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Excitation of $^{229m}$Th at Inelastic Scattering of Low Energy Electrons

Excitation of the anomalously low lying nuclear isomer $^{229m}$Th$(3/2^+, 8.28 \pm 0.17$ eV) in the process of inelastic electron scattering is studied theoretically in the framework of the perturbation theory for the quantum electrodynamics. The calculated cross sections of $^{229m}$Th by the extremely low energy electrons in the range 9 eV--12 eV for the Th atom and Th$^{1+,4+}$ ions lie in the range $10^{-25}$--$10^{-26}$ cm$^2$. Being so large, the cross section opens up new possibilities for the effective non-resonant excitation of $^{229m}$Th in experiments with an electron beam or electron (electric) current. This can be crucial, since the energy of the isomeric state is currently known with an accuracy insufficient for the resonant excitation by photons. In addition, the cross section of the time reversed process is also large, and as a consequence, the probability of the non-radiative $^{229m}$Th decay via the conduction electrons in metal is $\approx10^{6}$ s$^{-1}$, that is, close to the internal conversion probability in the Th atom.