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The center of mass (CM) energy in a collisional Penrose process - a collisiontaking place within the ergosphere of a Kerr black hole - can diverge undersuitable extreme conditions (maximal Kerr, near horizon collision and suitableimpact parameters). We present an analytic expression for the CM energy,refining expressions given in the literature. Even though the CM energydiverges, we show that the maximal energy attained by a particle that escapesthe black hole's gravitational pull and reaches infinity is modest. We obtainan analytic expression for the energy of an escaping particle resulting from acollisional Penrose process, and apply it to derive the maximal energy and themaximal efficiency for several physical scenarios: pair annihilation, Comptonscattering, and the elastic scattering of two massive particles. In allphysically reasonable cases (in which the incident particles initially fallfrom infinity towards the black hole) the maximal energy (and the correspondingefficiency) are only one order of magnitude larger than the rest mass energy ofthe incident particles. The maximal efficiency found is ~ 13.92 and it isobtained for the scattering of an outgoing massless particle by a massiveparticle.

On the maximal efficiency of the collisional Penrose process