Nearly Hydrogenic Energy-Levels of Wannier Excitons in Anisotropic Crystals

Abstract

Internal energy-levels of Wannier excitons in anisotropic crystals are treated in the case in which the anisotropy of the product ε_jμ_j is small, where ε_j and μ_j are the components of the dielectric constant of the crystal and the reduced effective-mass of the exciton, respectively, along the j-th axis. When this product is isotropic, exciton levels are hydrogenic. Typical combinations of anisotropies of electron and hole effective-masses which make ε_jμ_j isotropic are briefly examined. In the case of weak anisotropy in ε_jμ_j, shifts of exciton energy-levels from hydrogenic ones and removals of their degeneracies are studied by using a perturbation method and introducing new anisotropy parameters. The expressions of the energy corrections for low-lying levels of the excitons are obtained.