The influence of linewidths

Physically, this is readily understood in the following way in a classical system, chaos requires a finite time to develop. If the excitation can decay by some alternative path in a quantum system well before that time is reached, then chaos will be quenched. In the example of the previous section, two-step autoionisation occurs (cf section 7.15), and is an obstacle to the observation of chaos because it is an Auger effect and involves widths which do not scale as 1/n3. For quantum chaos to be possible, one must choose both the atom and the energy range such that (i) the excited core of the parent ion which defines the series limit is stable 

Such a situation exists in the doubly-excited spectrum of Ca (see section 7.13) which has served repeatedly as an example in the present book. The single and double excitation spectra come very close to each other in energy, and prominent doubly-excited series can be followed to very high members (see fig. 6.3) at the top end of the energy range concerned, which shows that the semiclassical limit is attainable. Ca is therefore a good candidate for the emergence of chaos in the spectrum [549]. 

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