Coalescence of metastable states in chemical reactions: double poles of the scattering matrix and exceptional points

Accidental degeneracy of two scattering resonances in chemical reactions is discussed. A novel analytical parameterization for the scattering matrix elements valid in the presence of two interacting resonances is derived and applied to investigate the coalescence of metastable states leading to double poles in the partial-wave amplitude. We show how double poles can manifest themselves in reaction cross-sections and discuss their relationship with exceptional points. The presence of two degenerate resonances interacting with each other can create a peculiar double-peak structure in the reaction probability. At the energy where the two decaying states coalesce the scattering matrix has a double pole and correspondingly the reaction probability reaches its minimum value. This novel formula has been tested with the well-established data obtained for the F + H-2 reaction, for which previous studies have revealed the existence of two interfering resonance pathways. The good agreement of model predictions and quantum scattering calculations shows that the present approach is reliable. Hence, we claim that it provides a way for the observation of interacting resonances in molecular collisions. Resonance positions and partial widths can be obtained by fitting the numerically calculated state-to-state reaction probabilities to the square modulus of the novel expression for the scattering matrix elements derived in the paper.