We develop a fully relativistic theoretical framework for calculating nuclear excitation cross sections induced by muon beams, covering a broad range of incoming energies from 1 to 1000 MeV. Focusing on experimentally accessible isotopes, ${}^{115}\mathrm{In}$ and ${}^{90}\mathrm{Zr}$, we calculate excitation cross sections to various nuclear states. To enhance relevance for potential experiments, we also estimate the effective cross sections for excitation to long-lifetime isomeric states, suitable for postexcitation detection. Additionally, we compare the excitation cross sections for ${\mu }^{-}$, ${\mu }^{+}$, and electrons, and we assess the impact of muon penetration into the nucleus on these cross sections.

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• Coulomb excitation
• Electromagnetic transitions
• Electron & muon capture
• Inelastic scattering reactions