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Additional resources for Advances in Chemical Physics: The Application of Wave Mechanical Methods to the Study of Molecular Properties, Volume 8
The intensities are adjusted to give equal values in the third transition, except in the top (pure crystal) spectrum. Hatching indicates very intense absorption. the spectral lines more dense, until in very low concentrations we expect a quasi-continuum of absorption lines. In a sufficiently thick crystal we might expect to find absorption with onset roughly at a frequency for the lowest level of the band and running with varying intensity to a maximum at the top of the band. It must be emphasized that these remarks apply to shallow traps, and to a host with inverted band structure: in an upright band the most intense absorption is at the lowest frequency and any 46 D.
15). a+S-E B B a-E B 0 0 B a,-E 0.. 0.. o B . O = o (15) For sufficiently large 6 the depression of the trap level is given by the perturbation expression (16): AE = 2B2/d and E = a + 6 + 2/la18 (16) X. Energies for the Example rn = 6 The general character of the solutions to the energy problem can be shown in a specific example. We choose m = 6 because the analogue in molecular-orbital theory, namely the orbitals of benzene and heterocyclic derivatives, is a familiar one. The results hold independently of n, the total number of centres 38 D.
For 0 1 2 8- 3 4 5 W Fig. 4. Relative intensities of transitions in a one-dimensional mixed crystal (upright band). The curve labelled C? gives the relative intensity in the lowest energy transition. In the limit of large 6 t h i s becomes a transition localized in the trapping molecule. cf and c: refer to transitions of increasing energy. 6 is measured in units of 8, the nearest-neighbour coupling energy. shallow traps the conclusion from these calculations is that there should be one single absorption frequency.