Fano lineshapes

In the Sharf and Fischer treatment the real manifold is subdivided into n idealized submanifolds where each one conforms with the Bixon-Jortner model. By taking suitable linear combinations of the n idealized submanifolds the problem may be reduced to that of a discrete state and two manifolds, both of which carry intensity but only one of which is associated with a non-zero interaction. The Bixon-Jortner procedure applied to this situation leads to a Fano lineshape superposed on a constant background absorption. 

Brown SDM, Jorio A, Corio P, Dresselhaus MS, Dresselhaus G, Saito R, Kneipp K (2001) Origin of the Breit-Wigner-Fano lineshape of the tangential G-band feature of metallic carbon nanotuhes. Phys Rev B 63 155414... 

Autoionisation is one of the most fundamental correlation phenomena. There are different ways of arriving at the Fano lineshape formula for an autoionising resonance. Since these are also alternative approaches to... 

Fig. 6.2. Family of curves generated from the Fano lineshape formula for different values of the shape index q. For negative values of q, reverse the abscissa, (after U. Fano [256]).

When the maximum occurs on the same side of the half-hydrogenic point as the minimum, the appearance of the profile is similar to the Fano lineshape. However, if the maximum and minimum become sufficiently separated in energy to straddle the half-hydrogenic point, then the shape of the profile changes to a more sinusoidal form. 

Fig. 8.8. Evolution of a Rydberg series of Dubau-Seaton profiles as a function of the parameter C, for D = 1.2 and (a) B = —0.578 (b) B = +0.578. Values of C are given in the figure. The narrower resonances tend towards a Fano lineshape, whereas the broader resonances are more sinusoidal in shape. This is illustrated by some experimental examples in fig. 8.9 (after J.-P. Connerade [413, 414]).

The intensity interference pattern illustrated by Fig. 6.8 for bound-bound transitions is very similar to the Beutler-Fano lineshape for bound-free transitions discussed in Sections 7.9 and 8.9. The 101,000-106,000 cm-1 region of Fig. 6.8 is a band-by-band rather than a continuous representation of a Fano profile with q < 0 [see Fig. 7.26 and compare Eq. (7.9.6) to Eq. (6.3.17)]. 

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 [

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