Destruction of vertical transitions and increase in the matrix elements of the electron-photon interaction in small crystals

Abstract

Abstractauthoren The matrix elements of electron–photon interaction were investigated in a one-dimensional model of a finite length crystal lattice. Its electronic stationary states belong both to quasi-discrete and to continuous energy band spectra. We analyze formation and degree of applicability for the law of “momentum” conservation and for the vertical transitions approximation as the lattice length increases. The values of matrix elements and their dependence on lattice length are different for the cases when the final state is lying under the vacuum level and when the final state is lying above this level. In the latter case, the resonant penetration of electrons in the lattice may increase the matrix elements by many orders of magnitude. The results are different in the middle and near the thresholds of the energy bands, for the cases of tight and weak binding of electrons in the lattice cell. The selection rules of the “momentum” conservation and the approximation of vertical transitions disappear at extremely weak binding.