Example of an outer-limb curve crossing

Mulliken (1960) has distinguished several classes of predissociation based on the location of the curve crossing (Ec, Rc) relative to the dissociation energy (D°) and the Re of the predissociated state. Cases b, a, and c correspond to Ec D°,Ec = D°, and Ec D°, respectively. The superscripts —, i, +, and 0 specify the cases Rc Re,Rc = Re-, Rc Re, and non crossing potentials, respectively. For the present discussion, it is useful to retain only Mulliken s —, +, and 0 classifications. It is immaterial whether the predissociating curve is partly attractive or completely repulsive. These three classes of predissociation 

at any iZ-value, the centrifugal energy is identical for all potential curves, Rc does not change with J. Consequently, the J-dependent energy of the curve crossing is given by 

At the right of Fig. 7.22 is a plot of the calculated variation of T versus E at a constant J-value, designated as Jmax- The oscillations in T versus J within a given u-level are rapid for hydrides because of their large rotational constants. For heavier molecules such as O2, the linewidths show only a slight, 7-dependence (Lewis, et al., 1980). The linewidth maximum occurs at an energy 

To a good approximation, the vibrational overlap integral is determined in the region near Rc, the point of stationary phase. This means that (Xv,j Xe,j) will be a function of the energy difference, Evj — Ec(J), and will be largely insensitive to the values of v and 7. However, 

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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).]...

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