Fano lineshape in

In order to find a value for q that is different from 00, the transition into the continuum must have its own absorption strength. Usually, the transition into the continuum state, t 2, has no absorption because f 2 has a spin multiplicity different from that of the initial state, i.e., (fo /x po) = 0, therefore q — 00, and the continuum is observable because interacts with the bound state by spin-orbit coupling. In the case of H2, however, q has a finite value because the continuum state is 1E+. In the case of O2, the Rydberg state, E3E , is predissociated by the valence state, B3E , of the same symmetry. In the case of Cs2, the continuum state is 3E+, but due to the relatively weak spin-orbit coupling (primarily with a 1IIU state) (30 cm-1, Kim, et al., 1994) it borrows some absorption strength. 

Changes of sign of the Fano asymmetry parameter, q, with v and isotope, have been found in the predissociation of O2 (Lewis, et al., 1988a, b, 1995b) and with v for CS2 (Kim and Yoshihara, 1993). 

This phenomenon is called q reversal and has only quite recently been observed in predissociation. It has been shown that q reversal can occur even in the absence of interference effects, e.g., with only one closed and one open 

Much work has been done to predict the locations of the zeroes of the line width. Child (1976) has demonstrated that, in the case of intermediate coupling strength, a zero occurs in the linewidth whenever the energies of the diabatic and adiabatic levels coincide (and this conclusion is also valid in the case of weak coupling). However, until the work of Kim, et al., (1994) and recently of Cornett, et al., (1999), it seems that the connection between zeroes of predissociation linewidth and q reversal was not appreciated. 

Assuming that the two other overlap integrals in the Eq. (7.9.6) definition of xe,j xo) and (Xv,j Xo)i do not oscillate rapidly in sign with v and E and are non-zero, it is clear that if Xv,j xe,j) changes sign with v,q also changes sign and produces the q reversal (see example of Cs2 in Kimura, et al., 2000). 

---

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... 

Figure 7.28 Fano lineshape in H2. The predissociation of the N=2 [R(l) line] and N=1 [R(0) line] levels of the D1ri,ie(u = 5) state by the continuum of B 1is detected by monitoring the Lyman-a emission from one of the fragment atoms. The dots represent the lineshape calculated from the Fano formula [Eq. (7.9.1)] with parameter values Y(N = 2) = 14.5 cm 1,g(N = 2) = -9 r(jV = 1) = 4.8 cm 1,q(N = 1) = —18. These lineshapes should be compared to the symmetric profile of Fig. 7.16 (q = 00). The horizontal dotted line separates the interacting continuum Oi from the noninteracting continua [

---