  The center of mass (CM) energy in a collisional Penrose process - a collision
taking place within the ergosphere of a Kerr black hole - can diverge under
suitable extreme conditions (maximal Kerr, near horizon collision and suitable
impact parameters). We present an analytic expression for the CM energy,
refining expressions given in the literature. Even though the CM energy
diverges, we show that the maximal energy attained by a particle that escapes
the black hole's gravitational pull and reaches infinity is modest. We obtain
an analytic expression for the energy of an escaping particle resulting from a
collisional Penrose process, and apply it to derive the maximal energy and the
maximal efficiency for several physical scenarios: pair annihilation, Compton
scattering, and the elastic scattering of two massive particles. In all
physically reasonable cases (in which the incident particles initially fall
from infinity towards the black hole) the maximal energy (and the corresponding
efficiency) are only one order of magnitude larger than the rest mass energy of
the incident particles. The maximal efficiency found is ~ 13.92 and it is
obtained for the scattering of an outgoing massless particle by a massive
particle.
