Abstract
When negatively charged particles are scattered by atomic nuclei before the thresholds of excitation of nuclei, the formation of a metastable system "charged particle + excited nucleus" is possible. In particular, during the scattering of μ-mesons by nuclei, mesoatoms with an excited nucleus in the states of the entire atomic spectrum of hydrogen-like atoms can arise. This infinite set of states of a quasi-bound system generates an infinite series of elastic scattering resonances in the continuous spectrum, which condenses to the threshold energy of the excitation of the nucleus. In cases where the elastic scattering widths of mesons are smaller than the decay width of the excited state of the nucleus, inelastic meson resonance decay channels arise, which make it possible to observe them experimentally in the process of resonant scattering. In the present work, an analytical expression is obtained for the widths of subthreshold resonances arising from the scattering of μ mesons by atomic nuclei. The widths of subthreshold resonances in such systems are explicitly expressed in terms of the reduced multipole matrix elements of nuclear transitions The paper presents estimates for dipole excitations of nuclei corresponding to the farthest resonant states. It is shown that modern meson facilities make it possible to directly determine the reduced matrix elements of dipole transitions in experiments on elastic meson scattering. For a group of nuclei with large widths of E1 γ-radiation, it is possible to set up an experiment to determine these widths, and for known widths, to determine the chemical composition of the target.