Overlapping resonances in nuclei coupling to the atomic shells

The resonant process of nuclear excitation by electron transition (NEET) in highly charged ions is investigated. In NEET, a bound electronic decay transition occurs with the simultaneous excitation of the nucleus, provided that the energies of the atomic and nuclear transitions match. By varying the atomic charge state, the atomic transition energy can be tuned to a better match of the nuclear transition energy. We propose a new way to create the atomic hole in highly charged ions by dielectronic capture of a free electron. In order to derive the cross section for the three-step process composed of dielectronic capture, nuclear excitation by electron transition, and the subsequent nuclear decay, a Feshbach projection operator formalism is developed. With the help of this formalism, the resonances in nuclei coupling to the atomic shell and the possible interference between several direct and resonant electronic and nuclear processes such as radiative recombination, dielectronic recombination, and nuclear excitation by electron capture are described.