Limitations of empirical QDT

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. 

One should remember, also, that near an avoided crossing it is often the case that one interaction dominates the others, so that a projection onto one face of the cube contains the most relevant information. The generalisation of MQDT to many limits has been discussed by Armstrong et al. [117]. 

So far, we have discussed what is called empirical QDT, namely the fitting of experimental data using the finite number of adjustable parameters required to represent interchannel coupling. Unfortunately, while the procedure works well for simple cases, one eventually runs into two problems (1) for complex cases involving many parameters, it can turn out that more than one set is found which will represent the same experimental data equally well and (2) it may prove necessary to introduce energy-dependent parameters in order to represent observations. 

There is, of course, no objection in principle to the occurrence of energy-dependent parameters, provided this dependence is weak 2 after all, the constancy of p was the approximation in the first place, as the numbers in table 2.1, in the absence of perturbations, show quite clearly. However, the consequence of an energy dependence is that the variations in pi and p2 are no longer perfectly periodic, and it may then become unclear which part of the variation with energy is intrinsic (i.e. existed before interchannel coupling was turned on) and which part is produced by coupling between channels. 

The first difficulty is more fundamental, and suggests that, in complex cases, more information is needed to determine quantum defect parameters completely than is available in a set of experimental transition energies. 

---