Lu-Fano plot

Fig. 22.3 Lu-Fano plot of the high lying Ba even parity 7=2 levels above the 6s22d 3E>2 level. The full curve is calculated with the QDT parameters of ref. 8 observed 6snd3E>2 states (+), observed 6snd1D2 states ( ) observed 5d7d perturber (V) (from ref. 8).

The relatively well localized interaction of the Ba 5d7d D2 state with the Ba 6snd uD2 states is shown by the section of the Lu-Fano plot of Fig. 22.3.8 The... 

In Fig. 22.6(a) we show the spectrum of the transition from the Ba 5d6p F3 state to the 5d5/216d3/2 5/2 states which lie just above the Ba+5d 3/2 limit, and in Fig. 22.6(b) we show the spectrum from the same initial state to the 5d5/214d3/2 5/2 states which lie just below the Ba+ 5d3/2 limit. It is apparent that the envelopes of the excitations are identical. We have been discussing these states as if they were bound states, and in fact for our present purpose they might as well be. First, below the 5d3/2 limit the observed linewidths equal the laser linewidth, and second, there is no visible excitation of the 6seH continua below the 5d3/2 limit. It is also useful to note that a three channel quantum defect treatment of the 5d nd / = 4 series reproduces both the Lu-Fano plot of Fig. 22.2, and the spectra shown in Fig. 22.6. The experimental spectra were reproduced by QDT models using both the a and i channel dipole moment parametrizations described in Chapter 21. 

Lu-Fano plot is contained in a unit cube, and more generally, it will give rise to a curve in an JV-dimensional cube, at which point the simplicity of visualisation is lost, although a mathematical representation is still completely feasible. 

We now plot the usual Lu-Fano graph, using, as before ... 

Fig. 8.31. The remaining figures in this chapter show a sequence of spectra and Lu-Fano graphs in which the q parameters and coupling strengths are changed, but all other parameters are held constant. For this figure, the q = 1000 for both series, and the coupling strength = 2. A zero coupling strength, zero combined asymmetry plot is shown as a dashed curve for reference. X = 0.3, X

Such model calculations display a rich variety of effects even on a very simple model. They show that the essential structure of two-dimensional quantum defect plots is preserved, but that conclusions as to the strength of inter-series coupling cannot be reached merely by inspecting Lu-Fano graphs a simultaneous study of the spectra is also required. 

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