A consistent four-body CDCC model of low-energy reactions: Application to 9Be + 208Pb

We investigate the ${}^9$Be + ${}^{208}$Pb elastic scattering, breakup and fusion at energies around the Coulomb barrier. The three processes are described simultaneously, with identical conditions of calculations. The ${}^9$Be nucleus is defined in an $\alpha +\alpha$ + n three-body model, using the hyperspherical coordinate method. We first analyze spectroscopic properties of ${}^9$Be, and show that the model provides a fairly good description of the low-lying states. The scattering with ${}^{208}$Pb is then studied with the Continuum Discretized Coupled Channel (CDCC) method, where the $\alpha +\alpha$

• n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $\alpha$+ ${}^{208}$Pb and n+ ${}^{208}$Pb systems are taken from the literature. We present elastic-scattering and fusion cross sections at different energies.