Resonance and Photodetachment Cross Section of Anions

Quite often one will find there are multiple resonant states lying in the continua under consideration. Some of them may interfere with each other through their mutual interaction with the same continua. The interference may dramatically alter the profile of the resonance structure from what they d look like if no interference occurred. These resonant states are said to overlap. On the other hand, there is usually more than one available channel within the range of photon energy under study. The formalism for photodetachment calculations should then be able to treat the case of multiple discrete states embedded in multiple continua. The configuration interaction in the continuum (CIC) theory is our theory of choice. 

Extension of Fano s formalism to the general case of multiple discrete states embedded in multiple continua was first conducted by Mies [54]. Like Fano, Mies assumed a prediagonalized basis. By imposing the asymptotic condition for the continuum state from the scattering theory, Mies derived the complete solution to the total continuum problem and gave formulas for energies and widths of resonances. 

A concurrent work with that of Ramaker and Schrader was done by Davis and Feld-kamp [56]. Their work was similar to Mies s, and pre-diagonalization was assumed. Their approach divided the solution into two cases - when there are more discrete states than continuum states and when there are more continuum states than discrete states. For the first case, their approach was expected to reduce computation time. Unlike Mies [54], scattering theory was not employed in the derivation. 

Although the abovementioned theories were formulated in the context of either photoionization of atoms or electron scattering with atoms, they lend themselves equally well to photodetachment of negative ions, where an essential question is again to construct the wavefunction for the total continuum state in the presence of transient states embedded in continua. The main results from Mies s work [54] for calculating cross sections are summarized below. 

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