Predissociation overlap factor

In general the bound (predissociated) potential curve is much better characterized experimentally than the repulsive (predissociating) curve. Predissociation linewidths and shifts are usually the best available experimental informal tion about the repulsive state. Indeed, as for bound bound interactions, the vibrational variation of the overlap factor is related to the relative locations of the nodes of the bound and continuum vibrational wavefunctions near Rq (the point of stationary phase of the product x jXe, j, which is where x jXe>,j oscillates most slowly). The Xv,J and Xe,j functions are solutions of the following nuclear Schrodinger equations expressed in atomic units ... 

The interaction H12 can often be factored into electronic and vibrational parts, as in the case of predissociation, but here it is the electronic part that has the continuous character. In some cases, the vibrational part is simply an overlap factor and... 

It is found that the lifetimes change as v and J vary in the upper state. For example, Capelle and Broida found that the lifetime decreased from 1420 to 690 ns as v decreased from 40 to 21, a drop that can be accounted for by more favorable overlap of ground and excited state wavefunctions (Franck-Condon factors) for lower v levels. The effect of a change in rotational state is less Castano, Martinez, and Martinez found for the v = 25 level that the lifetime decreased from 745 ns to 625 ns as J increased from 0 to 106. Such a shortening of the lifetime is consistent with enhanced predissociation at higher rotational levels due to bond lengthening by the increased centrifugal force. 

The first observations of Fano lineshapes in predissociation have been in the spectrum of the H2 molecule (Fig. 7.27 and Fig. 7.28). The v = 3, J = 1 level of H2 D1 is predissociated by the B/XE+ state (Herzberg, 1971). Also Fano profiles are found in v — 1 of BwlE+ which also mixes with the continuum of BnE+. Since Franck-Condon factors for absorption from X E+ (v = 0) into the continuum of BnE+ are favorable, the overlap term Xe,j Xo)) in the... 

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