The atomic ionization processes induced by scattering of neutrinos play key roles in the experimental searches for a neutrino magnetic moment. Current experiments with reactor (anti)neutrinos employ germanium detectors having energy threshold comparable to typical binding energies of atomic electrons, which fact must be taken into account in the interpretation of the data. Our theoretical analysis shows that the so-called stepping approximation to the neutrino-impact ionization is well applicable for the lowest bound Coulomb states, and it becomes exact in the semiclassical limit. Numerical evidence is presented using the Thomas-Fermi model for the germanium atom.
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We are grateful to A.S. Starostin and Yu.V. Popov for stimulating discussions. The work of K.A.K. was supported in part by the Russian Foundation for Basic Research, project nos. 11 02 01509 a and 11 01 00523 a. The work of A.I.S. was supported by the Rus sian Foundation for Basic Research, project no. 11 02 01509 a. The work of M.B.V. is supported in part by the U.S. Department of Energy, grant no. DE FG02 94ER40823.