Abstract <p>Muon-catalyzed fusion occurs with wave effects of varying duration. The aim of this study is to determine the response of the electron system of helium atoms and molecules to muon absorption. Due to electron–phonon coupling, perturbations in the form of oscillations of the electron system generate vibrations of the atoms. The fundamental frequency of the damped oscillations of the electron system of a helium atom fused with a muon is 8.265 × 10¹⁶ s^–1. The spectral density of the oscillations of electronic states of a mesomolecule consisting of a helium atom and a muon is represented as a peak in the frequency dependence. Muon capture by a helium molecule leads to beats with an oscillation frequency of ~2 × 10¹² s^–1 commensurable with the frequency corresponding to the heat transfer mode.</p>