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Cross-section fluctuations in chaotic scattering systems
Exact analytical expressions for the cross-section correlation functions of chaotic scattering sys- tems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on...
Autores principales: | , , |
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Lenguaje: | eng |
Publicado: |
2016
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1103/PhysRevE.94.042207 http://cds.cern.ch/record/2265758 |
Sumario: | Exact analytical expressions for the cross-section correlation functions of
chaotic scattering sys- tems have hitherto been derived only under special
conditions. The objective of the present article is to provide expressions that
are applicable beyond these restrictions. The derivation is based on a
statistical model of Breit-Wigner type for chaotic scattering amplitudes which
has been shown to describe the exact analytical results for the scattering
(S)-matrix correlation functions accurately. Our results are given in the
energy and in the time representations and apply in the whole range from
isolated to overlapping resonances. The S-matrix contributions to the
cross-section correla- tions are obtained in terms of explicit irreducible and
reducible correlation functions. Consequently, the model can be used for a
detailed exploration of the key features of the cross-section correlations and
the underlying physical mechanisms. In the region of isolated resonances, the
cross-section correlations contain a dominant contribution from the
self-correlation term. For narrow states the self-correlations originate
predominantly from widely spaced states with exceptionally large partial width.
In the asymptotic region of well-overlapping resonances, the cross-section
autocorrelation functions are given in terms of the S-matrix autocorrelation
functions. For inelastic correlations, in particular, the Ericson fluctuations
rapidly dominate in that region. Agreement with known analytical and with
experimental results is excellent. |
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