OPTICAL LINESHAPES OF IMPURITIES IN CRYSTALS - A LATTICE MODEL OF INHOMOGENEOUS BROADENING BY POINT-DEFECTS

Previous theories of inhomogeneous broadening by point defects of impu rity transitions in crystals have invoked a continuum approximation fo r the defect positions. We generalize these theories by treating the c rystal as a discrete lattice. At low defect densities we recover the r esults of the continuum theory, finding a Lorentzian lineshape. At hig h defect densities the lineshape is approximately Gaussian. At interme diate densities, the lineshape displays satellite structure due to dif ferent configurations of nearby defects. For all densities we derive a pproximate analytic expressions for the lineshape that are in good agr eement with exact numerical results.