Bright $\gamma$ rays source and copious nonlinear Breit-Wheeler pairs in the collision of high density particle beams.

The collision of ultrashort high-density $e^-$ or $e^-$ and $e^+$ beams at 10s of GeV, to be available at the FACET II and in laser wakefield accelerator experiments, can produce highly collimated $\gamma$ rays (few GeVs) with peak brilliance of $10^{27}~\mathrm{ph/s~mm^2 mrad^2 0.1\% BW}$ and up to $10^5$ nonlinear Breit-Wheeler pairs. We provide analytical estimates of the photon source properties and of the yield of secondary pairs, finding excellent agreement with full-scale 3D self-consistent particle-in-cell simulations that include quantum electrodynamics effects. Our results show that beam-beam collisions can be exploited as secondary sources of $\gamma$ rays and provide an alternative to beam-laser setups to probe quantum electrodynamics effects at the Schwinger limit.