Abstract <p>The effect of the volume capture of fast charged particles in a curved single crystal is studied. The transverse energy losses, the hovering effect, and the criterion for the volume capture of fast charged particles are studied. Possible mechanisms of volume capture are considered: transverse energy losses due to crystal excitation by a fast charged particle (proton, lepton), multiple scattering of particles in a curved crystal, and elastic scattering and diffraction of particles in a curved crystal. It is shown that in the hovering region, the ratio of the loss rates of the transverse and longitudinal energy of fast charged particles increases significantly compared to the ratio of the longitudinal and transverse energies and is equal in order of magnitude to the ratio of the off-diagonal elements of the inverse dielectric permittivity matrix to the diagonal ones. It is established that the effect of the volume capture of fast protons (leptons) is due to diffraction in a curved crystal, as well as the effects of damping of the off-diagonal elements of the particle density matrix. The proposed diffraction mechanism is based on taking into account the quantum coherent scattering of a fast proton (lepton) in a curved crystal.</p>