The absolute position of a resonance peak

TL;DR

This paper reveals that the true position of a resonance peak corresponds to the absolute value of the complex energy pole, challenging the conventional association with the real part, and extends the applicability of local resonance theories.

Contribution

It demonstrates that the resonance peak aligns with the absolute value of the pole's complex energy, not just its real part, and shows local theories remain valid in broader cases.

Findings

Resonance peak occurs at the absolute value of the complex energy.

Local resonance theories are applicable in more cases than previously thought.

Challenges conventional interpretation linking peak position solely to the real part.

Abstract

It is common practice in scattering theory to correlate between the position of a resonance peak in the cross section and the real part of a complex energy of a pole of the scattering amplitude. In this work we show that the resonance peak position appears at the absolute value of the pole's complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in cases previously thought impossible.