  The new generation of laser facilities is expected to deliver short (10 fs -
100 fs) laser pulses with 10 - 100 PW of peak power. This opens an opportunity
to study matter at extreme intensities in the laboratory and provides access to
new physics. Here we propose to scatter GeV-class electron beams from
laser-plasma accelerators with a multi-PW laser at normal incidence. In this
configuration, one can both create and accelerate electron-positron pairs. The
new particles are generated in the laser focus and gain relativistic momentum
in the direction of laser propagation. Short focal length is an advantage, as
it allows the particles to be ejected from the focal region with a net energy
gain in vacuum. Electron-positron beams obtained in this setup have a low
divergence, are quasi-neutral and spatially separated from the initial electron
beam. The pairs attain multi-GeV energies which are not limited by the maximum
energy of the initial electron beam. We present an analytical model for the
expected energy cutoff, supported by 2D and 3D particle-in-cell simulations.
The experimental implications, such as the sensitivity to temporal
synchronisation and laser duration is assessed to provide guidance for the
future experiments.
