Configuration Interaction Theory. Effects of Overlapping Resonances

Fano's resonance theory is extended to include the interaction of many resonances with many continua and inelastic couplings between continuum states. In particular a new parameter is introduced; the overlap matrix between the continua to which neighboring resonances are coupled. Resonances which are coupled to the same channel states may be said to overlap. If their widths are comparable to their spacings the resultant effects on photoabsorption or on the scattering matrix can be quite profound. The apparent widths may bear little relation to the widths due to configuration interaction, and the resultant structure may not fit the usual Fano-Buetler profiles for isolated resonances.The effects of overlapping are examined for various models which are representative of atomic photoabsorption and electron-diatomic molecule scattering. It is demonstrated that without prior knowledge of the overlap matrix it is impossible to uniquely characterize a resonance from limited experimental observations. Scattering and photoabsorption experiments should be designed to examine all possible channels, i.e., both differential and inelastic cross sections. Even so, without the parallel support of theoretical estimates of partial widths, and the signs of the configuration interaction matrix elements, the interpretation of resonance phenomena and in particular the parameters which are extracted must be accepted with severe reservations.