Method of Moments for Optical Absorption Bands of Impurities in Solids

Abstract

An attempt to reformulate and extend the method given by HSS (C. H. Henry, S. E. Schnattely, and C. P. Slichter: Phys. Rev. 137 (1965) A583) is made. The unperturbed electronic Hamiltonian H₀ responsible for the absorption lines is chosen only under the condition that its solution has many degenerate levels. Using the perturbation theory, the moments are calculated up to the third order in the perturbing Hamiltonian H₁, in contrast to the first order in the HSS’s theory. Since the spin-orbit interaction H_SO may be contained in H₀ or H₁, the obtained formulae of moments are applicable to many kinds of systems, although the HSS’s treatment is restricted to the systems in which H_SO is regarded as the perturbation. The results are applied to the absorption bands of the alkali halide phosphors containing heavy-metal ions with (s)² configuration, and the method to determine the values of energy parameters for these ions is discussed.