The ability of a recently developed square-integrable discrete basis to represent the properties of the continuum of a two-body system is investigated. The basis is obtained performing a simple analytic local scale transformation to the harmonic oscillator basis. Scattering phase-shifts and the electric transition probabilities $B(E1)$ and $B(E2)$ have been evaluated for several potentials using the proposed basis. Both quantities are found to be in excellent agreement with the exact values calculated from the true scattering states. The basis has been applied to describe the projectile continuum in the ${}^6\mathrm{He}$ scattering by ${}^{12}\mathrm{C}$ and ${}^{208}\mathrm{Pb}$ targets at 240 MeV/nucleon and the ${}^{11}\mathrm{Be}$ scattering by ${}^{12}\mathrm{C}$ at 67 MeV/nucleon. The calculated breakup differential cross sections are found to be in very good agreement with the available experimental data for these reactions.

• Received 27 April 2010

DOI:https://doi.org/10.1103/PhysRevC.82.024605