  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
6He scattering by 12C and 208Pb targets at 240 MeV/nucleon and the 11Be
scattering by 12C 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.
