Time-delay matrix analysis of resonances in electron scattering: - and

In electron scattering from complex targets such as complex atoms or molecules, resonance features often occur at energies where the target has many excited electronic states. Standard methods of determining resonance positions and widths are unreliably close to electronic thresholds or fail when a resonance is too wide or found to overlap another resonance. By finding the time-delay matrix given by it is possible to fit the resonance positions and widths more precisely and with greater certainty. It is also possible to find the `branching ratios', the probabilities of decay of the resonance to the continuum of each target state. This helps in the accurate assignment of the resonance (particularly for core-excited shape resonances), reducing the extensive detective work that is often required. The usefulness of the time-delay matrix is demonstrated with two R-matrix electron - molecule scattering calculations: - and - , although the method is not restricted to any particular type of calculation or target species. Resonance positions and widths are found for - . For the case of - , resonances with symmetry are tracked as a function of bondlength. Their changing character is discussed and an avoided crossing at short internuclear separation is reported for the first time. The parentage of the 12 eV resonance has been classified as a contrary to previous classifications. Evidence of the notoriously shy series b resonances has been found.