Scattering singularities

Fig. 1.6. Lifetime function l ip) for box C. The spikes in I indicate the presence of scattering singularities.

The intricate structure of the set S of scattering singularities we encountered in connection with the reaction function in Section 1.1 can be characterized using the concept of fractals introduced by Mandelbrot in 1975 (see also Mandelbrot (1977, 1983)). Fractals are discussed in Section 2.3. 

Fig. 9.1. A trivial scattering singularity. A particle lamiched with energy E = Vo towards x = 0 gets stuck while approaching, but never quite reaching, the top of the potential barrier. (Prom Bliimel (1993b).)...

Static scattering singularities are well known in atomic and nuclear physics. A prominent example is the phenomenon of orbiting, which occurs whenever the effective scattering potential exhibits a local maximum (see, e.g., Norenberg and Weidenmiiller (1976)). 

Fig. 9.3. Sketch of a model potential which allows for three scattering singularities to occur. (From Bliimel (1993b).)...

The Hamiltonian (9.3.1) contains the control parameter Vq. On the classical level it was found that for small values of Vq there is no chaotic scattering. There exists a critical value which marks the first appearance of a nontrivial set of scattering singularities. Well developed chaotic scattering characterized by a large set of scattering singularities is observed for Vq > Thus, the control parameter Vb allows us to... 

Fig. 10.6. Distribution of lifetimes for a chaotic scattering experiment with the one-dimensional model. Irregular behaviour and dynamic scattering singularities in the interval 4.7 < 6i < 5.7 indicate the presence of chaotic scattering in the stretched helium atom. (Adapted from Bliimel and Reinhardt (1995).)...

Eckhardt, B. (1987). Rractal properties of scattering singularities, J. Phys. A20, 5971-5979. 

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