Honl-London factor

In the Born-Oppenheimer approximation, the relative importance of channels (la) and (lb), together with their dependence on wavelength would depend upon the matrix elements for the transition between the electronic states, the Franck-Condon factors, the Honl-London factors, and upon the probabilities for spontaneous dissociation of the excited state formed. In principle, except for the last one, these are well known quantities whose product is the transition probability for that particular absorption band of Cs. When multiplied by the last quantity, and with an adjustment of numerical constants i becomes the cross section for the photolysis of Cs into Cs + Cs. It is the measurement of this cross section that lies at the focus of this work. 

The rotational linestrength (Honl-London) factors can also be expressed in terms of 3-j coefficients (see, for one-photon transitions, Eq. (6.1.45) ). 

Equation (6.4.5) looks like the usual product of electronic, vibrational, and rotational factors except that fx2 is an effective parameter, which may be strongly dependent on Vi, flj, e/f, and J (rather than a function of the Rv3,va //-centroid), and q and S are the Franck-Condon and Honl-London factors appropriate for the j, Vj, f2j —> 0, vq, fi0 transition rather than the i,Vi, —> 0, vq. Qq transition... 

The assumptions required to obtain Eqs. (6.4.9) and (6.4.10) are more drastic than those for Eqs. (6.4.5) and (6.4.6), but their failure can often be absorbed into a strongly f -centroid dependent effective p2 parameter. Note that Eq. (6.4.9) contains the intuitive Franck-Condon factors but the Honl-London factors are those appropriate to the Q-value of the remote perturber. 

Only those transitions for which all three factors are nonzero appear as lines in the fluorescence spectrum. The Honl-London factor is always zero unless... 

For molecular transitions the matrix elements Dim and Dmf are composed of three factors the electronic transition dipole element, the Franck-Condon factor, and the Honl-London factor (Sect. 1.7). Within the two-photon dipole approximation a co) becomes zero if one of these factors is zero. The calculation of linestrengths for two- or three-photon transitions in diatomic molecules can be found in [243, 244]. 

For unperturbed transitions the relative transition propabilities of different rotational lines in the same vibrational bands are given by the corresponding Honl-London factors [411] and can thus be readily calculated. In case of perturbed spectra this may be no longer true. Here the following alternatives can be used ... 

The first factor is associated with the electronic dipole transition probability between the electronic states the second factor is associated between vibrational levels of the lower state v" and the excited state V, and is commonly known as the Franck-Condon factor, the third factor stems from the rotational levels involved in the transition, J" and /, the rotational line-strength factor (often termed the Honl-London factor). In particular, the Franck-Condon information from the spectrum allows one to gain access to the relative equilibrium positions of the molecular energy potentials. Then, with a full set of the spectroscopic constants that are used to approximate the energy-level structure (see Equations (2.1) and (2.2)) and which can be extracted from the spectra, full potential energy curves can be constructed. 

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