The working notes on theoretical issues of the coherent neutrino less conversion of a negatively charged muon into an electron in the field of a nucleus, the so-called μ→ e conversion, are presented. Here we briefly report on our studies of the physical backgrounds toμ→e conversion. During the present reporting period our attention was paid to the study of theoretical problems related to the main background signals coming from the so-called muon decay-in-orbit (DIO), a process in which the muon

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... decays in the normal way, i.e. e , while in the orbit of the atom. The existing literature on this s subject have been studied and the set of problem to be solved for improvement of theoretical estimates on DIO spectrum have been formulated. The first steps towards theoretical description of quantum correction due to the interaction of decaying particles have been undertaken.