Cross section of the Coulomb excitation of ${}^{229m}$Th by low energy muons

Abstract

The inelastic scattering cross section for muons, ${\mu }^{-}$, with energies $E$=9--100~eV from the ${}^{229}$Th nuclei is calculated in the framework of the second order of the perturbation theory for the quantum electrodynamics. The dominant contribution to the excitation of the low energy isomer ${}^{229m}$Th$(3/2^{+},8.19\pm 0.12$~eV) comes from the $E2$ multipole. The excitation cross section reaches the value of $10^{-21}$ cm${}^2$ in the range $E\approx$10~eV. This is four to five orders of magnitude larger than the electron excitation cross section and enough for efficient excitation of ${}^{229m}$Th on the muon beam at the next generation of muon colliders.

9 pages, 4 figures

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