The seminar focuses on discussing the application of three-body Faddeev equations to describe thermonuclear reactions between hydrogen isotopes in the presence of a negatively charged lepton in the interaction zone. Attention is paid to the search for bound and resonant states of nucleus-lepton-nucleus systems with the analytical continuation of two-body interactions within the framework of the three-body eigenvalue problem. The behaviour of the Fredholm determinant is analysed as a function of the grid parameters of the three-body eigenvalue problem. The behaviour of the regions of logarithmic singularities of the integral kernels of the Faddeev equations is analysed in detail, and a method for automatically and numerically traversing these zones for a system of three bodies with different masses is presented. A comparison is made between the solutions of the Faddeev equations obtained by iterations and Pade-approximants using the example of neutrondeuteron breakup and elastic scattering reactions. Estimates are given for the dynamic role of the muon in the interaction zone of dd and dt nuclei in comparison with the analogous role of the electron.