New decomposition of the S matrix for multichannel resonant collisions

The usual decomposition of the multichannel scattering matrix near an isolated, narrow resonance is given as a sum of a direct and resonant part. The direct part of the S matrix which describes the background scattering is regular and unitary. The resonant part features a pole at the complex resonance energy, and both its magnitude and phase change rapidly as the energy varies. Given the S matrix, it is often a cumbersome task to extract the resonance energy and partial widths from the usual decomposition. We propose a new decomposition (which is related to the usual one) that overcomes this difficulty. The new resonant part is a complete analog of the single-channel S matrix. Its magnitude is constant and its phase jumps by 2π as the energy passes through the resonance. The resonant time delays for each state-to-state transition are independent of the channel indices, and exhibit the same Lorentzian shape from which the resonance energy and total width are readily obtained. The square of the magnitude of the resonant S-matrix elements are the state-to-state transition probabilities of the resonant scattering and are expressed in terms of the channel partial widths. The applicability of the proposed decomposition is demonstrated in a coupled-channel study of multichannel resonances in H-CO collisions using a global ab initio potential-energy surface