Schwarzschild black hole as particle accelerator of spinning particles

It is shown that in the Schwarzschild background there exists a direct counterpart of the Bañados-Silk-West effect for spinning particles. This means that if two particles collide near the black-hole horizon, their energy in the centre-of-mass frame can grow unbounded. In doing so, the crucial role is played by the so-called near-critical trajectories when the particle parameters are almost fine-tuned. A direct scenario of the collision under discussion is possible with restriction on the energy-to-mass ratio $E/m<\frac{1}{2\sqrt{3}}$ only. However, if one takes into account multiple scattering, this becomes possible for $E\geq m$ as well