Explicit forms of the off-shell Jost solutions for general central potentials

We derive explicit forms of the regular solutions and the Jost solutions off the energy shell, which satisfy the inhomogeneous Schrödinger equation. The used forms of the Yukawa-like and Gauss-like potentials are related to the two known integral representations of the Hankel functions. The explicit form of the introduced fully off-shell Jost functions enables us to write it in the alternative integral forms, which contain the Jost solutions or the regular solution.     

Non-radiative ionization of perturbation centres by means of excitons in semi-conducting and dielectric crystals

Non-radiative ionization of a perturbation centre formed by an electron trapped in the Coulomb field of the perturbation by means of excitons of large radius in semi-conducting and dielectric crystals is theoretically investigated. It is shown that such non-radiative ionization may occur by two processes: the direct non-radiative transfer of the excitation energy from the exciton to the electron of the perturbation and by exchange non-radiative ionization whereby the electron on the perturbation recombines non-radiatively with the hole in the exciton and the electron of the exciton with the energy released during this recombination passes to the ionized state of the perturbation.The corresponding probabilities per sec and recombination coefficients are calculated as a function of the concentration of perturbation centres and the type of exciton according to its optical origin. The result is used for a theoretical estimate of the influence of perturbation centres of the given type on the optical life-time of the exciton.     

Thermal and non-radiative transitions of electrons at imperfections in ionic crystals

The theory of non-radiative and thermal transitions of electrons at imperfections in ionic crystals is elaborated. The results obtained are used to confirm Mott's and Gurney's theories on the detachment process in two steps of electrons from F centres during the absorption of light in the F band and to explain theoretically the temperature dependence of quantum efficiency. Good agreement with experiment was obtained. The possibility of the luminescence of alkali halide crystals containing F centres at sufficiently low temperatures was also determined.     

The diffusion of the excitation energy in molecular crystals

A theory of the coefficient of diffusion of an exciton in molecular crystals is elaborated, based on the conception of the exciton as the excited state of the molecule of a crystal propagating through the crystal by chance transition from one molecule to another. The theoretical results are compared with the experimental data for an anthracene crystal.     

The interaction of excitons in the superliquid state with phonons in molecular crystals

The energy spectrum of excitons in the superliquid state has been investigated in interaction with phonons in molecular crystals. The corresponding branches of the energy spectrum of elementary excitations have been determined and the effect of the interaction with phonons on their stability has been investigated and discussed. The possibility of the resonance excitation of hydrons by means of phonons is discussed.     

Incoherent singlet-triplet biexcitons in organic molecular crystals

The conditions of the existence, the energy spectrum of internal motion and the dynamics of propagation as a whole of incoherent singlet-triplet biexcitons in organic molecular crystals is studied theoretically. It is assumed that the group velocity of the propagation of singlet excitons is very high with respect to that of triplet excitons.