Symmetry of Vibrationally Assisted Electronic Absorption and Emission Band Shapes of Impurities in Solids

Abstract

For impurities that couple to the lattice through an interaction containing both linear and quadratic terms, mirror symmetry, at and above $T=0\mathrm{}$, of the resulting absorption and emission spectra about the zero-phonon line is highly dependent on the strength of the quadratic interaction parameter. Exact symmetry at all temperatures occurs only for the linear interaction. Overlap of the linear-plus-quadratic interaction spectra, although always in the vicinity of the zero-phonon line, is exactly coincident with the zero-phonon line at $T=0\mathrm{}$. Values of the linear and quadratic interaction parameters can be determined from the shapes of experimental broad-band spectra, the spacings of "hot lines," and the intensities of the zero-phonon lines.