The nuclear reaction e + 3 He + 4 He → e + 7 Be is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the 3 He − 4 He scattering state is calculated using an effective 3 He− 4 He potential constructed via the Marchenko inverse scattering method. The reaction rate thus obtained for solar interior conditions is approximately 10 −4 of the corresponding rate for the radiative capture 3 He + 4 He → 7 Be + γ. However, at the conditions corresponding to the early stages of the primordial nucleosynthesis, the non-radiative fusion is five times faster than the radiative one. The importance of the non-radiative processes for the energy balance in the sun, which for electrons is totally opaque, is discussed.PACS number: 21.45.+v, 97.10.Cv