Cross-Section Fluctuations in Chaotic Scattering Systems

TL;DR

This paper develops generalized analytical expressions for cross-section correlation functions in chaotic scattering systems, applicable across the full resonance spectrum, and validates them against known results and experiments.

Contribution

It introduces a comprehensive statistical model for cross-section correlations that extends beyond special cases, covering isolated to overlapping resonances.

Findings

Accurate expressions for cross-section correlations across all resonance regimes.

Dominance of self-correlation terms in isolated resonances.

Rapid emergence of Ericson fluctuations in inelastic correlations.

Abstract

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.