Predissociation level shift

Calculations of predissociation level shifts in the diabatic representation are simplified by the Eq. (7.5.14) factorization,... 

The predissociation level shift, 5Ev,j, for Ev J > Ec has also been treated semiclassically (Bandrauk and Child, 1970) ... 

One of the most dramatic manifestations of an interference effect is the vanishing of a line or of an entire band that, on the basis of known Franck-Condon factors and inappropriately simple intensity borrowing ideas, should be quite intense (see Fig. 6.6). This effect can easily be mistaken as an accidental predissociation (Section 7.13). Yoshino, et al, (1979) have studied the valence Rydberg N2 b, E+ cVE+ perturbations. Abrupt decreases in emission intensity for c 4 — X1E+ (v = 1 and 4) and b — X (v = 4) bands had been attributed to weak predissociation rather than perturbation effects (Gaydon, 1944 Lofthus, 1957 Tilford and Wilkinson, 1964 Wilkinson and Houk, 1956). The b (v = 4) C4 (v = 1) and b (v = 13) C4 (v = 4) deperturbation models of Yoshino et al., (1979) provide a predissociation-ffee unified account of both level shift and intensity effects. Weak predissociation effects cannot be ruled out, but are not needed to account for the present experimental observations. 

The effect of predissociation on spectral features depends on whether it is the initial or final state of the transition that is predissociated. Predissociation can be detected either by direct measurements of lifetimes (r), linewidths (T), or level shifts (5E), or indirectly by observation of fragments. Table 7.2 surveys the range of predissociation rates sampled by different methods. Erman (1979) has reviewed the experimental methods for characterizing predissociation phenomena. 

In addition to line broadening, the predissociation process can cause line shifts. Each discrete or diffuse level can be shifted by its interaction with the entire continuum of the predissociating state, but this effect is considerably smaller than level shifts caused by interactions between discrete levels. The orders of magnitude of predissociation-induced level shifts and linewidths are comparable. 

In principle, rotational constants and fine structure parameters of the predissociated state may also be affected by the predissociating state, as in the case of perturbations. Levels below the dissociation limit, which therefore cannot be predissociated, will also be shifted by their interaction with the continuum. In the case of strong predissociation, only this level shift affecting bound (sharp) levels will be seen, because the levels above the crossing point become too diffuse to be observed. This is the situation for the homogeneously predissociated Se2 B0+ (Atabek and Lefebvre, 1972) and NO G2 - states (Ben-Aryeh, 1973). 

Figure 7.20 Example of an outer-limb curve crossing an electrostatic predissociation of the N2 C3nu state by the continuum of the C 3nu state. The curves relate the values of level shifts calculated by the coupled equations approach [Eq. (7.12.1)] for energies below the dissociation limit of the C,3ITU state to the level shifts and level widths obtained by the semiclassical method [Eq. (7.6.3) and Eq. (7.6.12)] for energies above the dissociation limit. The points shown on the level shift and width curves correspond to the vibrational energies of the C3nu state (indicated by the turning points on the potential curve). If all of these values had been observed, they would have been insufficient to suggest the actual shape of the SE and T curves. [Courtesy of J.M. Robbe from data of Robbe (1978).]...

The Golden Rule formula Eq. (7.5.16) for the FWHM and Eq. (7.5.9) for the level shift are expressed in terms of the unperturbed vibrational wavefunc-tions. For strong predissociations, this approximation becomes untenable. Exant methods exist that can determine both the linewidth and the level shift. One method consists of numerically solving the following coupled equations (Lefebvre-Brion and Colin, 1977 Child and Lefebvre, 1978) ... 

Sometimes two higher electronic levels, stable state II and unstable state III may exist quite close to each other (Fig. 5.1(d)). By absorption of light, the molecule is raised to higher stable electronic state II. If the oscillations are relatively slow, there is a chance of the molecule of shifting from stable state II to unstable state III. If such a shift takes place, the molecule would dissociate producing atoms or radicals. The spectrum would show fine structure at lower levels of vibrations followed by a continuum. This is called predissociation. 

Photolysis of CO occurs by absorption of stellar UV radiation in the wavelength range 90-100 nm. The reaction proceeds by a predissociation mechanism, in which the excited electronic state lives long enough to have well-defined vibrational and rotational energy levels. As a consequence, the three isotopic species—C O, C O, and C O—absorb at different wavelengths, corresponding to the isotope shift in vibrational frequencies. Because of their different number densities, the abundant C O becomes optically thick in the outermost part of the cloud (nearest to the external source of UV radiation), while the... 

Figure 7.19a is a pictorial description of Ev) for an outer wall curve crossing. In phase space, bound motion in the uth vibrational level appears as an ellipse in the harmonic approximation. Motion on a linear unbound potential is represented as a parabola. The shaded area is 2unbound motion parabola shifts to the left so that the minimum value of R at P = 0 occurs at V2 Rmin) = Ev consequently, d> increases with u for E > Ec Whenever the value of maximum value [except for the first maximum, v = 0, at which Eq. (7.6.11) is invalid] (Child, 1980b). 

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