Cumulative reaction probability without absorbing potentials

Cumulative reaction probability, introduced in the collision theory by W.H.Miller [J. Chem. Phys. 62, 1899 (1975)], characterizes a net efficiency of a rearrangement process as a function of the total energy of the collision system. We derive a formula that expresses this quantity in terms of the outgoing wave Green function. Our formula is free from the ambiguities of previous formulations; in particular, no absorbing potentials are required for its implementation. The formula has a potentially wide range of applications in atomic and molecular collision physics. As an illustration, we consider the rearrangement processes in the dt mu system for the energies up to the n = 6 threshold.