Theory of resonance conversion is presented. Being a natural extension of the traditional internal conversion into the subthreshold area, resonance conversion in a number of cases strongly affects the nuclear processes. Moreover, concentrating the transition strength on the narrow bands corresponding to the spectral atomic lines, it offers a unique tool capable of accelerating nuclear decay rates. Furthermore, along with the conventional nonradiative process of nuclear excitation through NEET and its reverse, TEEN, resonance conversion offers an appropriate mathematics for consideration of a number of cross-invariant processes involving both nuclei and electrons: excitation and deexcitation of the nuclei by hyperfine magnetic field, nuclear spin mixing, hyperfine interaction and magnetic anomalies in the atomic spectra, collisional nuclear excitation via ionization of the shells in the muon decay in the orbit, etc. The mechanisms of the optical pumping of the isomers are also considered, as well as triggering their energy in the resonance field of a laser. The effect is especially high in the hydrogen-like heavy ions due to practical absence of any damping of the resonance.
The theory is also generalized to the case of the discrete Auger transitions.

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