Unbounded energies of debris from head-on particle collisions near black holes

If two particles move toward a black hole and collide near the horizon, the energy E_{c.m.} in the centre of mass can grow unbounded. This is a so-called Ba\~nados-Silk-West (BSW) effect. One of problems creating obstacles to the possibility of its observation consists in that individual energy E of a fragment at infinity remains finite because of redshift. We show that in the case of head-on collision, debris may have unbounded energy E. An essential ingredient of this scenario is a particle moving away from a black hole in the near-horizon region. It can appear due to precedent collision that implies multiple scattering.