Cross-section fluctuations in chaotic scattering systems
Torleif E O Ericson1, Barbara Dietz2,3, Achim Richter2
1Theory Department, CERN, CH-1211 Geneva, Switzerland.
Physical Review. E
|November 15, 2016
Summary
This study presents new analytical expressions for chaotic scattering cross-section correlations, applicable across all resonance types. The findings improve understanding of scattering phenomena and Ericson fluctuations.
Area of Science:
- Nuclear Physics
- Quantum Scattering Theory
Background:
- Exact analytical expressions for cross-section correlations in chaotic systems are limited.
- Previous models accurately described scattering (S)-matrix correlations but had restrictions.
Purpose of the Study:
- To provide general analytical expressions for cross-section correlation functions in chaotic scattering.
- To extend applicability beyond special conditions and explore underlying physical mechanisms.
Main Methods:
- Utilized a statistical Breit-Wigner type model for chaotic scattering amplitudes.
- Derived expressions in both energy and time representations.
- Analyzed S-matrix contributions using irreducible and reducible correlation functions.
Main Results:
- Developed general expressions for cross-section correlations applicable from isolated to overlapping resonances.
- Identified dominant self-correlation terms in isolated resonance regions.
- Showcased rapid dominance of Ericson fluctuations in well-overlapping resonance regions for inelastic correlations.
Conclusions:
- The developed model accurately describes cross-section correlations and their physical mechanisms.
- Results show excellent agreement with existing analytical and experimental data.
- Provides a robust framework for studying chaotic scattering phenomena.
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