Association of bound states of the coulomb potential with resonances of the coulomb potential perturbed by a barrier

In the present article we show how the bound states of the Coulomb potential may be associated with resonances that occur when this potential is perturbed by a barrier potential. The main idea is to trace the bound states on successive switching on of the barrier perturbation. It is found that those bound states that are localized inside the barrier are highly sensitive to variation with respect to the barrier height, whereas those that are localized outside are less sensitive. However, there are certain intervals for the barrier height when the role of being “a state localized inside the barrier” is shifted from one bound state to another. The result can be pictured as a “relay race,” where the “deliveries of the baton” are carried out over corresponding avoided crossings. The baton is ultimately handed over to a shape-type resonance state.