Ericson regime

Although ubiquitous in nuclear physics, schematic scattering models and simple models of atoms and molecules, the topic of Ericson fluctuations in atomic physics has only recently attracted attention (Main and Wunner (1994)). A possible reason may be that in the Ericson regime... 

Although not yet firmly established with the help of computer calculations, there are strong numerical indications that the Ericson regime actually exists. Numerical and analytical arguments for the existence of the Ericson regime are presented in Section 10.5.1. 

In Chapter 9 we saw that the regime of strongly overlapping resonances is especially interesting in connection with the manifestations of chaos in atomic physics. In Section 9.4 we defined the Ericson regime via the... 

In order to corroborate the numerical results with analytical estimates of the onset of the Ericson regime we need estimates of the mean level density p — /D and the average resonance width F. The following analytical arguments are based on the assumption that subsets of classical phase space decay exponentially to the continuum. This assumption may not be true as indicated by the powerlaw results obtained in Chapter 8. Nevertheless, the argument is illustrative, and may be modified eventually to take the true decay mechanism of the hehum phase space into account. 

Since we expect the onset of the Ericson regime in the hehum atom at high values of the actions of the two electrons, we make use of classical scaling arguments. First, we compute the scaling behaviom- of the average resonance widths. 

Since the most interesting states for the Ericson regime are characterized by m n, we demand that m< is such that E is located exactly in the middle of the discrete states of the m< series. This results in... 

Fig. 9.11. Simulated cross-sections for (a) the regime of isolated and weakly overlapping resonances, A <, 1, and (b) the Ericson fluctuation regime characterized by A 1. A = r/jD is the Ericson parameter. The real parts (locations) of the resonances are indicated by the vertical bars.

Fig. 10.11. Qualitative sketch (because of graphical reasons not to scale) of the repetitive sequence of three different dynamical regimes in the helium atom Ericson, Wigner and Rydberg. The Ericson and the Wigner regimes are manifestations of chaos in the helium atom.

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