Ericson fluctuations

In this section we define the concept of Ericson fluctuations and discuss their relevance in quantum chaotic scattering systems of atomic and molecular physics. Our discussion follows the excellent introduction to Ericson fluctuations in Ericson s own paper of 1963. A nuclear compound reaction is taken as an illustrative example. 

According to Feshbach (1962) the S matrix splits into two parts according to 

The first part of the S matrix in (9.4.2) is due to potential scattering, indicated by the superscript p . This part of the S matrix is only weakly dependent on the energy, i.e. its energy dependence is smooth . The second part of (9.4.2) is a sum over pole terms where 

The resulting cross-section is shown in Fig. 9.11(a). The distinguishing feature of Fig. 9.11(a) is that every peak or shoulder in the cross-section can be lined up uniquely with one of the bars in Fig. 9.11(a), i.e. every feature of the cross-section (9.4.6) can be assigned uniquely to one of the resonances Ek. Another typical feature is the characteristic Lorentzian shape of the isolated resonances in a. 

Ericson s central result (1960) is the extraction of the average width r from the fluctuating cross-sections. This is done in the following way. We define the energy auto-correlation function Caa (e) of the cross-section a a according to 

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While the investigation of the statistics of energy levels is a well established technique in atomic and molecular physics, the study of cross-section fluctuations is not a standard technique. The purpose of the following section is to discuss the subject of Ericson fluctuations in some... 

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.

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... 

The theory of isolated resonances is well understood and is discussed below. Some initial work has been done on the theory of overlapping resonances (Remade et al., 1989 Desouter-Lecomte and Culot, 1993 Someda et al., 1994a,b) and its relation to experiment (Reid et al., 1994). Much of the research of overlapping resonances has its origins in nuclear physics, where the dissociation of a compound nucleus is treated (Ericson, 1960, 1963 Satchler, 1990 Rotter, 1991). For example, fluctuations in product state populations, called Ericson fluctuations (Satchler, 1990 Rotter, 1991), may arise from coherent excitation of overlapping resonances. However, more work needs to be done to develop a complete theory of overlapping resonances and this topic is not discussed here. Mies and Krauss (1966, 1969) and Rice (1971) were pioneers in treating unimolecular rate theory in terms of the decomposition of isolated Feshbach resonances. 

Ericson, T. (1960). Fluctuations of nuclear cross sections in the continuum region, Phys. Rev. Lett. 5, 430-431. 

Ericson, T. (1963). A theory of fluctuations in nuclear cross sections, Ann. Phys. 23, 390 14. 

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