Time-delay in a multi-channel formalism

TL;DR

This paper revisits the time-delay formalism for resonances, corrects a propagated error in Smith's work, and clarifies the relationship between Eisenbud and Smith's results, impacting recent studies.

Contribution

It identifies and corrects a longstanding error in Smith's time-delay formalism and clarifies the connection between Eisenbud and Smith's approaches.

Findings

Corrected Smith's error in the time-delay formalism

Clarified the relationship between Eisenbud and Smith results

Implications for recent time-delay resonance studies

Abstract

We reexamine the time-delay formalism of Wigner, Eisenbud and Smith, which was developed to analyze both elastic and inelastic resonances. An error in the paper of Smith has propagated through the literature. We correct this error and show how the results of Eisenbud and Smith are related. We also comment on some recent time-delay studies, based on Smith's erroneous interpretation of the Eisenbud result.