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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
E. l/m. Thus in the upright band, to be dealt with first, we have to follow a change of spectrum from that of the pure crystal, with all the intensity in the lowest transition, to the deep-trap limit, with a fraction l / m in the lowest transition. The m = 6 system will again be used as an example. The guest molecules cause the mixing of the lowest (I = 0) wave function with three other wave functions derived from p = f l , p = f2, and p = 3, as described in the secular equation (14). If cl, . , c5 are the coefficientsof the basis functions in order of increasing energy in the perturbed lowest state, we have, by perturbation theory for small CT, The squares of the normalized coefficients c:, .
There are zero projections for 1 = 2 and 4 on account of symmetry. The squares of the other projections are given in the last line of Table 11. The fractional intensities of transitions to levels of the host add up to five-sixths, the remaining one-sixth appearing in the transition to the trap molecule. For the other cases in Table I1 intensities have been calculated by perturbation theory based on the residual host wave functions (17)and the free guest wave function. Values are listed for trap depths from B = 38 downward, but are of dubious accuracy at the top of this range.
Relative intensities of transitions in a one-dimensional mixed crystal (inverted band). The curve labelled c: refers to the lowest energy transition, and c: and ci to transitions of higher energy. In the inverted band a quite different pattern of intensity distribution is to be expected. In the pure crystal the topmost level alone is active; it remains the strongest under all conditions. As the trap is deepened, some intensity moves from the topmost level downward through the band into the bottom level, which breaks out of the band and eventually becomes practically a localized state of the trapping molecule..