Exciton and Impurity States in Rare-Gas Solids

The formalism of the preceding paper is applied to a calculation of the first excited states of (1) pure crystals of Kr and Xe; and (2) rare-gas solids containing a substitutional Xe impurity. A Hartree potential for the bare electron-hole interaction is constructed for each system, and is screened within the random-phase approximation. Matrix elements of the corresponding pseudopotentials, projected according to the Cohen-Heine prescription, are derived in the Wannier representation. Band structures inferred from optical data are fitted to simple interpolation formulas. By transformation to a symmetric representation for the envelope function, the Wannier difference equations are reduced to manageable form and solved by a matrix technique. Although the calculations contain no disposable parameters, obtained binding energies and oscillator strengths are found to be in excellent agreement with experiment.