Shape resonances in photoionization cross sections and time delay

TL;DR

This paper explores shape resonances in photoionization, linking cross sections with scattering phase shifts and time delays, enabling experimental validation of quantum scattering theories through laser interferometry.

Contribution

It establishes a direct relation between photoionization cross sections, scattering phases, and time delays in shape resonances, facilitating experimental testing of quantum scattering models.

Findings

Connection between cross section and phase shift via $\sigma o ext{sin}^2 ext{delta}_ ext{l}$

Extraction of photoelectron time delay from cross section data

Validation of theoretical models against experimental measurements

Abstract

Shape resonances in photoionization of atoms and molecules arise from a particular geometry of the ionic potential which traps the receding photoelectron in a quasi-bound state in a particular partial wave. This mechanism allows us to connect the photoionization cross section in the resonant region with the photoelectron scattering phase in this partial wave by a simple formula $\sigma \propto \sin^2\delta_\ell$. Due to this relation, the phase $\delta_\ell$ can be extracted from an experimentally known cross section and then converted to the photoelectron group delay (Wigner time delay) $\tau_{\rm W} = \partial \delta_\ell/\partial E$ which is measurable by recently developed laser interferometric techniques. Such a direct connection of the photoionization cross section and the time delay is a fundamental property of shape resonances which provides a comprehensive test of novel measurements against a large body of older synchrotron data.