Compatibility restrictions in the theory of antiresonance line shapes

The quasicontinuum correlation parameters that occur in the theory of antiresonance line shapes and radiationless decay, by virtue of being defined in terms of averages over the same set of quasicontinuum states, are shown to be restricted by conditions of mutual compatibility. These restrictions are analyzed in geometrical terms and some of their consequences are examined. A new correlation parameter λ is introduced and shown to qualitatively measure in many ways the overall consequences of correlations among the quasicontinuum couplings for many sparsely spaced states. A method is given for parametrizing the line shape and radiationless decay theory so as to satisfy the compatibility restrictions implicitly, thereby facilitating the analysis of experimental data. The application of the compatibility relations to the analysis of some recently reported line shape studies for molecules and solids is then discussed, including recent work on the optical absorption spectrum of boron‐doped silicon.