Multichannel configuration-interaction theory: Application to some resonances in helium

Using the method of configuration interaction as applied to autoionization by Fano, expressions involving the reaction matrix K in the basis of the original configurations are given for the width and resonance energy. The expression obtained for the width is a Fermi "golden rule" type formula similar to that proposed by Miller. The expression for the resonance energy changes only slightly as the independent energy parameter varies, and therefore it is possible to consider a particular resonance among closely spaced resonances without elaborate search procedures. Application is made to the $\left(n{l}^2\right){}_{}{}^1{}_{}{}^{}S$ autoionizing states of He below the $n=4\mathrm{}$ threshold. No significant near-neighbor resonance interactions were found despite the small energy intervals between adjacent levels. The results indicate the $5s^2$ state falls below the $n=4\mathrm{}$ threshold, which is reflected in the small width given by our results. Widths, resonance energies, relative decay probabilities for each of the open channels, and Fano-Cooper cross-section parameters are given for all the states considered. Comparison is made with experiment and other theories where possible.