9 Li + n + n three-body description of the projectile. The 11 Li wave functions are defined in the hyperspherical formalism for bound and scattering states and are obtained from effective 9 Li + n and n + n interactions. We first determine 0 + , 1 − , and 2 + 9 Li + n + n phase shifts, which suggest the existence of a narrow 1 − resonance near 0.5 MeV above threshold. The calculated breakup cross sections show a peak at low energies, in agreement with the data. The influence of monopole and quadrupole components is analyzed and shown to be non-negligible. We discuss the derivation of dipole strengths from experimental breakup cross sections and suggest that the simple Coulomb dipole approximation, traditionally used in the literature, should be replaced by more elaborate models. We also show that 11 Li + 208 Pb elastic scattering measurements would provide an indirect test of the model.

Breakup cross sections are determined for the Borromean nucleus 22 C by using a four-body eikonal model, including Coulomb corrections. Bound and continuum states are constructed within a 20 C + n + n three-body model in hyperspherical coordinates. We compute continuum states with the correct asymptotic behavior through the R-matrix method. For the n + n potential, we use the Minnesota interaction. As there is no precise experimental information on 21 C, we define different parameter sets for the 20 C + n potentials. These parameter sets provide different scattering lengths, and resonance energies of an expected 3/2 + excited state. Then we analyze the 22 C ground-state energy and rms radius, as well as E1 strength distributions and breakup cross sections. The E1 strength distribution presents an enhancement at low energies. Its amplitude is associated with the low binding energy, rather than with a three-body resonance. We show that the shape of the cross section at low energies is sensitive to the ground-state properties. In addition, we suggest the existence of a low-energy 2 + resonance, which should be observable in breakup experiments.

No abstract

We discuss properties of three-body continuum states in the hyperspherical formalism. The associated coupled-channel system is solved on a Lagrange basis, and is complemented by the R-matrix theory for the treatment of scattering states. Three-body α + n + n phase shifts are determined under various conditions. Two approximations of the continuum are considered: the complex scaling and the pseudostate methods. Both are briefly outlined, and compared with the R-matrix approach for the dipole-strength distribution of 6 He. A fair agreement is obtained between the three methods. We also discuss the influence of the α + n and n + n interactions, as well as the effect of the Pauli principle. Some differences are obtained, but all calculations predict a broad 1 − resonance near 1 MeV. §1.

We apply a microscopic version of the Continuum Discretized Coupled Channel (CDCC) method, referred to as MCDCC, to 8 Li and 8 B scattering on different targets. The 8 Li and 8 B nuclei are described in a microscopic three-cluster model (α + t + n and α + 3 He + p), using the hyperspherical coordinates. We first present spectroscopic properties of these nuclei. Then, we determine 8 Li+nucleus and 8 B+nucleus potentials by using proton+target and neutron+target interactions. We compute various elastic-scattering cross sections and confirm that breakup effects are important, in particular at low energies. In general, we find a fair agreement with experiment, except for 8 B+ 58 Ni where we suggest that the data might be overestimated.