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The optical theorem is a fundamental aspect of quantum scattering theory.Here, we generalize this theorem to the case where the incident scatteringstate is a superposition of internal states of the collision partners,introducing additional interference contributions and, e.g., providing a routeto control the total integral cross section. As in its standard form, forwardscattering plays an essential role in the generalized optical theorem, but withinterference terms being related to the inelastic forward scattering amplitudesbetween states in the initial superposition. Using the resultant control index,we show that extensive control is possible over ultracold collisions of oxygenmolecules in their rovibrational ground states, and of 85Rb-85Rb collisions,promising systems for the first experimental demonstration of the quantuminterference control of the total scattering cross section.

Generalized multichannel optical theorem: Coherent control of the total scattering cross section