Analytic theory of resonances and bound states near Coulomb thresholds

The passage of an electronic resonance through the continuum threshold in the presence of a Coulomb potential is analysed. The approach is based on Feshbach's projection operator formalism combined with analytic continuation and a threshold expansion of the complex level shift function. Resonances and bound states are obtained as the poles of the analytically continued fixed-nuclei S matrix, S(k), for electron scattering. Close to threshold the behaviour of resonances and bound states is completely determined by the long-range Coulomb potential which causes an essential singularity of S(k) at k=0. Both the attractive and the repulsive Coulomb potentials are considered. The relationship between the Feshbach formalism and the quantum defect theory is established. The relevance of these results for the understanding of nuclear dynamics in electron-ion scattering is illustrated by a model calculation.