A SELF-CONSISTENT F-CENTER CALCULATION FOR OPTICAL ABSORPTION AND EMISSION

A theoretical investigation of the luminescence processes associated with F-centers has been made. It assumes that the marked Stokes's shift arises from the electrostatic interaction between the F-electron and the neighboring ions. A semi-continuum model was employed. First, an examination of most of the previous F -center calculations in NaCI and KC1 was made. These were classified into four categories: (1) the semi-continuum model; (2) the semi-continuum polaron model; (3) the pointion model (a) without polarization and (b) with polarization: and (4) the Hartree-Fock model where the internal structure of the ions which surround the vacancy is taken into account. Some models were omitted. In all calculations, the differences in the eigenvalues associated with the lowest and the first excited state give approximately the measured values of the peak absorption and the peak emission bands. The actual eigenvalues show a large scatter, indicating no reliability in the present calculating techniques. Next, a new self-consistent approach is made. The following results were derived for NaCI and KC1: (1) self-consistent potentials for the absorption and emission; (2) energy level diagrams (relative to the bottom of the conduction band) and wavefunctions for both processes; (3) self-consistent values for the displacements of the first nearest neighbors; and (4) the lifetime of the first excited state (which agrees approximately with the measured result). The loose binding approximation is manifested during emission, whereas tight binding occurs during absorption. These calculations indicate that a self-consistent use of the semi-continuum model can describe the simplest optical properties of the F-center. © 1969.